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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 6. Attractor Syntax and Perceptual Constituency 259

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CHAPTER 6 Attractor Syntax and Perceptual Constituency 1. “From pixels to predicates”: the seven pillars of cognition In this last chapter we want to unify singularity theory with attractor syntax and draw a link between three things: (i) the perceptual morphological models developed in Chapter 3; (ii) the attractor syntax in the sense of Chapters 4 and 5; (iii) the concept of actantiality in structural syntax, case grammars, and cognitive grammars. The problem is the following. If we want to complete the research program eloquently qualified by Pentland [255] by the slogan “From pixels to predi- cates”, we have to articulate at least seven different levels of representation. Moving up from perception to language we meet (at least) four levels: P1. perception first provides static visual scenes (3D-models: objects with relations); P2. time provides a temporal evolution of these configurations; P3. their schematization provides image-schemata; P4. their further categorization (in the sense of a morphological “algebraic topology”) provides actantial graphs. Moving down from language to perception, we meet (at least) three levels: L1. linguistic surface structures; L2. deep formal predicative structures; L3. AI symbolic structures such as frames or scripts. We will first show how it is possible to define an equivalence—a reciprocal coding, a translation, a reformatting, a representational redescription “iconic↔ symbolic”—between P4 and L3.1 We will then address the other question of this chapter, namely the nature of the link between P3 and P4, i.e., between image-schemata and attractor syntax. 2. Apparent...

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