  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.
