Characterization Theorems for Revision of Logic Programs

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. [5] adapted the AGM postulates to identify the rational behavior of generalized logic program (GLP) revision operators and introduced some specific operators. In this paper, a constructive characterization of all rational GLP revision operators is given in terms of an ordering among propositional interpretations with some further conditions specific to SE interpretations. It provides an intuitive, complete procedure for the construction of all rational GLP revision operators and makes easier the comprehension of their semantic properties. In particular, we show that every rational GLP revision operator is derived from a propositional revision operator satisfying the original AGM postulates. Taking advantage of our characterization, 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.