AUTOEPISTEMIC LOGICS AS A UNIFYING FRAMEWORK FOR THE SEMANTICS OF LOGIC PROGRAMS

In this paper, it is shown that a three-valued autoepistemic logic pro vides an elegant unifying framework for some of the major semantics of normal and disjunctive logic programs and logic programs with classic al negation, namely, the stable semantics, the well-founded semantics, supported models, Fitting's semantics, Kunen's semantics, the station ary semantics, and answer sets. For the first time, so many semantics are embedded into one logic. The framework extends previous results-by Gelfond, Lifschitz, Marek, Subrahmanian, and Truszczynski-on the rela tionships between logic programming and Moore's autoepistemic logic. T he framework suggests several new semantics for negation-as-failure. I n particular, we will introduce the epistemic semantics for disjunctiv e logic programs. In order to motivate the epistemic semantics, an int eresting class of applications called ignorance tests will be formaliz ed; it will be proved that ignorance tests can be defined by means of the epistemic semantics, but not by means of the old semantics for dis junctive programs. The autoepistemic framework provides a formal found ation for an environment that integrates different forms of negation. The role of classical negation and various forms of negation-by-failur e in logic programming will be briefly discussed.