Stochastic Process Semantics for Dynamical Grammar Syntax: An Overview

W e define a class of probabilistic models in terms of an operat or algebra of stochastic processes, and a representation for this class in terms of stochastic param eterized grammars. A syntactic specification of a grammar is mapped to semantics given in terms of a rin g of operators, so that grammatical composition corresponds to operator addition or multiplic ation. The operators are generators for the time-evolution of stochastic processes. Within this mo deling framework one can express data clustering models, logic programs, ordinary and stochasti c differential equations, graph grammars, and stochastic chemical reaction kinetics. This mathemati cal formulation connects these apparently distant fields to one another and to mathematical methods fro m quantum field theory and operator algebra.