Statistical Abduction with Tabulation

We propose statistical abduction as a first-order logical framework for representing, inferring and learning probabilistic knowledge. It semantically integrates logical abduction with a parameterized distribution over abducibles. We show that statistical abduction combined with tabulated search provides an efficient algorithm for probability computation, a Viterbi-like algorithm for finding the most likely explanation, and an EM learning algorithm (the graphical EM algorithm) for learning parameters associated with the distribution which achieve the same computational complexity as those specialized algorithms for HMMs (hidden Markov models), PCFGs (probabilistic context-free grammars) and sc-BNs (singly connected Bayesian networks).

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