Forgetting in Answer Set Programming -- A Survey

TL;DR

This survey comprehensively reviews various approaches to forgetting in Answer Set Programming, analyzing properties, operators, and their relations to guide users in selecting suitable methods.

Contribution

It provides the first complete overview of forgetting operators in ASP, including new insights on properties, relations, and computational complexity.

Findings

Many novel relations between properties and operators

Analysis of concrete operators and their computational complexity

Guidance for selecting appropriate forgetting operators

Abstract

Forgetting - or variable elimination - is an operation that allows the removal, from a knowledge base, of middle variables no longer deemed relevant. In recent years, many different approaches for forgetting in Answer Set Programming have been proposed, in the form of specific operators, or classes of such operators, commonly following different principles and obeying different properties. Each such approach was developed to address some particular view on forgetting, aimed at obeying a specific set of properties deemed desirable in such view, but a comprehensive and uniform overview of all the existing operators and properties is missing. In this paper, we thoroughly examine existing properties and (classes of) operators for forgetting in Answer Set Programming, drawing a complete picture of the landscape of these classes of forgetting operators, which includes many novel results on relations between properties and operators, including considerations on concrete operators to compute results of forgetting and computational complexity. Our goal is to provide guidance to help users in choosing the operator most adequate for their application requirements.