The generalized logic of only knowing (GOL) that covers the notion of epistemic specifications

Abstract

We define GOL, the generalized logic of only knowing, and propose to use it as a unified framework for non-monotonic reasoning. The GOL logic is a generalization of the logic of only knowing (OL) by Levesque [8], and it covers the important notion of epistemic specification by Gelfond [3, 5] which is very useful in knowledge representation. By giving a model-theoretic account for epistemic specifications, the GOL helps clarify the conceptual understanding for 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. In recent works [1–2], we established the relations between OL logic and MBNF (the logic of minimal belief and negation as failure by Lifschitz