Logic programming and reasoning with incomplete information

The purpose of this paper is to expand the syntax and semantics of logic programs and disjunctive 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 new modal operators K and M (where for the set of rulesT and formulaF, KF stands for F is known to be true by a reasoner with a set of premisesT and MF means F may be believed to be true by the same reasoner). Sets of rules in the extended language will be called epistemic specifications. We will define the semantics of epistemic specifications (which expands the semantics of disjunctive databases from) and demonstrate their applicability to formalization of various forms of commonsense reasoning. In particular, we suggest a new formalization of the closed world assumption which seems to better correspond to the assumption's intuitive meaning.