Belief revision in the propositional closure of a qualitative algebra (extended version)
This work addresses a theoretical limitation in belief revision for AI and knowledge representation, offering a practical solution for researchers and practitioners in formal reasoning, though it is incremental in extending existing QA frameworks.
The paper tackles the problem of belief revision in qualitative algebras (QAs) by extending the formalism to their propositional closures, ensuring results remain representable within the framework, and provides an algorithm and open-source implementation for a family of revision operators.
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.)