Double preference relations for generalised belief change
In 2002, \textit{H. Andréka, M. Ryan} and \textit{P.-Y. Schobbens} [``Operators and laws for combining preference relations'', J. Log. Comput. 12, No.~1, 13--53 (2002; Zbl 1008.91027)] proposed a very general semantic framework for the logic of belief change using multiple preference relations coordinated by a further `guiding relation'. The paper under review shows that even when there is only one preference relation, we can use the guiding relation to create a framework broad enough to cover quite a variety of systems of belief change from the literature, notably AGM contraction (and also revision), Rott and Pagnucco's severe withdrawal, systematic withdrawal of Meyer et al., and the liberation operators of Booth et al. Roughly speaking, one minimalizes under the guiding relation and then closes downwards under the preference relation. Appropriate completeness theorems are established, and the constructions are briefly compared with some others seeking similar generality, notably ones due to Bochman and of Cantwell. Bibliographical note: This paper develops a conference publication by the same authors [``A unifying semantics for belief change'', in: R. López de Mántaras et al. (eds.), Proceedings of the 16th European conference on artificial intelligence, ECAI'2004, including Prestigious applicants of intelligent systems, PAIS 2004, Valencia, Spain, August 22--27, 2004. Amsterdam: IOS Press. 793--797 (2004)]. In both papers, the context is restricted to finite classical propositional languages. In the meantime, \textit{D. M. Gabbay} and \textit{K. Schlechta} [``A comment on work by Booth and co-authors'', Stud. Log. 94, No. 3, 403--432 (2010; Zbl 1198.03024)] have worked on extending its constructions to the the infinite case.
scientific article; zbMATH DE number 5843092
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