Belief revision in the propositional closure of a qualitative algebra

TL;DR

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

Contribution

It introduces a novel approach for belief revision in propositional closures of qualitative algebras, ensuring results are representable within the formalism.

Findings

Developed an algorithm for belief revision in propositional closure

Proposed a family of revision operators with formal guarantees

Provided open-source implementation for practical use

Abstract

Belief revision is an operation that aims at modifying old be-liefs 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 repre-sentable in a QA. This motivates the study of belief revision in formalisms extending QAs, namely, their propositional clo-sures: 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 al-gorithm for a family of revision operators is designed, and an open-source implementation is made freely available on the web.