On Strong and Default Negation in Logic Program Updates (Extended Version)
This work tackles the problem of improving logic program updates for researchers and practitioners in knowledge representation and reasoning, though it appears incremental as it builds on existing semantics.
The paper addresses the limitations of existing answer-set program update semantics, which either handle only strong negation or rely on default negation with optional support for strong negation, by arguing that both negations should be first-class citizens in updates. It extends an advanced semantics to directly support strong negation, showing that it satisfies newly identified principles and other desirable properties.
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.