Well-Founded Completions of Logic Programs

Abstract goes here. 1 Introduction Let us recall that a logic program is a set of clauses of the form A / B 1 : : : Bm ¸C 1 : : : ¸C n where m; n 0 and A, B i and C i 's are atoms. However, the negation symbol ¸C does not denote the classical negation of C but rather the so called negation as failure, whose informal meaning is roughly "negation of C can be assumed by default". The problem of explaining the precise meaning of negation as failure, i.e., of formalizing negation as failure, was the major stumbling block in solving the problem of semantics for logic programs. The first mathematically precise formalization of negation as failure has been given by Clark who defined the so called Predicate Completion comp(P ) of a program P [Cla78, Llo84] (see also [Fit85, Kun87, Kun88]) thus providing an elegant and precise semantics for many logic programs. While Clark's semantics undoubtedly played an important role in the theoretical development of logic programming, it has been..