On Positive Occurrences of Negation as Failure

Logic programs with positive occurrences of negation as failure have recently been introduced as a subset of the logic of minimal belief and negation as failure (MBNF). A unique feature of such programs, which other traditional logic programs lack, is that the minimality of answer sets does not hold. We reveal in this paper that this property is important for applying logic programming to represent abduction and inclusive disjunctions. With its rich expressiveness, however, the computational complexity of such extended programs is shown to remain in the same complexity class as normal disjunctive programs. Through the elimination of negation as failure from programs, computation of such extended programs is realized using bottom-up model generation techniques. A simple translation of programs into autoepistemic logic is also presented.