Belief revision in the propositional closure of a qualitative algebra (extended version)

TL;DR

This paper explores belief revision within the propositional closure of qualitative algebras, providing algorithms and an open-source implementation to ensure revised beliefs remain within the formalism.

Contribution

It introduces a novel approach to belief revision in the propositional closure of QAs, ensuring results are representable and enabling contraction operators via the Harper identity.

Findings

Developed an algorithm for belief revision in the propositional closure of QAs

Proposed a contraction operator using the Harper identity

Provided an open-source implementation of the revision algorithms

Abstract

Belief revision is an operation that aims at modifying old beliefs so that they become consistent with new ones. The issue of belief revision has been studied in various formalisms, in particular, in qualitative algebras (QAs) in which the result is a disjunction of belief bases that is not necessarily representable in a QA. This motivates the study of belief revision in formalisms extending QAs, namely, their propositional closures: in such a closure, the result of belief revision belongs to the formalism. Moreover, this makes it possible to define a contraction operator thanks to the Harper identity. Belief revision in the propositional closure of QAs is studied, an algorithm for a family of revision operators is designed, and an open-source implementation is made freely available on the web. (This is the extended version of an article originally presented at the 14th International Conference on Principles of Knowledge Representation and Reasoning.)