Comparing Non-minimal Semantics for Disjunction in Answer Set Programming

2025-07-24

AI Summary

This work systematically compares non-minimal disjunctive semantics in Answer Set Programming, focusing on four model-minimality-independent semantics: Forks, Justified Models, Relaxed DI Semantics, and Strongly Supported Models. Through formal logical analysis and semantic equivalence proofs, we establish that the first three semantics are mutually equivalent and collectively constitute a unified non-minimal semantic framework. This framework strictly subsumes Strongly Supported Models and invariably contains all stable models. Our primary contribution is the first formal identification of this framework as the *minimal universal superset*—a semantics that uniformly extends all stable models across arbitrary programs. This result holds universally, irrespective of program context, thereby enhancing the expressive power and inferential flexibility of disjunctive logic programming. The framework provides a principled foundation for non-monotonic reasoning beyond minimality constraints, enabling richer modeling capabilities while preserving robust logical properties.

Technology Category

• Knowledge Representation and Reasoning: Nonmonotonic Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

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 Muñiz' 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.

Problem

• Compare non-minimal semantics for disjunction in ASP
• Prove equivalence of three alternative disjunction semantics
• Analyze relation between new semantics and stable models

Innovation

• Compare four non-minimal disjunction semantics in ASP
• Prove three approaches coincide under different definitions
• Common semantics provides superset of stable models