A sound and complete proof theory for the generalized logic of only knowing
We present a sound and complete proof theory for the generalized logic of only knowing (GOL). The GOL logic is a modal logic proposed recently (Chen 1997) as a unified logical framework for non-monotonic reasoning, which extends the logic of only knowing (OL) of Levesque (1990), and covers the important notion of epistemic specification (Gelfond 1991, Gelfond and Przymusinska 1993) which is very useful for knowledge representation. The OL logic has been shown to have close connections with Lifschitz's minimal belief and negation as failure (Lifschitz 1994) and various other major non-monotonic formalisms. The GOL logic is more general and powerful than OL. The completeness result for the GOL proof theory establishes the theoretical foundation for answering queries in epistemic theories. This work is restricted to the propositional case only.
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Document Type: Research Article
Publication date: 01 October 1998