A logical study of partial entailment

Authors:
Yi Zhou;Yan Zhang
Affiliations:
Intelligent Systems Laboratory, School of Computing and Mathematics, University of Western Sydney, NSW, Australia;Intelligent Systems Laboratory, School of Computing and Mathematics, University of Western Sydney, NSW, Australia
Venue:
Journal of Artificial Intelligence Research
Year:
2011

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Abstract

We introduce a novel logical notion-partial entailment-to propositional logic. In contrast with classical entailment, that a formula P partially entails another formula Q with respect to a background formula set Γ intuitively means that under the circumstance of Γ, if P is true then some "part" of Q will also be true. We distinguish three different kinds of partial entailments and formalize them by using an extended notion of prime implicant. We study their semantic properties, which show that, surprisingly, partial entailments fail for many simple inference rules. Then, we study the related computational properties, which indicate that partial entailments are relatively difficult to be computed. Finally, we consider a potential application of partial entailments in reasoning about rational agents.