Symbolic dynamics and representations

Symbolic dynamics and representations

The object of study of symbolic dynamics are discrete dynamical systems made of infinite sequences of symbols, with the shift acting on them. They come as codings of trajectories of points in a dynamical system according to a given partition. They are used as discretization tools for analyzing such trajectories, but they also occur in a natural way in arithmetics for instance. We first will rec...

Symbolic , Conceptual and Subconceptual Representations

Cognitive science aims at understanding how information is represented and processed in different kinds of agents, biological as well as artificial. The research has two overarching goals. One is explanatory: By studying the cognitive activities of humans and other animals, one formulates theories of different kinds of cognition. The theories are tested either by experiments or by computer simu...

Symbolic Distributed Representations

Complex Dynamics and Symbolic Dynamics

Robert L. Devaney, Boston University Synopsis As so often happens in mathematics, there is a surprising connection between two quite distinct subfields of dynamical systems theory, namely the structure of the automorphism group of the one sided shift map on d-symbols and the topology of the analogue of the Mandelbrot set for degree d polynomials of one complex variable. In this lecture we will ...

A Framework for Integrating Symbolic and Sub-Symbolic Representations

This paper establishes a framework that hierarchically integrates symbolic and sub-symbolic representations in an architecture for cognitive robotics. It is formalised abstractly as nodes in a hierarchy, with each node a sub-task that maintains its own belief-state and generates behaviour. An instantiation is developed for a real robot building towers of blocks, subject to human interference; t...