Products of Weighted Logic Programs

Abstract. Weighted logic programming, a generalization of bottom-up logic programming, is a successful framework for specifying dynamic programming algorithms. In this setting, proofs correspond to the algorithm's output space, such as a path through a graph or a grammatical derivation, and are given a weighted score, often interpreted as a probability, that depends on the score of the base axioms used in the proof. The desired output is a function over all possible proofs, such as a sum of scores or an optimal score. We describe the PRODUCT transformation, which can merge two weighted logic programs into a new one. The resulting program optimizes a product of proof scores from the original programs, constituting a scoring function known in machine learning as a "product of experts." Through the addition of intuitive constraining side conditions, we show that several important dynamic programming algorithms can be derived by applying PRODUCT to weighted logic programs co...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Shay B. Cohen, Robert J. Simmons, Noah A. Smith
• Keywords: CORR 2010, Dynamic Programming Algorithms, Education, Logic Programming, Weighted Logic