We describe a mathematical models of grounded symbols in the brain. It also serves as a computational foundations for Perceptual Symbol System (PSS). 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 further to the static nature of classical logic. The new mathematical theory, DL, is a process-logic. A salient property of this process is evolution of vague representations into crisp. The paper first applies it to one aspect of PSS: situation learning from object perceptions. Then we relate DL to the essential PSS mechanisms of concepts, simulators, grounding, productivity, binding, recursion, and to the mechanisms relating grounded and amodal symbols. We discuss DL as a general theory describing the process of cognition on multiple levels of abstraction. We also discuss the implications of this theory for interactions between cognition and language, mechanisms of language grounding, and possible role of language in grounding abstract cognition. The developed theory makes experimental predictions, and will impact future theoretical developments in cognitive science, including knowledge representation, and perception-cognition interaction. Experimental neuroimaging evidence for DL and PSS in brain imaging is discussed as well as future research directions.
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