Chayan Chakrabarti, Roshan Rammohan, and George F. Luger, University of New Mexico,
We have created a logic-based, first-order, and Turing complete set of software tools for stochastic modeling. Because the inference scheme for this language is based on a variant of Pearl’s loopy belief propagation algorithm, we call it Loopy Logic. Traditional Bayesian belief networks have limited expressive power, basically constrained to that of atomic elements as in the propositional calculus. Our language contains variables that can capture general classes of situations, events, and relationships. A Turing-complete language is able to reason about potentially infinite classes and situations, with a Dynamic Bayesian Network. Since the inference algorithm for Loopy Logic is based on a variant of loopy belief propagation, the language includes an Expectation Maximization-type learning of parameters in the modeling domain. In this paper we briefly present the theoretical foundations for our loopy-logic language and then demonstrate several examples of stochastic modeling and diagnosis.