On Signings and the Well-Founded Semantics

Abstract: In this note, we use Kunen's notion of a signing to establish two theorems about the well-founded semantics of logic programs, in the case where we are interested in only (say) the positive literals of a predicate $p$ that are consequences of the program. The first theorem identifies a class of programs for which the well-founded and Fitting semantics coincide for the positive part of $p$. The second theorem shows that if a program has a signing then computing the positive part of $p$ under the well-founded semantics requires the computation of only one part of each predicate. This theorem suggests an analysis for query-answering under the well-founded semantics. In the process of proving these results, we use an alternative formulation of the well-founded semantics of logic programs, which might be of independent interest. Under consideration in Theory and Practice of Logic Programming (TPLP)