Connectionists: Preprint: Stochastic Process Semantics for Dynamical Grammar Syntax

[Eric Mjolsness]

A preprint is available:

Title: "Stochastic Process Semantics for Dynamical Grammar Syntax: An Overview"
Venue: 9th International Symposium on Artificial Intelligence and 
Mathematics, Jan. 2006.
Author: Mjolsness, E.
URL: http://arxiv.org/abs/cs.AI/0511073
     ...  which is a summary of the longer UCI Technical Report 05-14,
     "Stochastic Process Semantics for Dynamical Grammar Syntax",
     http://computableplant.ics.uci.edu/papers/StochProcSemanticsTR.pdf

Abstract: 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.

-- 
Eric Mjolsness
Institute for Genomics and Bioinformatics, and
Departments of Computer Science and Mathematics
University of California, Irvine
emj at uci.edu
www.ics.uci.edu/~emj