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Cognitive Morphodynamics

Dynamical Morphological Models of Constituency in Perception and Syntax

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Jean Petitot

This book – written in collaboration with René Doursat, director of the Complex Systems Institute, Paris – adds a new dimension to Cognitive Grammars. It provides a rigorous, operational mathematical foundation, which draws from topology, geometry and dynamical systems to model iconic «image-schemas» and «conceptual archetypes». It defends the thesis that René Thom’s morphodynamics is especially well suited to the task and allows to transform the morphological structures of perception into Gestalt-like, abstract, proto-linguistic schemas that can act as inputs into higher-level specific linguistic routines.
Cognitive Grammars have drawn upon the view that the deep syntactic and semantic structures of language, such as prepositions and case roles, are grounded in perception and action. This study raises difficult problems, which thus far have not been addressed as a mathematical challenge. Cognitive Morphodynamics shows how this gap can be filled.

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Chapter 4. Processes: What is an “Attractor Syntax”? 171

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CHAPTER 4 Processes: What is an “Attractor Syntax”? 1. Introduction Developing dynamical models of cognitive processes raises fundamental issues, some of which have been addressed by connectionist models implementing dy- namical systems. One of the most difficult questions is whether dynamical models implemented in connectionist networks have the capacity for adequately supporting syntactic constituency and constituent-structure, which are tradi- tionally expressed in a symbolic way. We have already shown that, for percep- tion, mereological dynamical models exist and can be used in a morphological approach to spatial relations. But in what concerns syntax, and especially ac- tantial syntax1, the difficulty is to model grammatical relations, semantic roles, constituency and compositionality in a purely dynamical fashion. In a nutshell, it can be formulated in the following manner: if terms of sentences are modeled by attractors of some underlying dynamics, what is the dynamical status of a “syntax” relating these attractors? What could be an attractor syntax? 2. Dynamical models of syntax In the late 1980’s and early 1990’s, following the 1988 debate that opposed Jerry Fodor and Zenon Pylyshyn [113] to Paul Smolensky [355] (see also Smolensky et al. [359] and Fodor, McLaughlin [111]), a great number of works have been devoted to this question. In 1991 and 1992 two conferences on the Composi- tionality in Cognition and Neural Networks organized by Daniel Andler, Elie Bienenstock and Bernard Laks (COMPCOG I [64] and COMPCOG II [65]) were held in Royaumont, France. Bernard Victorri and Catherine Fuchs orga- nized in...

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