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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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List of abbreviations 305

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List of abbreviations nD n-dimensional AC apparent contour BCS boundary contour system CG cognitive grammar CL classic CL cut locus CLC classical cognitivism CN connectionism CNC connectionist cognitivism CR cognitive representation CS conceptual structure CT cognitive topology DO direct object ES expanse scanning FCS featural contour system F-P (argument) Fodor-Pylyshyn FS field scanning GC ganglion cell LH localist hypothesis LM landmark MM mathematical morphology MT mathematical topology NP noun phrase OO oblique object PDE partial differential equation PhW phenomenal world PrW projected world PS periphery scanning PTC proper treatement of connectio- nism R field of real numbers RAM random access memory RF receptive field RH relational hierarchy RP receptive profile RW real world SKIZ skeleton by influence zones TR trajector WFT window Fourier transform WT wavelet transform European Semiotics: Language, Cognition, and Culture Sémiotiques Européennes: langage, cognition et culture Edited by / Série dirigée par Per Aage Brandt (Cleveland), Wolfgang Wildgen (Bremen/Brême), and/et Barend van Heusden (Groningen/Groningue) European Semiotics originated from an initiative launched by a group of researchers in Semiotics from Denmark, Germany, Spain, France and Italy and was inspired by innovative impulses given by René Thom and his “semiophysics”. The goal of the series is to provide a broad European forum for those interested in semiotic research focusing on semiotic dynamics and combining cultural, linguistic and cognitive perspectives. This approach, which has its origins in Phenomenology, Gestalt Theory, Philosophy of Culture and Structuralism, views semiosis primarily as a cognitive process,...

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