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A Propositional Logic That Handles Conditional Probabilities

by C.Pulley. Unpublished

Abstract

In [FagHalMeg90], two logics for reasoning about probabilities were introduced. The first was unable to reason about conditional probabilities. To rectify this [FagHalMeg90] introduce their second probabilistic logic. However, unlike their first, they find it necessary to introduce quantifiers. In this paper we rectify this defect by presenting a propositional logic that can reason about conditional probabilities. Our method of proof is such that we may generalize it to encapsulate soundness and completeness for numerous other logics (eg. the first probabilistic logic of [FagHalMeg90]; fuzzy logic etc.). Our main requirement for these generalizations is that our logics should have a first-order metatheory.

References:

  • [FagHalMeg90]: Fagin, R., Halpern, J.Y., and Megiddo, N. (1990), A Logic for Reasoning about Probabilities, Information and Control Vol. 87 pp.78-128.

Full paper: [PDF]