The Design and Testing of a First-order Logic-based Stochastic Modeling Language

We have created a logic-based Turing-complete language for stochastic modeling. Since 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 Networks have limited expressive power, basically constrained to finite domains as in the propositional calculus. This language contains variables that can capture general classes of situations, events, and relationships. A first-order language is able to reason about potentially infinite classes and situations such as hidden Markov models(HMMs). The language uses an Expectation-Maximization (EM) type learning of parameters. This has a natural fit with the Loopy Belief Propagation used for inference since both can be viewed as iterative message passing algorithms. We present the syntax and theoretical foundations for our Loopy Logic language. We then demonstrate three examples of stochastic modeling and diagnosis that explore the representational power of the language. A mechanical fault detection example displays how Loopy Logic can model time-series processes using an HMM variant. A digital circuit example exhibits the probabilistic modeling capabilities, and finally, a parameter fitting example demonstrates the power for learning of unknown stochastic values.