
Summary: We propose to use the logic of only knowing (OL) by Levesque 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 ``\(\alpha\) is all I know'' (in symbols, \(O \alpha)\) and to perform inferencing based on only-knowing, which is very useful for common-sense 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 propositional case. We establish the relations between OL and various nonmonotonic logics (such as default logic, circumscription) and logic programming, thus extending the existing works relating the OL logic with other nonmonotonic reasoning formalisms (e.g., Levesque showed that autoepistemic logic can be embedded 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, which is known to have close relationship with logic programming and other nonmonotonic logics. Our results show that OL can be used as a unified framework to compare different non-monotonic formalism based on the same domain.
Logic in artificial intelligence, only knowing, negation as failure, Logic programming, minimal belief
Logic in artificial intelligence, only knowing, negation as failure, Logic programming, minimal belief
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