Characterization of Logic Program Revision as an Extension of Propositional Revision

TL;DR

This paper provides a comprehensive, constructive characterization of rational belief revision operators for logic programs, extending AGM principles to various classes including generalized, disjunctive, and normal logic programs, with insights into their semantic and computational properties.

Contribution

It introduces a complete, intuitive procedure for constructing all rational logic program revision operators based on propositional revision, and analyzes their properties across different logic program classes.

Findings

All rational GLP revision operators derive from propositional AGM operators.

Embedding GLP revision operators into Boolean lattices reveals potential weaknesses in AGM postulates.

Characterization of two specific classes of GLP revision operators with distinct behaviors.

Abstract

We address the problem of belief revision of logic programs, i.e., how to incorporate to a logic program P a new logic program Q. Based on the structure of SE interpretations, Delgrande et al. adapted the well-known AGM framework to logic program (LP) revision. They identified the rational behavior of LP revision and introduced some specific operators. In this paper, a constructive characterization of all rational LP revision operators is given in terms of orderings over propositional interpretations with some further conditions specific to SE interpretations. It provides an intuitive, complete procedure for the construction of all rational LP revision operators and makes easier the comprehension of their semantic and computational properties. We give a particular consideration to logic programs of very general form, i.e., the generalized logic programs (GLPs). We show that every rational GLP revision operator is derived from a propositional revision operator satisfying the original AGM postulates. Interestingly, the further conditions specific to GLP revision are independent from the propositional revision operator on which a GLP revision operator is based. Taking advantage of our characterization result, we embed the GLP revision operators into structures of Boolean lattices, that allow us to bring to light some potential weaknesses in the adapted AGM postulates. To illustrate our claim, we introduce and characterize axiomatically two specific classes of (rational) GLP revision operators which arguably have a drastic behavior. We additionally consider two more restricted forms of logic programs, i.e., the disjunctive logic programs (DLPs) and the normal logic programs (NLPs) and adapt our characterization result to DLP and NLP revision operators.