A uniform approach to logic programming semantics

TL;DR

This paper introduces a unified method using level mappings to characterize various logic programming semantics, clarifying their relationships and providing new insights into well-known semantics.

Contribution

The paper presents a novel, uniform approach based on level mappings to characterize multiple logic programming semantics, including new characterizations of some major semantics.

Findings

Unified characterization of least model semantics for definite programs

New uniform descriptions of Fitting and well-founded semantics

A novel characterization of the weakly perfect model semantics

Abstract

Part of the theory of logic programming and nonmonotonic reasoning concerns the study of fixed-point semantics for these paradigms. Several different semantics have been proposed during the last two decades, and some have been more successful and acknowledged than others. The rationales behind those various semantics have been manifold, depending on one's point of view, which may be that of a programmer or inspired by commonsense reasoning, and consequently the constructions which lead to these semantics are technically very diverse, and the exact relationships between them have not yet been fully understood. In this paper, we present a conceptually new method, based on level mappings, which allows to provide uniform characterizations of different semantics for logic programs. We will display our approach by giving new and uniform characterizations of some of the major semantics, more particular of the least model semantics for definite programs, of the Fitting semantics, and of the well-founded semantics. A novel characterization of the weakly perfect model semantics will also be provided.