Towards a Systematic Account of Different Semantics for Logic Programs

TL;DR

This paper explores the relationships between various semantics for logic programs with negation, aiming to unify and clarify their connections through a systematic and coherent framework.

Contribution

It provides a unified, systematic account of different declarative semantics for logic programs, clarifying their interrelations and addressing asymmetries in existing characterizations.

Findings

Well-founded semantics as a stratified Fitting semantics

Unified characterization of multiple semantics

Clarification of asymmetries in existing constructions

Abstract

In [Hitzler and Wendt 2002, 2005], a new methodology has been proposed which allows to derive uniform characterizations of different declarative semantics for logic programs with negation. One result from this work is that the well-founded semantics can formally be understood as a stratified version of the Fitting (or Kripke-Kleene) semantics. The constructions leading to this result, however, show a certain asymmetry which is not readily understood. We will study this situation here with the result that we will obtain a coherent picture of relations between different semantics for normal logic programs.