ANYTIME DEDUCTION FOR PROBABILISTIC LOGIC

This paper proposes and investigates an approach to deduction in proba bilistic logic, using as its medium a language that generalizes the pr opositional version of Nilsson's probabilistic logic by incorporating conditional probabilities. Unlike many other approaches to deduction i n probabilistic logic, this approach is based on inference rules and t herefore can produce proofs to explain how conclusions are drawn. We s how how these rules can be incorporated into an anytime deduction proc edure that proceeds by computing increasingly narrow probability inter vals that contain the tightest entailed probability interval. Since th e procedure can be stopped at any time to yield partial information co ncerning the probability range of any entailed sentence, one can make a tradeoff between precision and computation time. The deduction metho d presented here contrasts with other methods whose ability to perform logical reasoning is either limited or requires finding all truth ass ignments consistent with the given sentences.