The rise and fall of semantic rule updates based onSE-models

Abstract

Logic programs under the stable model semantics, or answer-set programs, provide an expressive rule-based knowledge representation framework, featuring a formal, declarative and well-understood semantics. However, handling the evolution of rule bases is still a largely open problem. The AGM framework for belief change was shown to give inappropriate results when directly applied to logic programs under a non-monotonic semantics such as the stable models. The approaches to address this issue, developed so far, proposed update semantics based on manipulating the syntactic structure of programs and rules.More recently, AGM revision has been successfully applied to a significantly more expressive semantic characterisation of logic programs based on SE-models. This is an important step, as it changes the focus from the evolution of a syntactic representation of a rule base to the evolution of its semantic content.In this paper, we borrow results from the area of belief update to tackle the problem of updating (instead of revising) answer-set programs. We prove a representation theorem which makes it possible to constructively define any operator satisfying a set of postulates derived from Katsuno and Mendelzon's postulates for belief update. We define a specific operator based on this theorem, examine its computational complexity and compare the behaviour of this operator with syntactic rule update semantics from the literature. Perhaps surprisingly, we uncover a serious drawback of all rule update operators based on Katsuno and Mendelzon's approach to update and on SE-models.

Characterization of logic program revision as an extension of propositional revision

“…As to the case of update of logic programs Slota and Leite (2013) argued that semantic rule updates based on SE models seem to be inappropriate. Indeed they showed that in presence of the irrelevance-of-syntax postulate (whose counterpart in the context of revision is (RA4)), semantic rule update operators based on SE models violate some reasonable properties for rule updates, i.e., dynamic support and fact update (see (Slota and Leite 2013) for more details).…”

“…As to the case of update of logic programs Slota and Leite (2013) argued that semantic rule updates based on SE models seem to be inappropriate. Indeed they showed that in presence of the irrelevance-of-syntax postulate (whose counterpart in the context of revision is (RA4)), semantic rule update operators based on SE models violate some reasonable properties for rule updates, i.e., dynamic support and fact update (see (Slota and Leite 2013) for more details). The property of dynamic support can be expressed unformally as follows: an rule update operator ⊕ satisfies dynamic support if every atom true in an answer set from any updated program P ⊕ Q should be supported by a rule in P ∪ Q, i.e., it should have some "justification" in either the original program or the new one.…”

Syntax-Preserving Belief Change Operators for Logic Programs

“…While these two programs again share the same set of SE models, they too should not be interchangeable, since after a removal of the rule a., b should not be derived from the latter program any more. This property has become known as support [Slota and Leite 2013]. To address these two issues, Inoue and Sakama [2004] introduced a new notion of program equivalence that is stricter than strong equivalence, called C-update equivalence: any two programs P 1 ,…”

“…Such relationships are expressed on the rule-level, by the individual rules contained in a program. By neglecting information expressed on the rule-level, the distance-based approach fails to satisfy the property of preservation [Inoue and Sakama 2004] and the property of support [Inoue and Sakama 2004;Slota and Leite 2013]. This leads to some highly unintuitive results, as illustrated by the following two examples.…”

Minimal Change in Evolving Multi-Context Systems

“…Another important issue open for future work is a more finegrained characterization of updating bridge rules (and knowledge bases) as studied in [14] in light of the encountered difficulties when updating rules [24,25,27] and the combination of updates over various formalisms [25,26].…”