The Refined Extension Principle for Semantics of Dynamic Logic Programming

Abstract

Abstract. Over recent years, various semantics have been proposed for dealing with updates in the setting of logic programs. The availability of different semantics naturally raises the question of which are most adequate to model updates. A systematic approach to face this question is to identify general principles against which such semantics could be evaluated. In this paper we motivate and introduce a new such principle -the refined extension principle. Such principle is complied with by the stable model semantics for (single) logic programs. It turns out that none of the existing semantics for logic program updates, even though generalisations of the stable model semantics, comply with this principle. For this reason, we define a refinement of the dynamic stable model semantics for Dynamic Logic Programs that complies with the principle.

Operational Semantics for DyLPs

“…In this section we briefly recall the syntax of DyLPs, and the refined and well founded semantics defined, respectively, in [1] and [5].…”

“…Different semantics have been proposed [1,2,5,6,8,15,18,19,23] that assign meaning to arbitrary finite sequences P 1 , . .…”

“…A rule is rejected whenever it is in conflict with a newly added one (causal rejection of rules). Most of the semantics defined for DyLPs [1,2,5,6,8,15] are based on such a concept of causal rejection.…”

“…In [1] the authors provide theoretical results which strongly suggest that the refined semantics [1] should be regarded as the proper stable model-like semantics for DyLPs based on causal rejection. In particular, it solves some unintuitive behaviour of the other semantics in what regards updates with cyclic rules.…”

“…In [5] a well founded paraconsistent semantics for DyLPs (WFDy) is defined. The WFDy semantics is shown to be a skeptical approximation of the refined semantic defined in [1]. Moreover, it is always defined, even when the considered program is inconsistent, and its computational complexity is polynomial wrt.…”