An Approach to Forgetting in Disjunctive Logic Programs that Preserves Strong Equivalence

TL;DR

This paper presents a syntax-independent method for forgetting atoms in disjunctive logic programs that preserves strong equivalence, with practical and theoretical foundations, and includes a prototype implementation.

Contribution

It introduces a novel approach to atom forgetting in disjunctive logic programs that maintains strong equivalence and provides both theoretical and practical frameworks.

Findings

The approach preserves strong equivalence after forgetting.

The practical definition involves rules not mentioning the atom and inference steps.

Prototype implementation demonstrates feasibility.

Abstract

In this paper we investigate forgetting in disjunctive logic programs, where forgetting an atom from a program amounts to a reduction in the signature of that program. The goal is to provide an approach that is syntax-independent, in that if two programs are strongly equivalent, then the results of forgetting an atom in each program should also be strongly equivalent. Our central definition of forgetting is impractical but satisfies this goal: Forgetting an atom is characterised by the set of SE consequences of the program that do not mention the atom to be forgotten. We then provide an equivalent, practical definition, wherein forgetting an atom $p$ is given by those rules in the program that don't mention $p$, together with rules obtained by a single inference step from rules that do mention $p$. Forgetting is shown to have appropriate properties; as well, the finite characterisation results in a modest (at worst quadratic) blowup. Finally we have also obtained a prototype implementation of this approach to forgetting.