When You Must Forget: beyond strong persistence when forgetting in answer set programming

TL;DR

This paper explores alternative methods for forgetting in Answer Set Programming when the ideal strong persistence property cannot be maintained, analyzing their theoretical foundations, practical implications, and computational complexity.

Contribution

It introduces three natural alternative approaches to forgetting in ASP that relax strong persistence, addressing an open problem and analyzing their properties and complexity.

Findings

Three alternative forgetting methods are proposed.

The relations between these methods and relativized equivalence are clarified.

Computational complexity of the alternatives is thoroughly analyzed.

Abstract

Among the myriad of desirable properties discussed in the context of forgetting in Answer Set Programming (ASP), strong persistence naturally captures its essence. Recently, it has been shown that it is not always possible to forget a set of atoms from a program while obeying this property, and a precise criterion regarding what can be forgotten has been presented, accompanied by a class of forgetting operators that return the correct result when forgetting is possible. However, it is an open question what to do when we have to forget a set of atoms, but cannot without violating this property. In this paper, we address this issue and investigate three natural alternatives to forget when forgetting without violating strong persistence is not possible, which turn out to correspond to the different possible relaxations of the characterization of strong persistence. Additionally, we discuss their preferable usage, shed light on the relation between forgetting and notions of relativized equivalence established earlier in the context of ASP, and present a detailed study on their computational complexity.