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, productiveity, 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.
Highlights
Barsalou [1] developed Perceptual symbol system (PSS) that embodies cognition and grounds it in perception
“Simulation is the reenactment of perceptual, motor, and introspective states acquired during experience with the world, body, and mind... when knowledge is needed to represent a category, multimodal representations captured during experiences... are reactivated to simulate how the brain represented perception, action, and introspection associated with it”
We suggest that directly observable relations are learned as parts of a situation, similar to objects, and this learning is modeled by the dynamic logic (DL) formalism described above
Summary
Barsalou [1] developed Perceptual symbol system (PSS) that embodies cognition and grounds it in perception. Based on the mechanism of simulators, which approximately correspond to concepts and types in amodal theories, PSS implements the standard symbolic functions of type-token binding, inference, productivity, recursion, and propositions. This article develops a realistic and scalable mathematical model of grounded symbols and formalization of PSS based on a new computational technique of dynamic logic, DL [15,16]. We first concentrate on one example of PSS mechanism: a mathematical description of models and simulators for forming and enacting representations of situations (higher level symbols) from perceptions of objects (lower level symbols), and we discuss its general applicability.
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