Stochastic Process Semantics for Dynamical Grammar Syntax: An Overview

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We define a class of probabilistic models in terms of an operator algebra of stochastic processes, and a representation for this class in terms of stochastic parameterized grammars. A syntactic specification of a grammar is mapped to semantics given in terms of a ring of operators, so that grammatical composition corresponds to operator addition or multiplication. The operators are generators for the time-evolution of stochastic processes. Within this modeling framework one can express data clustering models, logic programs, ordinary and stochastic differential equations, graph grammars, and stochastic chemical reaction kinetics. This mathematical formulation connects these apparently distant fields to one another and to mathematical methods from quantum field theory and operator algebra.
Accepted for: Ninth International Symposium on Artificial Intelligence and Mathematics, January 2006

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Artificial Intelligence, Logic in Computer Science, Adaptation and Self-Organizing Systems, D.3.1

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http://salesiana.dossiersoluciones.com/handle/123456789/104416

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/cs/0511073
 http://arxiv.org/abs/cs/0511073

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arXiv