On Signings and the Well-Founded Semantics

TL;DR

This paper explores the well-founded semantics of logic programs using Kunen's notion of signing, providing new theorems that simplify computation and identify classes where semantics coincide, with implications for query-answering.

Contribution

It introduces theorems relating signings to the well-founded semantics, simplifying positive literal computation and identifying classes with coinciding semantics.

Findings

Identifies classes where well-founded and Fitting semantics coincide

Shows that signings enable computation of only one part of each predicate

Provides an alternative formulation of 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)