Mathematical Model of Embodied Symbols: Cognition and Perceptual Symbol System

Abstract

A mathematical model of perceptual symbol system is developed. This development requires new mathematical methods of dynamic logic (DL), which have overcome limitations of classical artificial intelligence and connectionist approaches. The paper discusses these past limitations, relates them to combinatorial complexity (exponential explosion) of algorithms in the past, and relates it further to the static nature of classical logic. DL is a process-logic; its salient property is evolution of vague representations into crisp. We first consider one aspect of PSS: situation learning from object perceptions. Next DL is related to PSS mechanisms of concepts, simulators, grounding, embodiment, productive-ity, binding, recursion, and to the mechanisms relating embodied-grounded and amodal symbols. We discuss DL capability for modeling cognition on multiple levels of abstraction. PSS is extended toward interaction between cognition and language. Experimental predictions of the theory are discussed. They might influence experimental psychology and impact future theoretical developments in cognitive science, including knowledge representation, and mechanisms of interaction between perception, cognition, and language. All mathematical equations are also discussed conceptually, so mathematical understanding is not required. Experimental evidence for DL and PSS in brain imaging is discussed as well as future research directions.