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A Statistical Learning Method for Logic Programs with Distribution Semantics

When a joint distribution P F is given to a set F of facts in a logic program DB = F [R where R is a set of rules, we can further extend it to a joint distribution P DB over the set of possible least models of DB. We then de ne the semantics of DB with the associated distribution P F as P DB , and call it distribution semantics. While the distribution semantics is a straightforward generalization of the traditional least model semantics, it can capture semantics of diverse information processing systems ranging from Bayesian networks to Hidden Markov models to Boltzmann machines in a single framework with mathematical rigor. Thus symbolic computation and statistical modeling are integrated at semantic level. With this new semantics, we propose a statistical learning schema based on the EM algorithm known in statistics. It enables logic programs to learn from examples, and to adapt to the surrounding environment. We implement the schema for a subclass of logic programs called BS-programs.