Syntactic Conditions for Antichain Property in Consistency Restoring Prolog

TL;DR

This paper identifies syntactic conditions, specifically acyclicity and dependency constraints, that ensure CR-Prolog programs have the antichain property, meaning no answer set is a proper subset of another.

Contribution

It introduces specific syntactic criteria that guarantee the antichain property in CR-Prolog programs, advancing understanding of their answer set structure.

Findings

Dependency graph acyclicity guarantees antichain property.

No directed path between cr-rule head literals ensures antichain property.

Provides syntactic guidelines for designing CR-Prolog programs with desired properties.

Abstract

We study syntactic conditions which guarantee when a CR-Prolog (Consistency Restoring Prolog) program has antichain property: no answer set is a proper subset of another. A notable such condition is that the program's dependency graph being acyclic and having no directed path from one cr-rule head literal to another.