The Rise and Fall of Semantic Rule Updates Based on SE-Models

TL;DR

This paper explores semantic rule updates for logic programs under stable model semantics, introducing a belief update approach based on SE-models, and reveals significant limitations of existing rule update operators.

Contribution

It presents a representation theorem for belief update operators in logic programs using SE-models and compares their behavior with existing syntactic update semantics.

Findings

A constructive method for belief update operators satisfying Katsuno and Mendelzon's postulates.

Analysis of the computational complexity of the proposed update operator.

Identification of fundamental drawbacks in current rule update semantics based on SE-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.