Towards a unified theory of logic programming semantics: Level mapping characterizations of selector generated models

TL;DR

This paper explores the relationship between two semantic characterization methods for logic programming with negation, demonstrating that selector generated models can be represented within the level mapping framework, unifying diverse semantics.

Contribution

It shows that selector generated models are captured by level mapping characterizations, advancing a unified theoretical framework for logic programming semantics.

Findings

Selector generated models are encompassed by level mapping characterizations.

Level mappings are a flexible framework for diverse semantics.

The study bridges different approaches to logic program semantics.

Abstract

Currently, the variety of expressive extensions and different semantics created for logic programs with negation is diverse and heterogeneous, and there is a lack of comprehensive comparative studies which map out the multitude of perspectives in a uniform way. Most recently, however, new methodologies have been proposed which allow one to derive uniform characterizations of different declarative semantics for logic programs with negation. In this paper, we study the relationship between two of these approaches, namely the level mapping characterizations due to [Hitzler and Wendt 2005], and the selector generated models due to [Schwarz 2004]. We will show that the latter can be captured by means of the former, thereby supporting the claim that level mappings provide a very flexible framework which is applicable to very diversely defined semantics.