On Strong and Default Negation in Logic Program Updates (Extended Version)

TL;DR

This paper advocates for treating strong and default negation equally in logic program updates, identifies limitations of existing semantics, and extends a leading semantics to support both types of negation as first-class citizens.

Contribution

It introduces a novel extension of an existing semantics to incorporate strong negation directly, addressing limitations of prior approaches.

Findings

Extended semantics satisfies key principles of negation interaction.

Supports both strong and default negation as first-class citizens.

Demonstrates improved properties over previous semantics.

Abstract

Existing semantics for answer-set program updates fall into two categories: either they consider only strong negation in heads of rules, or they primarily rely on default negation in heads of rules and optionally provide support for strong negation by means of a syntactic transformation. In this paper we pinpoint the limitations of both these approaches and argue that both types of negation should be first-class citizens in the context of updates. We identify principles that plausibly constrain their interaction but are not simultaneously satisfied by any existing rule update semantics. Then we extend one of the most advanced semantics with direct support for strong negation and show that it satisfies the outlined principles as well as a variety of other desirable properties.