J. Chen Computer Science Department, Louisiana State University, Baton Rouge, LA 70803, USA. E-mail: firstname.lastname@example.org
GOL, the generalized logic of only knowing is defined and its use proposed as a unified framework for non-monotonic reasoning. The GOL logic is a generalization of logic of Levesque's only knowing (OL) and it covers Gelfond's important notion of epistemic specification (ES), which is very useful for knowledge representation. By giving a model-theoretic account of epistemic specification, the GOL helps clarify the conceptual understanding of epistemic theories. The GOL logic contains the OL logic as a subset and thus it retains the important features of OL. The OL logic is a modal logic which can be used to formalize an agent's introspective reasoning and to answer epistemic queries to databases. The relations between OL logic and MBNF (the logic of minimal belief and negation as failure by Lifschitz), and between OL and extended logic programs have recently been established and it has been shown that OL is a fairly general logical framework for non-monotonic reasoning. In this paper, the OL logic is further generalized to enhance the expressive power to include epistemic specifications. A sound proof theory for GOL is also presented. This work is restricted to the propositional case only.
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