Strong Introspection

Michael Gelfond

The purpose of this paper is to expand the syntax and semantics of logic programs and deductive databases to allow for the correct representation of incomplete information in the presence of multiple extensions. The language of logic programs with classical negation, epistemic disjunction, and negation by failure is further expanded by a new modal operator K (where for the set of rules T and formula F, KF stands for "F is known to a reasoner with a set of premises T"). Theories containing such an operator will be called strongly introspective. We will define the semantics of such theories (which expands the semantics of deductive databases from [Gelfond and Lifschitz 199Ob]) and demonstrate the applicability of strongly introspective theories to formalization of some forms of commonsense reasoning.

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