The logic of only knowing as a unified framework for non-monotonic reasoning

Abstract

We propose to use the logic of only knowing (OL) by Levesque [6] as a unified framework that encompasses various non-monotonic formalisms and logic programming. OL is a modal logic which can be used to formalize an agent's introspective reasoning and to answer epistemic queries to databases. The OL logic allows one to formally express the statement “α is all I know” (in symbols, Oα) and to perform inferencing based on only-knowing, which is very useful for commonsense reasoning. Another nice thing about the OL logic is that it has a clear model-theoretic semantics and a simple proof theory, which is sound for the quantificational case, and both sound and complete for the prepositional case.

We establish the relations between OL and various non-monotonic logics (such as default logic, circumscription) and logic programming, thus extending the existing works relating the OL logic with other non-monotonic reasoning formalisms (e.g., Levesque showed [6] that autoepistemic logic can be embeded in OL). This is accomplished by finding the connection between OL and MBNF, the logic of Minimal Belief and Negation as Failure proposed by Lifschitz [8, 9], which is known to have close relationship with logic programming and other non-monotonic logics. Our results show that OL can be used as a unified framework to compare different non-monotonic formalisms based on the same domain.