QuickSearch:   Number of matching entries: 0.

Search Settings

Author Title Year Journal/Proceedings Reftype DOI/URL
Allefeld, C., beim Graben, P. & Kurths, J. Editorial 2007 Chaos and Complexity Letters
Vol. 2(2/3), pp. 135 - 138 
article  
BibTeX:
@article{AllefeldGrabenKurths07,
  author = {C. Allefeld and P. beim Graben and J. Kurths},
  title = {Editorial},
  journal = {Chaos and Complexity Letters},
  year = {2007},
  volume = {2},
  number = {2/3},
  pages = {135 -- 138}
}
      
Atmanspacher, H. & beim Graben, P. Contextual emergence of mental states from neurodynamics 2007 Chaos and Complexity Letters
Vol. 2(2/3), pp. 151 - 168 
article  
Abstract: The emergence of mental states from neural states by partitioning the neural phase space is analyzed in terms of symbolic dynamics. Well-defined mental states provide contexts inducing a criterion of structural stability for the neurodynamics that can be implemented by particular partitions. This leads to distinguished subshifts of finite type that are either cyclic or irreducible. Cyclic shifts correspond to asymptotically stable fixed points or limit tori whereas irreducible shifts are obtained from generating partitions of mixing hyperbolic systems. These stability criteria are applied to the discussion of neural correlates of consiousness, to the definition of macroscopic neural states, and to aspects of the symbol grounding problem. In particular, it is shown that compatible mental descriptions, topologically equivalent to the neurodynamical description, emerge if the partition of the neural phase space is generating. If this is not the case, mental descriptions are incompatible or complementary. Consequences of this result for an integration or unification of cognitive science or psychology, respectively, will be indicated.
BibTeX:
@article{AtmanspacherGraben07,
  author = {H. Atmanspacher and P. beim Graben},
  title = {Contextual emergence of mental states from neurodynamics},
  journal = {Chaos and Complexity Letters},
  year = {2007},
  volume = {2},
  number = {2/3},
  pages = {151 -- 168}
}
      
Abstract: We introduce symbolic dynamics to cognitive scientists with the aim of furthering constructive debate on representation. Symbolic dynamics is a mathematical framework in which both continuous and discrete states of a system can be considered jointly. We discuss a number of theoretical implications this framework has for cognitive science, and offer some consideration of the way in which it might be employed for comparing or conciliating discrete and continuous representational theories. Symbolic dynamics may thus serve as a common, level playing field for debate in theories of cognitive representation.
BibTeX:
@article{DaleSpivey05,
  author = {R. Dale and M. J. Spivey},
  title = {From apples and oranges to symbolic dynamics: a framework for conciliating notions of cognitive representation},
  journal = {Journal of Experimential & Theoretical Artificial Intelligence},
  year = {2005},
  volume = {17},
  number = {4},
  pages = {317 -- 342}
}
      
Review: "Folk Psychology as a Source of Theory" (p. 43)

"Chemistry has been shown to reduce, in some sense, to physics, it this is clearly a Good Thing, the sort of thing we should try for more of." (p. 45)

"[...] we do not really learn what beliefs are when we learn how to use these words." (p. 46)

"We use folk psychology all the time, to explain and predict each other's behavior; we attribute beliefs and desires to each other with confidence --- and quite unselfconsciously --- and spend a substantial portition of our waking lives formulating the world --- not excluding ourselves --- in these terms." (pp. 47f)

Eine Schlüsselstelle:

"They are reason-giving explanations, which make an ineliminable allusion to the rationality of the agent. Primarily for this reason, but also because of the pattern of strengths and weaknesses just described, I suggest that folk psychology might best be viewed as a rationalistic calculus of interpretation and predicting --- an idealizing, abstract, instrumentalistic interpretation method that has evolved because it works and works because we have evolved. We approach each other as intentional systems (Dennett 1971), that is, as entities whose behavior can be predicted by the method of attributing beliefs, desires, and rational acumen according to the following rough and ready principles:

(1) A system's beliefs are those it ought to have, given its perceptual capacities, its epistemic needs, and its biography. [...]

(2) A systems's desires are those it ought to have, given its biological needs and the most practicable means of satisfying them. [...]

(3) A systems's behavior will consist of those acts that it would be rational for an agent with those beliefs and desires to perform .

In (1) and (2) `ought to have' means `would have if it were ideally ensconced in its environmental niche.'" (pp. 48f)

P1. Das ist das Rezept der IS.

"In short, we treat each other as if we were rational agents, and this myth --- for surely we are not all that rational --- works very well because we are pretty rational." (p. 50)

P1. Hier wieder die "Philosophie des Als-Ob".

"I am claiming, then, that folk psychology can best be viewed as a sort of logical behaviorism: what it means to say that someone believes that $p$, is that that person is disposed to behave in certain ways under certain conditions. What ways under what conditions? The ways it would be rational to behave, given the person's other beliefs and desires." (p. 50)

P1. "Logical behaviorism" bezieht sich auf Ryle: mentalistische Prädikate drücken Verhaltensdispositionen aus.

"Folk psychology is abstract in that the beliefs and desires it attributes are not --- or need not be --- presumed to be intervening distinguishable states on an internal behavior-causing system. [...] The role of the concept of belief is like the role of the concept of a center of gravity, and the calculations that yield the predictions are more like the calculations one performs with a parallelogram of forces than like the calculations one performs with a blueprint of internal levers and cogs." (p. 52)

"Folk psychology is thus instrumentalistic in a way the most ardent realist should permit: people really do have beliefs and desires, on my version of folk psychology, just the way they really have centers of gravity and the earth has an Equator." (p. 53)

Es folgt eine Erörterung von Reichenbachs Unterscheidung zwischen "illata": theoretischen Entitäten, wie Elektronen, Feldern, Genen, Arten und "abstracta": logischen Konstruktionen. Eine andere Unterscheidung ist die zwischen "instrumentalism" und "fictionalism". "Folk psychology" ist nach D. instrumentalistisch (p. 53, Fußnote 5).

"Beliefs and desires of folk psychology [...] are abstracta." (p. 53)

P1. Auf die Physik angewendet: metaphorische Illata in einer fiktionalistischen Theorie (paßt das zu Descartes?) sind auf dem Rückzug und machen einer instrumentalistischen Theorie mit abstrakten Begriffen Platz.

Es folgt eine Erörterung von Fodors Theorie (pp. 53 -- 57), und deren Auflösung:

"The ordinary notion of belief is pulled in two directions. If we want to have good theoretical entities, good illata, or good logical constructs, good abstracta, we will have to jettison some of the ordinary freight of the concepts of belief and desire. So I propose a divorce. Since we seem to have both notions wedded in folk psychology, let's split them apart and create two new theories: one strictly abstract, idealizing, holistic, instrumentalistic --- pure intentional system theory --- and the other a concrete, microtheoretical science of the actual realization of those intentional systems --- what I will call sub-personal cognitive psychology." (p. 57)

P1. Das ist ein ambitioniertes Programm, auf dessen Durchführung ich jetzt richtig gespannt bin! Leider werden wir gleich enttäuscht werden. Allerdings gefällt mir der Hauch von Kantianismus, der den Aufsatz durchweht. 1. erinnert mich das Progamm an Kants GzMdS: "folk psychology" = "gemeine sittliche Vernunfterkenntnis", "sub-personal cognitive psychology" = "Metaphysik der Sitten", "intentional system theory" = "Kritik der reinen praktischen Vernunft"; naja, zumindest vom Aufbau? 2. "pure intentional system theory" könnte durchaus mit reiner praktischer Vernunft verglichen werden.

"Intentional System Theory as a Competence Theory" (p. 58)

P1. Der Titel spielt auf Chomskys Unterscheidung zwischen sprachlicher Kompetenz und Performanz an.

"The first new theory, intentional system theory, is envisaged as a close kin of, and overlapping with, such already existing disciplines as decision theory and game theory, which are similarly abstract, normative, and couched in intentional language. It borrows the ordinary terms 'belief' and 'desire' but gives them a technical meaning within the theory." (p. 58)

P1. Um zu ergänzen: Dynamische Semantik, Pragmatische Informationstheorie (beim Graben, 2006), evolutionäre Spieltheorie, interaktive Agentensysteme, ...

"The theory deals with the `production' of new beliefs and desires from old, via an interaction among old beliefs and desires, features in the environment, and the system's actions [...]" (p. 58)

P1. Das ist inspiriert von der Idee der Turing-Maschine (s. unten): Ein Agent ist ein abstrakter Automat mit internen Zuständen (beliefs und desires), externen Inputs (Wahrnehmung), externen Outputs (Handlungen) und interner Dynamik (Zustandsübergänge).

"Intentional system theory deals just with the performance specifications of believers while remaining silent on how the systems are to be implemented." (p. 59)

P1. Verstehe ich nicht: Ich dachte, es geht um eine Kompetenztheorie?

"Sub-personal Cognitive Psychology as a Performance Theory" (p. 61)

"The brain, as intentional systems theory and evolutionary biology shows us, is a semantic engine; its task is to discover what its multifarious inputs mean, to discriminate them by their significance and `act accordingly.' That's what brains are for. But the brain, as physiology or plain common sense shows us, is just a syntactic engine; all it can do is discriminate its inputs by their structural, temporal and physical features and let its entirely mechanical activities be governed by these `syntactic' features of its inputs. That's all brains can do. Now, how does the brain manage to get semantics from syntax? How could any entity [...] get the semantics of a system from nothing but its syntax? It couldn't. The syntax of a system doesn't determine its semantics. By what alchemy, then, does the brain extract semantically reliable results from syntactically driven operations? It cannot be designed to do an impossible task, but it could be designed to approximate the impossible task, to mimic the behavior of the impossible object (the semantic engine) by capitalizing on close (close enough) fortuitous correspondences between structural regularities --- of the environment and of its own internal states and operations --- and semantic types." (p. 61)

P1. Mir kommt eher diese Lösung wie Alchemie vor. Auch Smolensky spricht gerne von "approximation" eines Symbolprozessors durch ein neuronales Netzwerk, was beim Graben (2004) kritisiert hat. Die Auflösung dieses Rätsels ist natürlich, daß wir Semantik, Intentionalität und Subjektivität immer bereits voraussetzen müssen!

"It is the task of sub-personal cognitive psychology to propose and test models of such activity --- of pattern recognition or stimulus generalization, concept-learning, expectation, learning, goal-directed behavior, problem-solving --- that not only produce a simulacrum of genuine content-sensitivity, but that do this in ways demonstrably like the ways people's brains do it, exhibiting the same powers and the same vulnerabilities to deception, overload, and confusion. It is here, that we will find our good theoretical entities, our useful illata [...]." (p. 63)

P1. Hier geht's also um Implementationen oder Realisationen intentionaler Systeme.

"The macro level up to which we should relate microprocesses in the brain in order to understand them as psychological is more broadly the level of organism-environment interaction as a particularly important part [...]" (p. 65)

"There is no way to capture the semantic properties of things (word tokens, diagrams, nerbe impulses, brain states) by a micro-reduction. Semantic properties are not just relational but, you might say, super-relational, for the relation a particular vehicle of content, or token, must bear in order to have content is not just a relation, it bears to other similar things [...]" (p. 65)

"The Prospects of Reduction" (p. 65)

"Of our three psychologies --- folk psychology, intentional system theory, and sub-personal cognitive psychology --- what then might reduce to what?" (p. 65)

D. behauptet, "folk psychology" könne, begrifflich, auf "intentional system theory" reduziert werden, durch die Formel:

" (x) (x believes that p = x can be predictively attributed the belief that p) "

P1. D.h. Eine Person $x$ glaubt den Sachverhalt $p$, wenn die IS erfolgreich angewendet werden kann, indem man $x$ die Überzeugung $p$ zuschreiben kann.

Und hier die Schlüsselstelle zur Turing-Analogie:

"One doesn't reduce Turing machine talk to some more fundamental idiom; one legitimizes Turing machine talk by providing it with rules of attribution and exhibiting its predictive powers. If we can similarly legitimize `mentalistic' talk, we will have no need of a reduction, and that is the point of the concept of an intentional system. Intentional systems are supposed to play a role in the legitimization of mentalistic predicates parallel to the role played by the abstract notion of a Turing machine in setting down rules for the interpretation of artifacts as computational automata." (p. 67)

P1. Damit bin ich (fast) einverstanden. Aber ein Artefakt wird eben erst durch INTERPRETATION zu einem Automaten. Und Interpretation setzt immer einen Interpretierer voraus. D. wird die Subjektivität einfach nicht los!

"The final reductive task would be to show not how the terms of intentional system theory are eliminable in favor of physiological terms via sub-personal cognitive psychology, but almost the reverse: to show how a system described in physiological terms could warrant an interpretation as a realized intentional system" (p., 68)

P1. Dem stimme ich unumwunden zu!

BibTeX:
@inbook{Dennett89c,
  author = {D. C. Dennett},
  title = {Three kinds of intentional psychology},
  publisher = {MIT Press},
  year = {1989},
  pages = {43 -- 68},
  note = {Reprinted from R. Healy (Ed.): Reduction, Time and Reality. Cambridge University Press, Cambridge, 1981.}
}
      
Review: "I wish to examine the concept of a system whose behavior can be --- at least sometimes --- explained and predicted by relying on ascriptions to the system of beliefs and desires (and hopes, fears, intentions, hunches, ...). I will call such systems intentional systems, and such explanations and predictions intentional explanations and predictions, in virtue of the intentionality of the idioms of belief and desire (and hope, fear, intention, hunche, ...)." (p. 3)

P1. Es geht also um Vorhersage-, bzw. Erklärungsstrategien für das Verhalten von Systemen ("prediction" und "explanation"). D. definiert "intentional systems" als solche, deren Verhalten sich vorhersagen läßt, indem man ihnen intentionale Zustände ("beliefs": Glauben, besser: Überzeugungen, Meinungen, Fürwahrhalten --- religiöser Glaube ist eher "faith" --- und "desires": Wünsche) zuschreibt ("ascribe"). Es ist also nicht davon die Rede, daß intentionale Systeme diese Zustände tatsächlich haben.

"The first point to make about intentional systems as I have just defined them is that a particular thing is an intentional system only in relation to the strategies of someone who is trying to explain and predict its behavior." (pp. 3f)

P1. Hier haben wir die "Strategien". Ein Beobachter, der das Verhalten ("behavior") eines Dings (Systems) vorhersagen möchte, kann die intentionale Strategie verwenden, indem er dem System intentionale Zustände "zuschreibt".

Dann wendet sich D. dem Beispiel des Schachcomputers zu und definiert 3 Vorhersagestrategien:

"Design stance" (DS, "funktionale Einstellung" bei Bieri 1997). "If one knows exactly how the computer is designed [...] one can predict its designed response to any move one makes by following the computation instructions of the program. One's prediction will come true provided only that the computer performs as designs --- that is without breakdown." (p. 4)

P1. Die funktionale Einstellung erlaubt also Vorhersagen des ungestörten Systems, wenn dem Beobachter die Funktionen seiner Teile und seine Programmierung bekannt sind.

"Different varieties of design-stance predictions can be discerned, but all of them are alike in relying on the notion of function, which is purpose-relative or teleological." (p. 4)

P1. Mit "different varieties" meint D. weiter unten, daß der Computer auf den Ebenen der Verdrahtung von Bauteilen (Widerstände, Kondensatoren, Transistoren: alles funktionale Einheiten), von Modulen (Taktgebern, Registern, Speichern) und schließlich seiner Programmierung betrachtet werden kann. Die funktionale "Einstellung" (könnte man auch "Haltung" sagen?) ist also wesentlich teleologisch, nämlich "purpose-relative" (zweckabhängig). Ich würde es so formulieren: Bedingung der Möglichkeit der DS ist die Zweckmäßigkeit des betrachteten Systems. In meinem Brief habe ich behauptet, daß man aus dieser Perspektive vom "Verhalten" eines Systems sprechen könne. "Verhalten" ist nämlich genau das, was man im Tierreich als zweckmäßiges "Agieren" (mir fehlen die richtigen Worte) bezeichnen könnte.

"Physical stance" (PS, "physikalische Einstellung"). "From this stance our predictions are based on the actual physical state of the particular object, and are worked out by applying whatever knowledge we have of the laws of nature. It is from this stance alone that we can predict the malfunction of systems [...]." (p. 4).

P1. Hier möchte ich sagen: Bedingung der Möglichkeit der PS ist die Naturgesetzmäßigkeit des betrachteten Systems. Die PS ist wesentlich kausal. Allerdings --- und darüber sieht D. hinweg --- auch hier gibt es eine Varietät von Betrachtungsweisen: beschreibt man das System mechanisch, quantenmechanisch, oder lediglich phänomenologisch? Allen physikalischen Beschreibungen ist aber gemein, daß sie dynamisch sind. Daher habe ich im Brief davon gesprochen, daß man auf der PS "Dynamik" habe.

"Intentional stance" (IS, "intentionale Einstellung). "A mans's best hope of defeating such a machine in a chess match is to predict its responses by figuring out as best he can what the best or most rational move would be, given the rules and goals of chess. That is, one assumes not only (1) that the machine will function as designed, but (2) that the design is optimal as well, that the computer will 'choose' the most rational move. [...] Put another way, when one can no longer hope to beat the machine by utilizing one's knowledge of physics or programming to anticipate its responses, one may still be able to avoid defeat by treating the machine rather like an intelligent human opponent." (p. 5)

P1. Hier wird klar, daß die intentionale Strategie normativ ist. Bedingung der Möglichkeit der IS ist Rationalität (und zwar mehr als simple Zweckrationalität, wie sich unten noch zeigen wird). Die IS funktioniert nur dann, wenn der Beobachter dem System Rationalität oder "optimales Design" unterstellt. D.h. das System wird behandelt wie ein menschliches Gegenüber. Könnte man da nicht schon von "Handeln" und Moralität sprechen?

"A prediction relying on the assumption of the system's rationality is relative to a number of things. First, rationality here so far means nothing more than optimal design relative to a goal or optimal weighted hierarchy of goals [...] and a set of constraints [...]" (pp. 4f)

P1. Das klingt zwar doch schon wieder nach hypothetischer Zweckrationalität, geht aber tiefer. Doch später mehr dazu. Für mich ist dieses Zitat wichtig, weil es "Rationalität" vorerst relativiert. Damit ist es m.A. nach möglich, das Modell von Tschacher und Haken (2007) angemessen zu diskutieren. Das mache ich dann in einem späteren Lesebericht.

"Prediction itself is, moreover, relative to the nature and extent of the information the system has at the time about the field of endeavor." (p. 5)

P1. Damit werden die "Informationen", die das Verhalten des Systems beeinflussen, ebenfalls relativiert, oder besser: kontextabhängig. Das ist mit "beliefs" gemeint: Ein Satz von temporären Überzeugungen eines "kognitiven Agenten" (s. beim Graben 2006).

Zusammengefaßt: "One predicts behavior in such a case by ascribing to the system the possession of certain information and supposing it to be directed by certain goals, and then by working out the most reasonable or appropriate action on the basis of these ascriptions ad suppositions. It is a small step to calling the information possessed the computer's beliefs, its goals and subgoals its desires". What I mean by saying that this is a small step, is that the notion of possession of information or misinformation is just as intentional a notion as that of belief." (pp. 6f)

P1. D.h. der Besitz von Information und das Fürwahrhalten von Sachverhalten sind von der gleichen intentionalen Kategorie. Das wird in der Kognitionswissenschaft leider gerne übersehen. Das Sprechen über "Information" täuscht häufig Pseudo-Objektivität vor.

"Lingering doubt about whether the chess-playing computer really has beliefs and desires are misplaced, for the definition of intentional systems I have given does not say that intentional systems really have beliefs and desires, but that one can explain and predict their behavior by ascribing beliefs and desires to them." (p. 7)

P1. Eine der Schlüssel-Stellen! Intentionalität, oder die hinter ihr stehende Rationalität oder Subjektivität oder was-auch-immer, sind "regulative Prinzipien" für die Vorhersage komplexer Systeme. Wie können wir diesen Gedanken ausarbeiten?

"The decision to adopt the strategy is pragmatic, and is not intrinsically right or wrong. One can always refuse to adopt the intentional stance toward the computer, and accept its checkmates. One can switch stances at will without involving oneself in any inconsistencies or inhumanities, adopting the intentional stance in one's role as opponent, the design stance in one's role as redesigner, the the physical stance in one's role as repairman" (p. 7)

P1. Das mag so locker-flockig dahingesagt sein, bedeutet aber nichts weniger als die Freiheit des Beobachters eine --- von vielen möglichen --- Perspektiven, Haltungen, Einstellungen einzunehmen. Je nach subjektivem Zweck und Absicht (Intention!) kann man sich willkürlich für die IS, DS, oder PS entscheiden. Hier wird Primas (2007) eine gewisse Rolle spielen. Komisch nur, daß D. von "at will" sprechen mag, wo er doch gar nicht an die Willensfreiheit glaubt, oder?

"All that has been claimed is that on occasion, a purely physical system can be so complex, and yet so organized, that we find it convenient, explanatory, pragmatically necessary for prediction, to treat it as if it had beliefs and desires and was rational" (pp. 7f)

P1. Und hier haben wir das berühmte "als ob"! Ist D. vielleicht doch ein verkappter Kantianer, der sich nur nicht traut, seine Quellen offenzulegen, weil ihn das in der amerikanischen Philosophie bloßstellen würde? Was meinst Du, vielleicht doch eine Fußnote zu Vaihinger? Oder zu Peirce? Und wie zufällig ist die Entsprechung zwischen D.s DS, PS und IS mit Kants Unterscheidung zwischen Verstand, Vernunft und Urteilskraft? Und wo hatten wir die regulative Idee verortet? In einer Form der Urteilskraft, oder? Darum geht es ja schließlich, wenn man vor der Frage steht, welche Vorhersagestrategie anwendbar ist.

"When should we expect the tactic of adopting the intentional stance to pay off? Whenever we have reason to suppose the assumption of optimal design is warranted, and doubt the practicality of prediction from the design or physical stance." (p. 8)

P1. Die IS zahlt sich also immer aus, wenn man Rationalität in der Form von optimalen Design annehmen kann. Damit spricht sich D. allerdings keineswegs für "intelligent design" oder für kreationistische Kretins aus; ganz im Gegenteil: Optimales Design wir von der Evolution hervorgebracht. Der folgende Abschnitt ist etwas mau, endet dann aber furios:

"Having doped out these conditions [...] we can proceed at once to ascribe beliefs and desires to the creatures. Their behavior will 'manifest' their beliefs by being seen as the actions which, given the creatures' desires, would be appropriate to such beliefs as would be appropriate to the environmental stimulation. Desires, in turn, will be 'manifested' in behavior as those appropriate desires (given the needs of the creature) to which the actions of the creature would be appropriate, given the creatures beliefs. The circularity of these interlocking specifications is no accident. ascriptions of beliefs and desires must be interdependent [...]" (pp. 8f)

P1. Hier haben wir von Weizsäckers "Kreisgang", Platons "Aufhebung der Voraussetzungen" und nicht zuletzt die zirkuläre Kausalität in Hakens Synergetik. Diese Stelle eignet sich auch gut zur Interpretaton von Tschacher und Haken (2007). Um einem System auf Grund seines Verhaltens Überzeugungen zuschreiben zu können, müssen wir bestimmte Annahmen über seine Wünsche machen. Um andererseits aus dem Verhalten auf Wünsche schließen zu können, müssen wir Voraussetzungen über seine Überzeugungen annehmen.

"It might at first seem that this tactic unjustifiably imposes human categories and attributes [...] on these alien entities. It is a sort of anthropomorphizing, to be sure, but it is conceptually innocent anthropomorphizing." (p. 9)

War das nicht Dein genereller Einwand gegen die IS? D. gibt das also durchaus zu. Andererseits, brauchen wir aber dem System keine menschlichen Überzeugungen o.ä. zuzuschreiben. Auch eine Beschreibung in Ausdrücken der Informationsverarbeitung ist, wie wir gesehen haben, intentional.

Was folgt ist ein wenig Geschwafel über den Zusammenhang zwischen Rationalität und Logik. Hier nur ein paar bemerkenswerte Zitate dazu:

"So whether or not the animal is said to believe the truths of logic, it must be supposed to follow the rules of logic." (p. 11)

P1. Gab's dazu nicht eine Arbeit von Kripke?

"Will all logical truths appear among the beliefs of any intentional system? If the system were ideally or perfectly rational, all logical truths would appear, but any actual intentional system will be imperfect, and so not all logical truths must be ascribed as beliefs to any system." (p. 11)

P1. Die Bedeutung dieses Abschnitts ergibt sich aus dem Zusammenhang: muß man einem intentionalen System, das einen bestimmten "belief" hat, auch alle logischen Konsequenzen dieser Überzeugung zuschreiben? Da dies für konkrete, unvollkommene Systeme nicht der Fall, ist, kann man z.B. Default-Logiken oder Nichtmonotone Logiken verwenden.

Und jetzt kommt wieder eine Schlüssel-Stelle:

"This migration from common-sense intentional explanations and predictions to more reliable design-stance explanations and predictions that is forced on us when we discover that our subjects are imperfectly rational is, independently of any such discovery, the proper direction for theory builders to take whenever possible. In the end, we want to be able to explain the intelligence of man, or beast, in terms of his design, and this in turn in terms of natural selection of this design [...]." (p. 12)

P1. Anschließend an die Logik-Diskussion, kommt D. zu dem Schluß, das bei immer weniger anzutreffender Rationalität, die IS irgendwann untauglich wird, und man sich der DS als der geeigneteren Vorhersagestrategie behelfen müsse. Ich denke, hier können wir auch wieder mit der regulativen Idee ansetzen. Bei Steinvorth hatte ich mal gelernt, daß Kants regulative Ideen konstituierend sind. Kann man nicht sagen, die regulative Idee der Intentionalität konstituiert Rationalität? Oder eher umgekehrt?

Der Übergang zur DS ist für D. nun gerade das Charakteristikum jeglicher Theorie: Die intentionalen Annahmen irgendwann wieder loswerden zu können. D. kleidet diesen Gedanken im ökonomischen Gewand:

"Any time a theory builder proposes to call any event, state, structure, etc. in any system [...] a signal or message or command or otherwise endows it with content, he takes out a loan of intelligence. He implicitly posits along with his signals, messages, or commands, something that can serve as a signal-reader, message-understander, or commander, else his 'signals' will be for naught, will decay unreceived, uncomprehended. This loan must be repaid eventually by finding and analyzing away these readers or comprehenders; for, failing this, the theory will have among its elements unanalyzed man-analogues endowed with enough intelligence to read the signal, etc., and thus the theory will postpone answering the major question: what makes for intelligence? The intentionality of all such talk of signals and commands reminds us that rationality is being taken for granted, and in this way shows us where a theory is incomplete." (p. 12)

P1. Dies ist D.s reduktionistisches Programm. Hier haben wir die Intentionalitäts-Anleihe, die doch wohl eigentlich eine Schenkung ist! Ist er wirklich so naiv, daß er nicht merkt, daß es in all den reduktionistischen und intentional unverdächtigen Wissenschaften von metaphorischen Sprachbildern nur so wimmelt? Mein liebstes Beispiel ist natürlich die Physik in der es "Wärmebäder", "Kraftfelder" und dergleichen gibt. Sind die intentionalen Begriffe "Signal", "Information", "Arbeitsspeicher" der Psychologie nicht auch lediglich solche Metaphern? Aber selbst wenn D. recht hat: Wenn Intentionalität konstitutiv für die Psychologie ist, würde ein Rückzahlung der Intelligenz-Anleihe die Psychologie als Wissenschaft aufheben. So geht es gleich weiter:

"Intentionality abstracts from the inessential details of the various forms intelligence-loans can take [...] and serves as a reliable means of detecting exactly where a theory is in the red relative to the task of explaining intelligence; wherever a theory relies on a formulation bearing the logical marks of intentionality, there a little man is concealed." (p. 12)

P1. Die eine der IS verpflichte Theorie ist also in den "roten Zahlen". Und jeder solchen Theorie ist anzumerken, daß sie letztlich auf Homunkuli rekurriert. Ja, und? Sofern man sich als Wissenschaftler der Metaphorik bewußt bleibt, habe ich nichts gegen Homunkuli. Ich habe sie sogar in einem Artikel bewußt verwendet (beim Graben et al 2004). Sind sie nicht im Sinne von Descartes wissenschaftliche Fiktionen? Will D. jegliche Fiktion abschaffen? Schafft er damit nicht die Wissenschaft selbst ab?

Immerhin verteidigt D. im Folgenden die IS gegen Angriffe von Quine und Skinner, den er mit seinen eigenen Argumenten widerlegt. Hier findet sich dann die Stelle:

"[...] deciding on the basis of available evidence that something is (may be treated as) an intentional system permits predictions having a normative or logical basis rather than an empirical one [...]" (p. 13)

P1. Jo-mei, was drückt sich D. mit all dem Gerede von Abstraktheit, als-ob, Normativität, usw. vor des Pudels Kern herum? Die intentionale Einstellung ist transzendental.

Schließlich kommt D. auf die Bedeutung der Sprache zu sprechen. Dies ist ja auch bei Searle ein wesentliches Merkmal der Intentionaliät. Auch bei D. läuft wieder alles auf ein regulatives, konstituierendes Prinzip hinaus:

"[...] the capacity to believe would have no survival value unless it were a capacity to believe truths. [...] a false belief system is a conceptual impossibility. To borrow an example from a short story by MacDonald Harris, a soluble fish is an evolutionary impossibility, but a system of false beliefs cannot even be given a coherent description. [...] The same evolutionary bias in favor of truth prunes the capacity to communicate as it develops; a capacity for false communication would not be a capacity for communication at all, but just an emission proclivity of no systematic value to the species." (pp. 17f)

Und gleich darauf zitiert er NICHT Kant:

"The normative element of belief finds its home not in such injunctions but in the preconditions for the ascription of belief, what Phillips Griffiths calls 'the general conditions for the possibility of application of the concept'. For the concept of belief to find application, two conditions, we have seen, must be met: (1) In general, normally, more often than not, if $x$ believes $p$, $p$ is true. (2) In general, normally, more often than not, if $x$ avows that $p$, he believes $p$ [and by (1), $p$ is true]. Were these conditions not met, we would not have rational, communicating systems; we would not have believers or belief-avowers. The norm for belief is evidential well-foundedness (assuring truth in the long run), and the norm for avowal of belief is accuracy (which includes sincerity). These two norms determine pragmatic implications of our utterances." (p. 17)

P1. Aha, die "Bedingungen der Möglichkeiten" gehen also auf Griffiths zurück. (1) ist die Bedingung für Rationalität: Man glaubt normalerweise nur Wahrheiten; (2) besagt, daß Aufrichtigkeit die Bedingung für normale Kommunikation sei. Wenn das keine regulativen Prinzipen sind?

"If one wants to get away from norms and predict and explain the 'actual empirical' behavior of the poor chess-players, one stops talking of their chess moves and starts talking of their proclivities to move pieces of wood or ivory about on checkered boards". (p. 22)

BibTeX:
@inbook{Dennett78a,
  author = {D. C. Dennett},
  title = {Intentional Systems},
  publisher = {MIT Press},
  year = {1978},
  pages = {3 -- 22},
  note = {Reprinted from Journal of Philosopy 68(4), 87 -- 106, 1971.}
}
      
Drenhaus, H., beim Graben, P. & Frisch, S. When negation does make a difference: Processing German Positive Polarity Items 2009 Proc. 22nd Annual CUNY Conference on Human Sentence Processing, pp. 55  inproceedings  
Abstract: In an ERP experiment on the processing of Positive Polarity Items (PPIs) we tested sentences such as (1)-(3). A former study [4] using the traditional averaging analysis showed that the PPI “durchaus” (certainly) appearing in the scope of negation ((1) vs. (3)) elicits N400/P600 patterns which were interpreted as reflecting semantic and syntactic processing problems. However, this study did not test PPIs where negation linearly precedes but has no scope over the PPI as in (2). Here, we present an analysis of new ERP data ((1)-(3)) by means of the symbolic resonance (SRA) technique [1- 2], where ERP effects become highly amplified by a nonlinear filter. Using the average technique, we found a globally distributed N400 followed by a P600 on the PPI for the ungrammatical condition ((1) vs. (3)). Condition (2) showed no effect in both comparisons ((2) vs. (3) and (2) vs. (1)). Using the SRA, we found an early negativity (250-450ms) followed by a P600 on the PPI for the ungrammatical condition (1) vs. (3). Interestingly, condition (2) elicited a more centro-parietal distributed later negativity (350- 600ms) compared to (1). Our findings suggest: (a) ungrammatical PPI constructions (1) induce processing effects on the PPI (N400/P600) (b) linearly preceding but structurally inaccessible negation induces processing effects on the PPI in (2) (later negativity) (c) the later negativity in condition (2) suggests that the parser detects a possible violation of a PPI context We will discuss the latencies and distributions of the N400s in the structures (1) and (2) regarding semantic and pragmatic processing. The early negativity in (1) highlights the problems of integrating the PPI and is followed by a positivity (reanalysis). On the other hand, the PPI in (2) appears in a context which is semantically and syntactically grammatical but pragmatically more costly than in (3). The parser is rechecking whether the introduced alternatives by the polarity item [3] are in conflict with the negative sub-context in the relative clause. We suggest that this pragmatic rechecking, i. e. whether the introduced implicature is valid, induces a negative peak -different in latency and distribution- after the semantic integration process is completed (1). Our result gives new insight in the processing of PPI constructions, namely the interaction between the semantic/pragmatic components.
BibTeX:
@inproceedings{DrenhausGrabenFrisch09,
  author = {H. Drenhaus and P. beim Graben and S. Frisch},
  title = {When negation does make a difference: Processing German Positive Polarity Items},
  booktitle = {Proc. 22nd Annual CUNY Conference on Human Sentence Processing},
  year = {2009},
  pages = {55}
}
      
Drenhaus, H., beim Graben, P., Saddy, D. & Frisch, S. Diagnosis and repair of negative polarity constructions in the light of symbolic resonance analysis 2006 Brain and Language
Vol. 96(3), pp. 255 - 268 
article  
Abstract: In a post hoc analysis, we investigate diVerences in event-related potentials of two studies (Drenhaus et al., 2004, to appear; Saddy et al., 2004) by using the symbolic resonance analysis (Beim Graben & Kurths, 2003). The studies under discussion, examined the failure to license a negative polarity item (NPI) in German: Saddy et al. (2004a) reported an N400 component when the NPI was not accurately licensed by negation; Drenhaus et al. (2004, to appear) considered additionally the inXuence of constituency of the licensor in NPI constructions. A biphasic N400–P600 response was found for the two induced violations (the lack of licensor and the inaccessibility of negation in a relative clause). The symbolic resonance analysis (SRA) revealed an eVect in the P600 time window for the data in Saddy et al., which was not found by using the averaging technique. The SRA of the ERPs in Drenhaus et al., showed that the P600 components are distinguishable concerning the amplitude and latency. It was smaller and earlier in the condition where the licensor is inaccessible, compared to the condition without negation in the string. Our Wndings suggest that the failure in licensing NPIs is not exclusively related to semantic integration costs (N400). The elicited P600 components reXect diVerences in syntactic processing. Our results conWrm and replicate the eVects of the traditional voltage average analysis and show that the SRA is a useful tool to reveal and pull apart ERP diVerences which are not evident using the traditional voltage average analysis.
BibTeX:
@article{DrenhausGrabenEA06,
  author = {H. Drenhaus and P. beim Graben and D. Saddy and S. Frisch},
  title = {Diagnosis and repair of negative polarity constructions in the light of symbolic resonance analysis},
  journal = {Brain and Language},
  year = {2006},
  volume = {96},
  number = {3},
  pages = {255 -- 268}
}
      
Frisch, S. & beim Graben, P. The electrophysiology of vegetable language: A case study 2007 Journal of Irreproducible Results
Vol. 50(3), pp. 25 - 27 
article  
BibTeX:
@article{FrischGraben07,
  author = {S. Frisch and P. beim Graben},
  title = {The electrophysiology of vegetable language: A case study},
  journal = {Journal of Irreproducible Results},
  year = {2007},
  volume = {50},
  number = {3},
  pages = {25 -- 27}
}
      
Frisch, S. & beim Graben, P. Finding needles in haystacks: symbolic resonance analysis of event-related potentials unveils different processing demands 2005 Cognitive Brain Research
Vol. 24(3), pp. 476 - 491 
article  
Abstract: Previous ERP studies have found an N400–P600 pattern in sentences in which the number of arguments does not match the number of arguments that the verb can take. In the present study, we elaborate on this question by investigating whether the case of the mismatching object argument in German (accusative/direct object versus dative/indirect object) affects processing differently. In general, both types of mismatches elicited a biphasic N400–P600 response in the ERP. However, traditional voltage average analysis was unable to reveal differences between the two mismatching conditions, that is, between a mismatching accusative versus dative. Therefore, we employed a recently developed method on ERP data analysis, the symbolic resonance analysis (SRA), where EEG epochs are symbolically encoded in sequences of three symbols depending on a given parameter, the encoding threshold. We found a larger proportion of threshold crossing events with negative polarity in the N400 time window for a mismatching dative argument compared to a mismatching accusative argument. By contrast, the proportion of threshold crossing events with positive polarity was smaller for dative in the P600 time window. We argue that this difference is due to the phenomenon of bfree dativeQ in German. This result also shows that the SRA provides a useful tool for revealing ERP differences that cannot be discovered using the traditional voltage average analysis.
BibTeX:
@article{FrischGraben05,
  author = {S. Frisch and P. beim Graben},
  title = {Finding needles in haystacks: symbolic resonance analysis of event-related potentials unveils different processing demands},
  journal = {Cognitive Brain Research},
  year = {2005},
  volume = {24},
  number = {3},
  pages = {476 -- 491}
}
      
Frisch, S., beim Graben, P. & Schlesewsky, M. Parallelizing grammatical functions: P600 and P345 reflect different cost of reanalysis 2004 International Journal of Bifurcation and Chaos
Vol. 14(2), pp. 531 - 549 
article  
Abstract: It is well-known from psycholinguistic literature that the human language processing system exhibits preferences when sentence constituents are ambiguous with respect to their grammatical function. Generally, many theories assume that an interpretation towards the subject is preferred in such cases. Later disambiguations which contradict such a preference induce enhanced processing difficulty (i.e. reanalysis) which reflects itself in late positive defections (P345/P600) in event-related brain potentials (ERPs). In the case of anaphoric elements such as pronouns, a second strategy is known according to which an ambiguous pronoun preferentially receives the grammatical function that its antecedent has (parallel function strategy). In an ERP study, we show that this strategy can in principle override the general subject preference strategy (known for both pronominal and nonpronominal constituents) and induce an object preference, in case that the pronoun's antecedent is itself an object. Interestingly, the revision of a subject preference leads to a P600 component, whereas the revision of an object preference induces an earlier positivity (P345). In order to show that the latter component is indeed a positivity and not an N400-like negativity in the same time range, we apply an additional analysis based on symbolic dynamics which allows to determine the polarity of an ERP effect on purely methodological grounds. With respect to the two positivities, we argue that the latency differences reflect qualitative differences in the reanalysis processes.
BibTeX:
@article{FrischGrabenSchlesewsky04,
  author = {S. Frisch and P. beim Graben and M. Schlesewsky},
  title = {Parallelizing grammatical functions: P600 and P345 reflect different cost of reanalysis},
  journal = {International Journal of Bifurcation and Chaos},
  year = {2004},
  volume = {14},
  number = {2},
  pages = {531 -- 549}
}
      
Frisch, S., beim Graben, P., Schlesewsky, M. & Saddy, J.D. How to turn the subject preference into an object preference: A comparison of voltage event-related brain potentials and symbolic dynamics 2001 Journal of Cognitive Neuroscience
Vol. Supplement, pp. 166 
article  
BibTeX:
@article{FrischGrabenEA01,
  author = {S. Frisch and P. beim Graben and M. Schlesewsky and J. D. Saddy},
  title = {How to turn the subject preference into an object preference: A comparison of voltage event-related brain potentials and symbolic dynamics},
  journal = {Journal of Cognitive Neuroscience},
  year = {2001},
  volume = {Supplement},
  pages = {166}
}
      
Gerth, S. & beim Graben, P. Syntactic theory and sentence processing difficulty: A unification 2009 Proc. 22nd Annual CUNY Conference on Human Sentence Processing, pp. 81  inproceedings  
Abstract: Syntactic theory provides a rich array of representational assumptions about linguistic knowledge and processes. Such detailed and independently motivated constraints on grammatical knowledge ought to play a role in sentence comprehension. However, most grammar-based explanations of processing difficulty in the literature have naively attempted to use grammatical representations and processes per se to explain processing difficulty. They fail to take into account that the description of higher cognition in the mind encompasses two levels (Smolensky 2006): On the one hand, at the macrolevel symbolic computation is performed, and on the other hand, at the microlevel computation is achieved through processes within a dynamical system. One critical question is therefore how linguistic theory and dynamical systems can be unified to provide an explanation for processing effects. This work defines an explicit relationship between grammars (taking Minimalist Grammars, Stabler 1997, as the underlying formalism) and their use in cognitive modeling of human sentence processing. The fractal tensor product representation (Smolensky & Legendre 2006, Tabor 2000) is used to map syntactic categories onto filler vectors and positions in the binary tree onto role vectors. The model is able to capture the well-known differences between object before subject sentences in German as well as a mild garden path effect (Bader 1996, Hemforth 2000) by trajectories which explore functionally different regions in the activation space (beim Graben et al. 2008). The cognitively more costly scrambling operation is represented by a separation of the trajectories (figure 1) at the 6th parse step simulating the movement operation over a long distance. The garden path effect additionally leads to a breakdown of the parsing at the 7th parse step (figure 2). Modeling these kinds of processing difficulties with the combination of a grammar formalism and a dynamical system combines the functionalities of established linguistic theories and further accounts for the two levels of description of higher cognition in the brain.
BibTeX:
@inproceedings{GerthGraben09a,
  author = {S. Gerth and P. beim Graben},
  title = {Syntactic theory and sentence processing difficulty: A unification},
  booktitle = {Proc. 22nd Annual CUNY Conference on Human Sentence Processing},
  year = {2009},
  pages = {81}
}
      
Gerth, S. & beim Graben, P. Unifying syntactic theory and sentence processing difficulty through a connectionist minimalist parser. 2009 Cognitive Neurodynamics
Vol. 3(4), pp. 297 - 316 
article DOI  
Abstract: Syntactic theory provides a rich array of representational assumptions about linguistic knowledge and processes. Such detailed and independently motivated constraints on grammatical knowledge ought to play a role in sentence comprehension. However most grammar-based explanations of processing difficulty in the literature have attempted to use grammatical representations and processes per se to explain processing difficulty. They did not take into account that the description of higher cognition in mind and brain encompasses two levels: on the one hand, at the macrolevel, symbolic computation is performed, and on the other hand, at the microlevel, computation is achieved through processes within a dynamical system. One critical question is therefore how linguistic theory and dynamical systems can be unified to provide an explanation for processing effects. Here, we present such a unification for a particular account to syntactic theory: namely a parser for Stabler’s Minimalist Grammars, in the framework of Smolensky’s Integrated Connectionist/Symbolic architectures. In simulations we demonstrate that the connectionist minimalist parser produces predictions which mirror global empirical findings from psycholinguistic research.
BibTeX:
@article{GerthGraben09b,
  author = {S. Gerth and P. beim Graben},
  title = {Unifying syntactic theory and sentence processing difficulty through a connectionist minimalist parser.},
  journal = {Cognitive Neurodynamics},
  year = {2009},
  volume = {3},
  number = {4},
  pages = {297 -- 316},
  doi = {http://dx.doi.org/10.1007/s11571-009-9093-1}
}
      
Gerth, S., beim Graben, P. & Vasishth, S. Tensor product models for language-related brain potentials 2008 Proccedings of the 21st Annual CUNY Conference on Human Language Processing, pp. 40  inproceedings  
Abstract: One of the crucial questions in computational psycholinguistics is how symbolic processing capabilities such as language are realized by neurodynamics in the human brain. An important online measure of language processing are event-related brain potentials (ERPs). Yet these are understood purely phenomenologically, while computational accounts are by and large lacking (see Hagoort 2005 for a recent proposal). We shall use tensor product representations of symbolic structures (Smolensky 1990; Smolensky and Legendre 2006; Mizraji 1989, 1992) to describe syntactic parsing as nonlinear dynamics in neural activation space and argue that ERP differences are due to trajectories which explore different regions in that space. In an ERP experiment on the processing of German subject-object ambiguities, the sentence (1b) evoked a P600 ERP compared to (1a) reflecting an initial garden path interpretation. Starting from a Government and Binding description (Haegeman 1994) of the sentences (1a,b), we construct a locally ambiguous context-free grammar from the phrase structure trees. This grammar is decomposed into its unambiguous parts representing the two alternative processing strategies, namely subject preference against object preference in order to construct two appropriate deterministic pushdown recognizers (Aho & Ullman 1972). Using the tensor product representation, the syntactic categories of the disambiguated grammars are mapped onto linearly independent filler vectors, while positions in a labeled binary tree are given as a basis of three-dimensional space. In order to built a parallel processor (Lewis 1998) the two parses for the subject-object sentence (regular vs. garden path) and the other two for the object-subject sentence respectively were linearly superimposed in activation space. Then, model ERPs are obtained as the first principal component. Our model is able to describe, at least qualitatively, the obtained ERP results by trajectories that explore functionally and causally different regions in activation space in pursuing different language processing strategies. During its transient evolution, the trajectories of the model diverged exactly when the garden path was encountered which shows remarkable resemblance with the P600 effect in the ERP. (1a) Die Rednerin hat den Berater beim Kongress gesucht The speaker [AMBIG] has [the advisor][SUB] at the congress sought 'The speaker has sought the advisor at the congress' (1b) Die Rednerin hat der Berater beim Kongress gesucht The speaker [AMBIG] has [the advisor][OBJ] at the congress sought 'The speaker has been sought by the advisor'
BibTeX:
@inproceedings{GerthGrabenVasishth08,
  author = {S. Gerth and P. beim Graben and S. Vasishth},
  title = {Tensor product models for language-related brain potentials},
  booktitle = {Proccedings of the 21st Annual CUNY Conference on Human Language Processing},
  year = {2008},
  pages = {40}
}
      
beim Graben, P. Foundations of Neurophysics 2008 Lectures in Supercomputational Neuroscience: Dynamics in Complex Brain Networks, pp. 3 - 48  incollection  
Abstract: This chapter presents an introductory course to the biophysics of neurons, comprising a discussion of ion channels, active and passive membranes, action potentials and postsynaptic potentials. It reviews several conductance-based and reduced neuron models, neural networks and neural field theories. Finally, the basic principles of the neuroelectrodynamics of mass potentials, i.e.~dendritic fields, local field potentials, and the electroencephalogram are elucidated and their putative functional role as a mean field is discussed.
BibTeX:
@incollection{Graben08a,
  author = {P. beim Graben},
  title = {Foundations of Neurophysics},
  booktitle = {Lectures in Supercomputational Neuroscience: Dynamics in Complex Brain Networks},
  publisher = {Springer},
  year = {2008},
  pages = {3 -- 48}
}
      
beim Graben, P. Quantum representation theory for nonlinear dynamical automata 2008 Advances in Cognitive Neurodynamics, pp. 469 - 473  inproceedings  
BibTeX:
@inproceedings{Graben08b,
  author = {P. beim Graben},
  title = {Quantum representation theory for nonlinear dynamical automata},
  booktitle = {Advances in Cognitive Neurodynamics},
  publisher = {Springer},
  year = {2008},
  pages = {469 -- 473}
}
      
beim Graben, P. Lems Solaris im Lichte der Kybernetik 2007 SchriftZüge. Brandenburgische Blätter für Kunst und Literatur
Vol. 9(1), pp. 126 - 132 
article  
BibTeX:
@article{Graben07,
  author = {P. beim Graben},
  title = {Lems Solaris im Lichte der Kybernetik},
  journal = {SchriftZüge. Brandenburgische Blätter für Kunst und Literatur},
  year = {2007},
  volume = {9},
  number = {1},
  pages = {126 -- 132}
}
      
beim Graben, P. Pragmatic information in dynamic semantics 2006 Mind and Matter
Vol. 4(2), pp. 169 - 193 
article  
Abstract: In 1972, Ernst Ulrich and Christine von Weizsäcker introduced the concept of pragmatic information with three desiderata: (i) Pragmatic information should assess the impact of a message upon its receiver; (ii) Pragmatic information should vanish in the limits of complete (non-interpretable) "novelty" and complete "confirmation"; (iii) Pragmatic information should exhibit non-classical properties since novelty and confirmation behave similarly to Fourier pairs of complementary operators in quantum mechanics. It will be shown how these three desiderata can be naturally fulfilled within the framework of Gärdenfors' dynamic semantics of Bayesian belief models. (i) The meaning of a message is its impact upon the epistemic states of a cognitive agent. A pragmatic information measure can then be quantified by the average information gain for the transition from a prior to a posterior state. (ii) Total novelty can be represented by the identical proposition, total confirmation by the logical consequence of propositions. In both cases, pragmatic information vanishes. (iii) For operators that are neither idempotent nor commuting, novelty and confirmation relative to a message sequence can be defined within Gärdenfors' theory of belief revisions. The proposed approach is consistent with measures of relevance derived from statistical decision theory and it contains Bar-Hillel's and Carnap's theory of semantic information as a special case.
BibTeX:
@article{Graben06,
  author = {P. beim Graben},
  title = {Pragmatic information in dynamic semantics},
  journal = {Mind and Matter},
  year = {2006},
  volume = {4},
  number = {2},
  pages = {169 -- 193}
}
      
beim Graben, P. Hoch am Ätherwind 2005 SchriftZüge. Brandenburgische Blätter für Kunst und Literatur
Vol. 7(1), pp. 60 - 66 
article  
BibTeX:
@article{Graben05,
  author = {P. beim Graben},
  title = {Hoch am Ätherwind},
  journal = {SchriftZüge. Brandenburgische Blätter für Kunst und Literatur},
  year = {2005},
  volume = {7},
  number = {1},
  pages = {60 -- 66}
}
      
beim Graben, P. Incompatible implementations of physical symbol systems 2004 Mind and Matter
Vol. 2(2), pp. 29 - 51 
article  
Abstract: Classical cognitive science assumes that intelligently behaving systems must be symbol processors that are implemented in physical systems such as brains or digital computers. By contrast, connectionists suppose that symbol manipulating systems could be approximations of neural networks dynamics. Both classicists and connectionists argue that symbolic computation and subsymbolic dynamics are incompatible, though on different grounds. While classicists say that connectionist architectures and symbol processors are either incompatible or the former are mere implementations of the latter, connectionists reply that neural networks might be incompatible with symbol processors because the latter cannot be implementations of the former. In this contribution, the notions of "incompatibility" and "implementation" will be criticized to show that they must be revised in the context of the dynamical system approach to cognitive science. Examples for implementations of symbol processors that are incompatible with respect to contextual topologies will be discussed.
BibTeX:
@article{Graben04,
  author = {P. beim Graben},
  title = {Incompatible implementations of physical symbol systems},
  journal = {Mind and Matter},
  year = {2004},
  volume = {2},
  number = {2},
  pages = {29 -- 51}
}
      
beim Graben, P. Estimating and improving the signal-to-noise ratio of time series by symbolic dynamics 2001 Physical Reviews E
Vol. 64, pp. 051104 
article  
Abstract: We investigate the effect of symbolic encoding applied to times series consisting of some deterministic signal and additive noise, as well as time series given by a deterministic signal with randomly distributed initial conditions as a model of event-related brain potentials. We introduce an estimator of the signal-to-noise ratio (SNR) of the system by means of time averages of running complexity measures such as Shannon and Renyi entropies, and prove its asymptotical equivalence with the linear SNR in the case of Shannon entropies of symbol distributions. A SNR improvement factor is defined, exhibiting a maximum for intermediate values of noise amplitude in analogy to stochastic resonance phenomena. We demonstrate that the maximum of the SNR improvement factor can be shifted toward smaller noise amplitudes by using higher order Renyi entropies instead of the Shannon entropy. For a further improvement of the SNR, a half wave encoding of noisy time series is introduced. Finally, we discuss the effect of noisy phases on the linear SNR as well as on the SNR defined by symbolic dynamics. It is shown that longer symbol sequences yield an improvement of the latter.
BibTeX:
@article{Graben01a,
  author = {P. beim Graben},
  title = {Estimating and improving the signal-to-noise ratio of time series by symbolic dynamics},
  journal = {Physical Reviews E},
  year = {2001},
  volume = {64},
  pages = {051104}
}
      
beim Graben, P. Symbolische Dynamik Ereigniskorrelierter Potentiale in der Sprachverarbeitung 2001   book  
BibTeX:
@book{Graben01b,
  author = {P. beim Graben},
  title = {Symbolische Dynamik Ereigniskorrelierter Potentiale in der Sprachverarbeitung},
  publisher = {Shaker Verlag},
  year = {2001}
}
      
beim Graben, P. & Atmanspacher, H. Extending the philosophical significance of the idea of complementarity 2009 Recasting Reality. Wolfgang Pauli's Philosophical Ideas and Contemporay Science, pp. 99 - 113  incollection  
Abstract: We discuss a specific way in which the notion of complementarity can be based on the dynamics of the system considered. This approach rests on an epistemic representation of system states, reflecting our knowledge about a system in terms of coarse grainings (partitions) of its phase space. Within such an epistemic quantization of classical systems, compatible, comparable, commensurable, and complementary descriptions can be precisely characterized and distinguished from each other. Some tentative examples are indicated that, we suppose, would have been of interest to Pauli.
BibTeX:
@incollection{GrabenAtmanspacher09,
  author = {P. beim Graben and H. Atmanspacher},
  title = {Extending the philosophical significance of the idea of complementarity},
  booktitle = {Recasting Reality. Wolfgang Pauli's Philosophical Ideas and Contemporay Science},
  publisher = {Springer},
  year = {2009},
  pages = {99 -- 113}
}
      
beim Graben, P. & Atmanspacher, H. Complementarity in classical dynamical systems 2006 Foundations of Physics
Vol. 36(2), pp. 291 - 306 
article  
Abstract: The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions in terms of ensembles of epistemic states (symbols) with corresponding classical observables, it is shown that such observables are complementary to each other with respect to particular partitions unless those partitions are generating. This explains why symbolic descriptions based on an ad hoc partition of an underlying phase space description should generally be expected to be incompatible. Related approaches with different background and different objectives are discussed.
BibTeX:
@article{GrabenAtmanspacher06a,
  author = {P. beim Graben and H. Atmanspacher},
  title = {Complementarity in classical dynamical systems},
  journal = {Foundations of Physics},
  year = {2006},
  volume = {36},
  number = {2},
  pages = {291 -- 306}
}
      
beim Graben, P. & Atmanspacher, H. Editorial 2006 Mind and Matter
Vol. 4(2), pp. 131 -139 
article  
Abstract: The present issue of Mind and Matter on the concept of "pragmatic information" has originated from a frutiful collaboration with Peter beim Graben, whose active involvement as a co-editor was decisive for its production and is greatly appreciated. The following extended editorial introduces the topic within a broader background. In particular, the concept of pragmatic information will be related to the study of complex systems and to concepts of complexity that are not in detail addressed in the individual contributions to the issue. Finally, possible connections to an epistemically understood distinction of mental and material domains of discourse will be indicated.
BibTeX:
@article{GrabenAtmanspacher06b,
  author = {P. beim Graben and H. Atmanspacher},
  title = {Editorial},
  journal = {Mind and Matter},
  year = {2006},
  volume = {4},
  number = {2},
  pages = {131 --139}
}
      
beim Graben, P., Barrett, A. & Atmanspacher, H. Stability criteria for the contextual emergence of macrostates in neural networks 2009 Network: Computation in Neural Systems
Vol. 20(3), pp. 178 - 196 
article DOI  
Abstract: More than thirty years ago, Amari and colleagues proposed a statistical framework for identifying structurally stable macrostates of neural networks from observations of their microstates. We compare their stochastic stability criterion with a deterministic stability criterion based on the ergodic theory of dynamical systems, recently proposed for the scheme of contextual emergence and applied to particular inter-level relations in neuroscience. Stochastic and deterministic stability criteria for macrostates rely on macro-level contexts, which make them sensitive to differences between different macro-levels.
BibTeX:
@article{GrabenBarrettAtmanspacher09,
  author = {P. beim Graben and A. Barrett and H. Atmanspacher},
  title = {Stability criteria for the contextual emergence of macrostates in neural networks},
  journal = {Network: Computation in Neural Systems},
  year = {2009},
  volume = {20},
  number = {3},
  pages = {178 -- 196},
  doi = {http://dx.doi.org/10.1080/09548980903161241}
}
      
beim Graben, P., Drenhaus, H., Brehm, E., Rhode, B., Saddy, D. & Frisch, S. Enhancing dominant modes in nonstationary time series by means of the symbolic resonance analysis 2007 Chaos
Vol. 17, pp. 043106 
article DOI  
Abstract: We present the symbolic resonance analysis (SRA) as a viable method for addressing the problem of enhancing a weakly dominant mode in a mixture of impulse responses obtained from a nonlinear dynamical system. We demonstrate this using results from a numerical simulation with Duffing oscillators in different domains of their parameter space, and by analyzing event-related brain potentials (ERPs) from a language processing experiment in German as a representative application. In this paradigm, the averaged ERPs exhibit an N400 followed by a sentence final negativity. Contemporary sentence processing models predict a late positivity (P600) as well. We show that the SRA is able to unveil the P600 evoked by the critical stimuli as a weakly dominant mode from the covering sentence final negativity.
BibTeX:
@article{GrabenEA07,
  author = {P. beim Graben and H. Drenhaus and E. Brehm and B. Rhode and D. Saddy and S. Frisch},
  title = {Enhancing dominant modes in nonstationary time series by means of the symbolic resonance analysis},
  journal = {Chaos},
  year = {2007},
  volume = {17},
  pages = {043106},
  doi = {http://dx.doi.org/10.1063/1.2795434}
}
      
beim Graben, P. & Frisch, S. Is it positive or negative? On determining ERP components 2004 IEEE Transactions on Biomedical Engineering
Vol. 51(8), pp. 1374 - 1382 
article  
Abstract: In most experiments using event-related brain potentials (ERPs), there is a straightforward way to define ? on theoretical grounds ? which of the conditions tested is the experimental condition and which is the control condition. If, however, theoretical assumptions do not give sufficient and unambiguous information to decide this question, then the interpretation of an ERP effect becomes difficult, especially if one takes into account that certain effects can be both a positivity or a negativity on the basis of the morphology of the pattern as well as with respect to peak latency (regard for example, N400 and P345). Exemplified with an ERP experiment on language processing, we present such a critical case and offer a possible solution on the basis of nonlinear data analysis. We show that a generalized polarity histogram, the word statistics of symbolic dynamics, is in principle able to distinguish negative going ERP components from positive ones when an appropriate encoding strategy, the half wave encoding is employed. We propose statistical criteria which allow to determine ERP components on purely methodological grounds.
BibTeX:
@article{GrabenFrisch04,
  author = {P. beim Graben and S. Frisch},
  title = {Is it positive or negative? On determining ERP components},
  journal = {IEEE Transactions on Biomedical Engineering},
  year = {2004},
  volume = {51},
  number = {8},
  pages = {1374 -- 1382}
}
      
beim Graben, P., Frisch, S. & Drenhaus, H. Evidence for nonlinear dynamics during sentence processing 2006 Journal of Cognitive Neuroscience
Vol. Supplement, pp. 128 
article  
BibTeX:
@article{GrabenFrischDrenhaus06,
  author = {P. beim Graben and S. Frisch and H. Drenhaus},
  title = {Evidence for nonlinear dynamics during sentence processing},
  journal = {Journal of Cognitive Neuroscience},
  year = {2006},
  volume = {Supplement},
  pages = {128}
}
      
beim Graben, P., Frisch, S., Fink, A., Saddy, D. & Kurths, J. Topographic voltage and coherence mapping of brain potentials by means of the symbolic resonance analysis 2005 Physical Reviews E
Vol. 72, pp. 051916 
article  
Abstract: We apply the recently developed symbolic resonance analysis to electroencephalographic measurements of event-related brain potentials ERPs in a language processing experiment by using a three-symbol static encoding with varying thresholds for analyzing the ERP epochs, followed by a spin-flip transformation as a nonlinear filter. We compute an estimator of the signal-to-noise ratio SNR for the symbolic dynamics measuring the coherence of threshold-crossing events. Hence, we utilize the inherent noise of the EEG for sweeping the underlying ERP components beyond the encoding thresholds. Plotting the SNR computed within the time window of a particular ERP component the N400 against the encoding thresholds, we find different resonance curves for the experimental conditions. The maximal differences of the SNR lead to the estimation of optimal encoding thresholds. We show that topographic brain maps of the optimal threshold voltages and of their associated coherence differences are able to dissociate the underlying physiological processes, while corresponding maps gained from the customary voltage averaging technique are unable to do so.
BibTeX:
@article{GrabenFrischEA05,
  author = {P. beim Graben and S. Frisch and A. Fink and D. Saddy and J. Kurths},
  title = {Topographic voltage and coherence mapping of brain potentials by means of the symbolic resonance analysis},
  journal = {Physical Reviews E},
  year = {2005},
  volume = {72},
  pages = {051916}
}
      
beim Graben, P., Gerth, S., Saddy, D. & Potthast, R. Fock space representations in neural field theories 2007 Proc. Waves 2007. The 8th International Conference on Mathematical and Numerical Aspects of Waves, pp. 120 - 122  inproceedings  
Abstract: We outline a computational model of syntactic language processing based on Smolensky's Fock space representations of symbolic expressions using spherical wave functions. Symbolic computation, regarded as nonlinear operators acting upon these waves, provides a discrete sequence of training patterns that could be used to solve the inverse problem of neural field theories in order to determine the synaptic connectivity/weight kernels. The solutions of a neural field equation should then provide a model of event-related brain potentials that are elicited by syntactic processing problems.
BibTeX:
@inproceedings{GrabenGerthEA07,
  author = {P. beim Graben and S. Gerth and D. Saddy and R. Potthast},
  title = {Fock space representations in neural field theories},
  booktitle = {Proc. Waves 2007. The 8th International Conference on Mathematical and Numerical Aspects of Waves},
  publisher = {Dept. of Mathematics, University of Reading},
  year = {2007},
  pages = {120 -- 122}
}
      
beim Graben, P., Gerth, S. & Vasishth, S. Towards dynamical system models of language-related brain potentials 2008 Cognitive Neurodynamics
Vol. 2(3), pp. 229 - 255 
article DOI URL 
Abstract: Event-related brain potentials (ERP) are important neural correlates of cognitive processes. In the domain of language processing, the N400 and P600 reflect lexical-semantic integration and syntactic processing problems, respectively. We suggest an interpretation of these markers in terms of dynamical system theory and present two nonlinear dynamical models for syntactic computations where different processing strategies correspond to functionally different regions in the system's phase space.
BibTeX:
@article{GrabenGerthVasishth08,
  author = {P. beim Graben and S. Gerth and S. Vasishth},
  title = {Towards dynamical system models of language-related brain potentials},
  journal = {Cognitive Neurodynamics},
  year = {2008},
  volume = {2},
  number = {3},
  pages = {229 -- 255},
  url = {http://www.springerlink.com/content/620524852488126q},
  doi = {http://dx.doi.org/10.1007/s11571-008-9041-5}
}
      
beim Graben, P., Gerth, S. & Vasishth, S. Modeling language-related brain potentials by dynamical recognizers 2008 Proccedings of the 21st Annual CUNY Conference on Human Language Processing, pp. 105  inproceedings  
Abstract: Event-related brain potentials (ERP) are important neural correlates of cognitive processes. In the domain of language processing, the N400 reflects lexical-semantic integration processes. Every incoming new word is known to evoke a "bump" in the ERP wave whose amplitude co-varies with the ease of integration (Coles and Rugg 1995). Starting from experimental findings of Osterhout, Holcomb and Swinney (1994) for sentences such as (1) The judge believed the defendant was lying. We propose a computational model that is able to account for the N400 word integration effect. Our model combines two different approaches from dynamical system theory, 1. Nonlinear Dynamical Automata (Moore 1990, beim Graben et al. 2004, beim Graben et al. accepted), implementing Turing machines by autonomous nonlinear dynamics in a phase space, and 2. Dynamical Recognizer (Pollack 1991; see also Tabor 1998) where symbols, which are represented by iterated function systems, act non-autonomously upon a phase space. In a first step, we describe the sentence (1) by an appropriate context-free grammar, and construct a deterministic top-down recognizer for processing this grammar in a second step. In a third step, the parser is represented by a nonlinear dynamics at the unit square through a Gödel encoding of the syntactic categories (Moore 1990), yielding a nonlinear dynamical automaton. The initial conditions of the nonlinear dynamical automaton model are represented by the whole input string to be processed. However, this is cognitively implausible for two reasons: 1) Hearing or reading supplies lexical material successively to the human mind. 2) The nonlinear dynamical automaton's behavior is deterministic for a given initial condition. Hence, the preparation of initial conditions by the whole input string yields a completely predictable trajectory in phase space. In order to remedy these shortcomings, we suggest the following solution: 1) Restrict the parser's input to a "working memory" of two symbols (Frazier and Fodor 1978). 2) After each attachment, the next symbol is interactively scanned from the environment into the working memory (Wegner 1998). In our combined nonlinear dynamical automaton/dynamical recognizer model, the action of the scanned word upon the phase space of the nonlinear dynamical automaton is represented by one particular function from a dynamical recognizer's iterated function systems (beim Graben et al. accepted). Symbolically meaningful states of the combined nonlinear dynamical automaton/dynamical recognizer are rectangular macrostates moving through the phase space of the nonlinear dynamical automaton. As a model ERP we propose to measure the areas of these rectangles. Because each scan operation is reflected by a vertical squeezing of a macrostate, the measured ERP signal drops after each scanning, thus emulating the word integration N400. At the present stage, our model cannot account for differences in lexical gradience, context effects or plausibility, because only the structural changes of working memory during the scan operation are described. However, the model is consistent with the dynamical system interpretation of ERPs (Basar 1980) and the dynamical system approach to cognition, since different regions in phase space are functionally different with respect to the possible actions of the processor (Fodor and Pylyshyn 1988).
BibTeX:
@inproceedings{GrabenGerthVasishth08b,
  author = {P. beim Graben and S. Gerth and S. Vasishth},
  title = {Modeling language-related brain potentials by dynamical recognizers},
  booktitle = {Proccedings of the 21st Annual CUNY Conference on Human Language Processing},
  year = {2008},
  pages = {105}
}
      
beim Graben, P., Jurish, B., Saddy, D. & Frisch, S. Language processing by dynamical systems 2004 International Journal of Bifurcation and Chaos
Vol. 14(2), pp. 599 - 621 
article  
Abstract: We describe a part of the stimulus sentences of a German language processing ERP experiment using a context-free grammar and represent different processing preferences by its unambiguous partitions. The processing is modeled by deterministic pushdown automata. Using a theorem proven by Moore, we map these automata onto discrete time dynamical systems acting at the unit square, where the processing preferences are represented by a control parameter. The actual states of the automata are rectangles lying in the unit square that can be interpreted as cylinder sets in the context of symbolic dynamics theory. We show that applying a wrong processing preference to a certain input string leads to an unwanted invariant set in the parsers dynamics. Then, syntactic reanalysis and repair can be modeled by a switching of the control parameter - in analogy to phase transitions observed in brain dynamics. We argue that ERP components are indicators of these bifurcations and propose an ERP-like measure of the parsing model.
BibTeX:
@article{GrabenJurishEA04,
  author = {P. beim Graben and B. Jurish and D. Saddy and S. Frisch},
  title = {Language processing by dynamical systems},
  journal = {International Journal of Bifurcation and Chaos},
  year = {2004},
  volume = {14},
  number = {2},
  pages = {599 -- 621}
}
      
beim Graben, P. & Kurths, J. Simulating global properties of electroencephalograms with minimal random neural networks 2008 Neurocomputing
Vol. 71(4), pp. 999 - 1007 
article  
Abstract: The human electroencephalogram (EEG) is globally characterized by a $1/f$ power spectrum superimposed with certain peaks, whereby the ``alpha peak'' in a frequency range of 8 to 14 Hz is the most prominent one for relaxed states of wakefulness. We present simulations of a minimal dynamical network model of leaky integrator neurons attached to the nodes of an evolving directed and weighted random graph (an Erdős-Rényi graph). We derive a model of the dendritic field potential (DFP) for the neurons leading to a simulated EEG that describes the global activity of the network. Depending on the network size, we find an oscillatory transition of the simulated EEG when the mean degree reaches a critical connectivity. This transition, indicated by a suitably defined order parameter, is reflected by a sudden change of the network's topology when super-cycles are formed from merging isolated loops. After the oscillatory transition, the power spectra of simulated EEG time series exhibit a $1/f$ continuum superimposed with certain peaks.
BibTeX:
@article{GrabenKurths08,
  author = {P. beim Graben and J. Kurths},
  title = {Simulating global properties of electroencephalograms with minimal random neural networks},
  journal = {Neurocomputing},
  year = {2008},
  volume = {71},
  number = {4},
  pages = {999 -- 1007}
}
      
beim Graben, P. & Kurths, J. Detecting subthreshold events in noisy data by symbolic dynamics 2003 Physical Review Letters
Vol. 90(10), pp. 100602 
article DOI  
Abstract: We show that a symmetric threshold crossing detector can be described by a symbolic dynamics of a static three-symbol encoding which is highly efficient to detect subthreshold events in noisy nonstationary data. After computing instantaneous word statistics and running cylinder entropies, we introduce a mean-field transformation of the three-symbol dynamics considered as a Potts-spin lattice onto a distribution of two symbols. This transformed word statistics enables one to derive an estimator of the signal-to-noise ratio (SNR). Subthreshold events are then proven by a prominent peak of the SNR estimator as a function of the noise intensity.
BibTeX:
@article{GrabenKurths03,
  author = {P. beim Graben and J. Kurths},
  title = {Detecting subthreshold events in noisy data by symbolic dynamics},
  journal = {Physical Review Letters},
  year = {2003},
  volume = {90},
  number = {10},
  pages = {100602},
  doi = {http://dx.doi.org/10.1103/PhysRevLett.90.100602}
}
      
BibTeX:
@misc{GrabenLiebscher00,
  author = {P. beim Graben and T. Liebscher},
  title = {Einführung in die Neurophysik},
  year = {2000},
  note = {Skriptum, Universität Potsdam}
}
      
beim Graben, P., Liebscher, T. & Kurths, J. Neural and cognitive modeling with networks of leaky integrator units 2008 Lectures in Supercomputational Neuroscience: Dynamics in Complex Brain Networks, pp. 195 - 223  incollection  
Abstract: After reviewing several physiological findings on oscillations in the electroencephalogram (EEG) and their possible explanations by dynamical modeling, we present neural networks consisting of leaky integrator units as a universal paradigm for neural and cognitive modeling. In contrast to standard recurrent neural networks, leaky integrator units are described by ordinary differential equations living in continuous time. We present an algorithm to train the temporal behavior of leaky integrator networks by generalized back-propagation and discuss their physiological relevance. Eventually, we show how leaky integrator units can be used to build oscillators that may serve as models of brain oscillations and cognitive processes.
BibTeX:
@incollection{GrabenLiebscherKurths08,
  author = {P. beim Graben and T. Liebscher and J. Kurths},
  title = {Neural and cognitive modeling with networks of leaky integrator units},
  booktitle = {Lectures in Supercomputational Neuroscience: Dynamics in Complex Brain Networks},
  publisher = {Springer},
  year = {2008},
  pages = {195 -- 223}
}
      
beim Graben, P., Liebscher, T. & Saddy, J.D. Parsing Ambiguous Context-Free Languages by Dynamical Systems: Disambiguation and Phase Transitions in Neural Networks with Evidence from Event-Related Brain Potentials (ERP) 2000
Vol. II: Internalising KnowledgeLearning to Behave, pp. 119 - 135 
inproceedings  
BibTeX:
@inproceedings{GrabenLiebscherSaddy00,
  author = {P. beim Graben and T. Liebscher and J. D. Saddy},
  title = {Parsing Ambiguous Context-Free Languages by Dynamical Systems: Disambiguation and Phase Transitions in Neural Networks with Evidence from Event-Related Brain Potentials (ERP)},
  booktitle = {Learning to Behave},
  publisher = {Universiteit Twente},
  year = {2000},
  volume = {II: Internalising Knowledge},
  pages = {119 -- 135}
}
      
beim Graben, P., Pinotsis, D., Saddy, D. & Potthast, R. Language processing with dynamic fields 2008 Cognitive Neurodynamics
Vol. 2(2), pp. 79 - 88 
article DOI URL 
Abstract: We construct a mapping from complex recursive linguistic data structures to spherical wave functions using Smolensky's filler/role bindings and tensor product representations. Syntactic language processing is then described by the transient evolution of these spherical patterns whose amplitudes are governed by nonlinear order parameter equations. Implications of the model in terms of brain wave dynamics are indicated.
BibTeX:
@article{GrabenEA08b,
  author = {P. beim Graben and D. Pinotsis and D. Saddy and R. Potthast},
  title = {Language processing with dynamic fields},
  journal = {Cognitive Neurodynamics},
  year = {2008},
  volume = {2},
  number = {2},
  pages = {79 -- 88},
  note = {special issue on brain waves},
  url = {http://www.springerlink.com/content/x20251421k4263x7},
  doi = {http://dx.doi.org/10.1007/s11571-008-9042-4}
}
      
beim Graben, P. & Potthast, R. Inverse problems in dynamic cognitive modeling 2009 Chaos
Vol. 19(1), pp. 015103 
article DOI  
Abstract: Inverse problems for dynamical system models of cognitive processes comprise the determination of synaptic weight matrices or kernel functions for neural networks or neural/dynamic field models, respectively. We introduce dynamic cognitive modeling as a three tier top-down approach where cognitive processes are first described as algorithms that operate on complex symbolic data structures. Second, symbolic expressions and operations are represented by states and transformations in abstract vector spaces. Third, prescribed trajectories through representation space are implemented in neurodynamical systems. We discuss the Amari equation for a neural/dynamic field theory as a special case and show that the kernel construction problem is particularly ill-posed. We suggest a Tikhonov–Hebbian learning method as regularization technique and demonstrate its validity and robustness for basic examples of cognitive computations.
BibTeX:
@article{GrabenPotthast09a,
  author = {P. beim Graben and R. Potthast},
  title = {Inverse problems in dynamic cognitive modeling},
  journal = {Chaos},
  year = {2009},
  volume = {19},
  number = {1},
  pages = {015103},
  doi = {http://dx.doi.org/10.1063/1.3097067}
}
      
beim Graben, P. & Potthast, R. Editorial 2009 Cognitive Neurodynamics
Vol. 3(4), pp. 295 - 296 
article DOI  
BibTeX:
@article{GrabenPotthast09b,
  author = {P. beim Graben and R. Potthast},
  title = {Editorial},
  journal = {Cognitive Neurodynamics},
  year = {2009},
  volume = {3},
  number = {4},
  pages = {295 -- 296},
  doi = {http://dx.doi.org/10.1007/s11571-009-9091-3}
}
      
beim Graben, P., Potthast, R. & Saddy, D. Editorial 2008 Cognitive Neurodynamics
Vol. 2(2) 
article  
BibTeX:
@article{GrabenPotthastSaddy08,
  author = {P. beim Graben and R. Potthast and D. Saddy},
  title = {Editorial},
  journal = {Cognitive Neurodynamics},
  year = {2008},
  volume = {2},
  number = {2},
  note = {special issue on brain waves}
}
      
beim Graben, P., Saddy, D. & Frisch, S. Using stochastic resonance for analyzing event-related brain potentials 2002 Journal of Cognitive Neuroscience
Vol. Supplement, pp. 63 
article  
BibTeX:
@article{GrabenSaddyFrisch02a,
  author = {P. beim Graben and D. Saddy and S. Frisch},
  title = {Using stochastic resonance for analyzing event-related brain potentials},
  journal = {Journal of Cognitive Neuroscience},
  year = {2002},
  volume = {Supplement},
  pages = {63},
  note = {Abstract}
}
      
beim Graben, P., Saddy, D. & Kurths, J. Editorial 2004 International Journal of Bifurcation and Chaos
Vol. 14(2), pp. 355 - 361 
article  
Abstract: After Galileo Galilei, the founder of modern physics, had been condemned to lifelong house arrest by the Catholic Church in 1633 for defending Copernicus' cosmology in his Dialogue, the French philosopher and mathematician Rene Descartes abandoned his intention to publish his own philosophy of nature [Descartes, 1985a, p. 141]. The World appeared posthumously in 1664, 14 years after Descartes' death. It consists of two parts: the Treatise on Light dealt with physics and a fictitious cosmology [Descartes, 2002], while in the Treatise of Man Descartes established a mechanistic physiology [Descartes, 1972]. In this writing, he describes the human body in analogy to an automaton that is driven by several fluids, such as air, blood and the animal spirits, which are a very subtle matter similar to the spirit of wine [Wohlers, 2002]. Impressed and inspired by the art and skills of late renaissance engineers who built trick fountains in the gardens of, e.g. Saint-Germain-en-Laye near Paris, Descartes compared this automaton with...
BibTeX:
@article{GrabenSaddyKurths04b,
  author = {P. beim Graben and D. Saddy and J. Kurths},
  title = {Editorial},
  journal = {International Journal of Bifurcation and Chaos},
  year = {2004},
  volume = {14},
  number = {2},
  pages = {355 -- 361}
}
      
beim Graben, P., Saddy, D., Schlesewsky, M. & Kurths, J. Symbolic dynamics of event-related brain potentials 2000 Physical Reviews E
Vol. 62(4), pp. 5518 - 5541 
article  
Abstract: We apply symbolic dynamics techniques such as word statistics and measures of complexity to nonstationary and noisy multivariate time series of electroencephalograms EEG in order to estimate event-related brain potentials ERP. Their significance against surrogate data as well as between different experimental conditions is tested. These methods are validated by simulations using stochastic dynamical systems with time-dependent control parameters and compared with traditional ERP-analysis techniques. Continuous EEG data are cut into epochs according to stimuli events presented to the subjects. These ensembles of time series can be considered as ensembles of trajectories given by some dynamical systems. We employ a statistical mechanics approach motivated by the Frobenius-Perron equation and apply it to coarse-grained symbolic descriptions of the dynamics. We develop time-dependent measures of complexity founded on running cylinder sets and show that these quantities are able to distinguish simulated data obtained by different control parameters as well as experimental data between different experimental conditions. As a first finding, our approach restores the well-known ERP components and it reveals additionally qualitative changes in the EEG that cannot be detected by means of the traditional techniques. We criticize the prerequisites of the traditional approach to ERP analysis and propose to consider ERP instead in terms of dynamical system theory and information theory.
BibTeX:
@article{GrabenSaddyEA00,
  author = {P. beim Graben and D. Saddy and M. Schlesewsky and J. Kurths},
  title = {Symbolic dynamics of event-related brain potentials},
  journal = {Physical Reviews E},
  year = {2000},
  volume = {62},
  number = {4},
  pages = {5518 -- 5541}
}
      
Potthast, R. & beim Graben, P. Inverse problems in neural field theory 2009 SIAM Jounal on Applied Dynamical Systems
Vol. 8(4), pp. 1405 - 1433 
article DOI URL 
Abstract: We study inverse problems in neural field theory, i.e. the construction of synaptic weight kernels yielding a prescribed neural field dynamics. We address the issues of existence, uniqueness and stability of solutions to the inverse problem for the Amari neural field equation as a special case, and prove that these problems are generally illposed. In order to construct solutions to the inverse problem, we first recast the Amari equation into a linear perceptron equation in an infinite-dimensional Banach or Hilbert space. In a second step, we construct sets of bi-orthogonal function systems allowing the approximation of synaptic weight kernels by a generalized Hebbian learning rule. Numerically, this construction is implemented by the Moore-Penrose pseudo-inverse method. We demonstrate the instability of these solutions and use the Tikhonov regularization method for stabilization and to prevent numerical overfitting. We illustrate the stable construction of kernels by means of three instructive examples.
BibTeX:
@article{PotthastGraben09a,
  author = {R. Potthast and P. beim Graben},
  title = {Inverse problems in neural field theory},
  journal = {SIAM Jounal on Applied Dynamical Systems},
  year = {2009},
  volume = {8},
  number = {4},
  pages = {1405 -- 1433},
  url = {http://link.aip.org/link/?SJA/8/1405/1},
  doi = {http://dx.doi.org/10.1137/080731220}
}
      
Potthast, R. & beim Graben, P. Existence and properties of solutions for neural field equations 2009 Mathematical Methods in the Applied Sciences  article DOI  
Abstract: The first goal of this work is to study the solvability of the neural field equation (known as "Amari equation") which is an integro-differential equation in m+1 dimensions. In particular, we show the existence of global solutions for smooth activation functions f with values in [0; 1] and L1 kernels via the Banach fixpoint theorem. We note that this setting is much more general than in most related studies, e.g. Ermentrout and McLeod [Proceedings of the Royal Society of Edinburgh, 123A, 461-478, 1993]. For a Heaviside type activation function f we show that the approach above fails. However, with slightly more regularity on the kernel function w (we use Hoelder continuity with respect to the argument x) we can employ compactness arguments, integral equation techniques and the results for smooth nonlinearity functions to obtain a global existence result in a weaker space. Finally, general estimates on the speed and durability of waves are derived. We show that compactly supported waves with directed kernels decay exponentially after a finite time and that the field has a well defined finite speed.
BibTeX:
@article{PotthastGraben09b,
  author = {R. Potthast and P. beim Graben},
  title = {Existence and properties of solutions for neural field equations},
  journal = {Mathematical Methods in the Applied Sciences},
  year = {2009},
  doi = {http://dx.doi.org/10.1002/mma.1199}
}
      
Potthast, R. & beim Graben, P. Dimensional reduction for the inverse problem of neural field theory 2009 Frontiers in Computational Neuroscience
Vol. 3, pp. 17 
article DOI  
Abstract: Inverse problems in computational neuroscience comprise the determination of synaptic weight matrices or kernels for neural networks or neural fi elds respectively. Here, we reduce multidimensional inverse problems to inverse problems in lower dimensions which can be solved in an easier way or even explicitly through kernel construction. In particular, we discuss a range of embedding techniques and analyze their properties. We study the Amari equation as a particular example of a neural fi eld theory. We obtain a solution of the full 2D or 3D problem by embedding 0D or 1D kernels into the domain of the Amari equation using a suitable path parametrization and basis transformations. Pulses are interconnected at branching points via path gluing. As instructive examples we construct logical gates, such as the persistent XOR and binary addition in neural fi elds. In addition, we compare results of inversion by dimensional reduction with a recently proposed global inversion scheme for neural fi elds based on Tikhonov–Hebbian learning. The results show that stable construction of complex distributed processes is possible via neural field dynamics. This is an important fi rst step to study the properties of such constructions and to analyze natural or artifi cial realizations of neural field architectures.
BibTeX:
@article{PotthastGraben09c,
  author = {R. Potthast and P. beim Graben},
  title = {Dimensional reduction for the inverse problem of neural field theory},
  journal = {Frontiers in Computational Neuroscience},
  year = {2009},
  volume = {3},
  pages = {17},
  doi = {http://dx.doi.org/10.3389/neuro.10.017.2009}
}
      
Rodrigues, S., beim Graben, P., Lilith, M., Bedard, C. & Destexhe, A. Modelling the coupling of single neuron activity to local field potentials 2009 Proceedings of the 18th Annual Computational Neuroscience Meeting (CNS*2009)  inproceedings  
BibTeX:
@inproceedings{RodriguesGrabenEA09,
  author = {S. Rodrigues and P. beim Graben and M. Lilith and C. Bedard and A. Destexhe},
  title = {Modelling the coupling of single neuron activity to local field potentials},
  booktitle = {Proceedings of the 18th Annual Computational Neuroscience Meeting (CNS*2009)},
  year = {2009}
}
      
BibTeX:
@incollection{SaddyGraben02a,
  author = {D. Saddy and P. beim Graben},
  title = {Measuring the neural dynamics of language comprehension processes},
  booktitle = {Basic Fuctions of Language, Reading and Reading Disorder},
  publisher = {Kluwer Academic Publishers},
  year = {2002},
  pages = {41 -- 60}
}
      
Abstract: Complexity within the language system arises from two a priori distinct sources: the computational complexity inherent in the grammar of the language itself or ?formal linguistic complexity?, and the procedural complexity resulting from marshalling processing resources in order to produce or interpret utterances that correspond to the grammar. Whether or not these two aspects of language can be distinguished is a long debated issue. In this short paper we will outline how the use of symbolic encoding techniques may reveal both markers of procedural processing and markers of formal linguistic content.
BibTeX:
@inproceedings{SaddyGrabenEA04,
  author = {D. Saddy and P. beim Graben and H. Drenhaus and S. Frisch},
  title = {Distinguishing process from content in language processing: a new answer to an old question},
  booktitle = {Proc. 8th Experimental Chaos Conference 2004},
  publisher = {American Institute of Physics},
  year = {2004},
  volume = {742},
  pages = {94 -- 105}
}
      
BibTeX:
@inproceedings{SaddyGrabenSchlesewsky99a,
  author = {J. D. Saddy and P. beim Graben and M. Schlesewsky},
  title = {Cortical dynamics of language processes},
  booktitle = {Proc. European Conference on Cognitive Science (ECCS)},
  publisher = {Multimedia & Communication Laboratory, University Siena},
  year = {1999},
  pages = {323 -- 332}
}
      
BibTeX:
@article{SaddyGrabenSchlesewsky99b,
  author = {J. D. Saddy and P. beim Graben and M. Schlesewsky},
  title = {Measuring entropy during language processing},
  journal = {Journal of Cognitive Neuroscience},
  year = {1999},
  volume = {Supplement},
  pages = {95},
  note = {Abstract}
}
      
Abstract: It has been claimed that connectionist (artificial neural network) models of language processing, which do not appear to employ ‘‘rules’’, are doing something different in kind from classical symbol processing models, which treat ‘‘rules’’ as atoms (e.g., McClelland and Patterson in Trends Cogn Sci 6(11):465–472, 2002). This claim is hard to assess in the absence of careful, formal comparisons between the two approaches. This paper formally investigates the symbol-processing properties of simple dynamical systems called affine dynamical automata, which are close relatives of several recurrent connectionist models of language processing (e.g., Elman in Cogn Sci 14:179–211, 1990). In line with related work (Moore in Theor Comput Sci 201:99–136, 1998; Siegelmann in Neural networks and analog computation: beyond the Turing limit. Birkha¨user, Boston, 1999), the analysis shows that affine dynamical automata exhibit a range of symbol processing behaviors, some of which can be mirrored by various Turing machine devices, and others of which cannot be. On the assumption that the Turing machine framework is a good way to formalize the ‘‘computation’’ part of our understanding of classical symbol processing, this finding supports the view that there is a fundamental ‘‘incompatibility’’ between connectionist and classical models (see Fodor and Pylyshyn 1988; Smolensky in Behav Brain Sci 11(1):1–74, 1988; beim Graben in Mind Matter 2(2) 29–51,2004b). Given the empirical successes of connectionist models, the more general, super-Turing framework is a preferable vantage point from which to consider cognitive phenomena. This vantage may give us insight into ill-formed as well as wellformed language behavior and shed light on important structural properties of learning processes.
BibTeX:
@article{Tabor09,
  author = {W. Tabor},
  title = {A dynamical systems perspective on the relationship between symbolic and non-symbolic computation},
  journal = {Cognitive Neurodynamics},
  year = {2009},
  volume = {3},
  number = {4},
  pages = {415 -- 427},
  doi = {http://dx.doi.org/10.1007/s11571-009-9099-8}
}
      
Troll, G. & beim Graben, P. Zipf's law is not a consequence of the central limit theorem 1998 Physical Reviews E
Vol. 57(2), pp. 1347 - 1355 
article  
Abstract: It has been observed that the rank statistics of string frequencies of many symbolic systems ~e.g., word frequencies of natural languages! follows Zipf's law in good approximation. We show that, contrary to claims in the literature, Zipf's law cannot be realized by the central limit theorem~s!. The observation that a lognormal distribution of string frequencies yields an approximately Zipf-like rank statistics is actually misleading. Indeed, Zipf's law for the rank statistics is strictly equivalent to a power law distribution of frequencies. There are two natural ways to perform the infinite size limit for the vocabulary. The first one is the method of choice in the literature; it makes the upper word length bound tend to infinity and leads in the case of a multistate Bernoulli process via a central limit theorem to a log-normal frequency distribution. An alternative and for text samples actually better realizable way is to make the lower frequency bound tend to zero. This limit procedure leads to a power law distribution and hence to Zipf's law-at least for Bernoulli processes and to a very good approximation for natural languages where it passes the x2 test. For the Bernoulli case we will give a heuristic proof.
BibTeX:
@article{TrollGraben98,
  author = {G. Troll and P. beim Graben},
  title = {Zipf's law is not a consequence of the central limit theorem},
  journal = {Physical Reviews E},
  year = {1998},
  volume = {57},
  number = {2},
  pages = {1347 -- 1355}
}
      
BibTeX:
@proceedings{GrabenSaddyKurths04a,,
  title = {Cognition and Complex Brain Dynamics},
  publisher = {World Scientific},
  year = {2004},
  volume = {14},
  number = {2},
  note = {Special Theme Issue}
}
      

Lectures in Supercomputational Neuroscience: Dynamics in Complex Brain Networks 2008   book  
BibTeX:
@book{GrabenEA08a,,
  title = {Lectures in Supercomputational Neuroscience: Dynamics in Complex Brain Networks},
  publisher = {Springer},
  year = {2008}
}
      

Created by JabRef on 16/03/2010.