Comparing Non-minimal Semantics for Disjunction in Answer Set Programming

TL;DR

This paper compares four non-minimal semantics for disjunction in Answer Set Programming, revealing their relationships and showing that three of them coincide, always extending stable models and differing from the classical logic approach.

Contribution

It provides a comprehensive comparison and unification of four non-minimal disjunction semantics, clarifying their relationships and properties.

Findings

Three semantics coincide, forming a unified approach.

The common semantics always extends stable models.

One semantics aligns with classical logic disjunction.

Abstract

In this paper, we compare four different semantics for disjunction in Answer Set Programming that, unlike stable models, do not adhere to the principle of model minimality. Two of these approaches, Cabalar and Mu\~niz' \emph{Justified Models} and Doherty and Szalas' \emph{Strongly Supported Models}, directly provide an alternative non-minimal semantics for disjunction. The other two, Aguado et al's \emph{Forks} and Shen and Eiter's \emph{Determining Inference} (DI) semantics, actually introduce a new disjunction connective, but are compared here as if they constituted new semantics for the standard disjunction operator. We are able to prove that three of these approaches (Forks, Justified Models and a reasonable relaxation of the DI semantics) actually coincide, constituting a common single approach under different definitions. Moreover, this common semantics always provides a superset of the stable models of a program (in fact, modulo any context) and is strictly stronger than the fourth approach (Strongly Supported Models), that actually treats disjunctions as in classical logic.