On AGM for non-classical logics
The purpose of this paper is to review some of the work that has been done adapting the AGM theory of belief change to contexts where the background logic is non-classical. It is not intended as an exhaustive survey of the field; for example, it does not discuss the case of intuitionistic logic. But it does cover quite a broad range of constructions. As the author remarks, the AGM partial meet account already has some generality; it applies not only to classical consequence but to any compact supraclassical consequence satisfying disjunction in the premises. The paper begins by reviewing some results on what remains of the AGM account if we simply generalize those conditions. However, the greater part of the review concerns specific non-classical logics for belief change. They are of two main groups: those with a computational motivation, and those with a relevantist rationale. From a computational point of view, the goal is to develop a formal account of belief change that cuts down on the complexity of calculating the background classical consequence relation. A first step in this direction was to restrict attention to belief bases, and a second step was to develop criteria for ignoring part of the base, so that classical consequence is applied only to a distinguished subset whose choice is conditioned by the proposition that is being eliminated or introduced. Another way of tackling the problem is to restrict the language in which the belief sets or bases, and the inserted or discarded formulae, may be expressed. The main candidates here are languages using only Horn clauses, and various kinds of description logic. The author explains the main proposals from the literature, with their known properties, but does not attempt to assess the extent to which complexity savings really ensue. The paper also reports on several constructions that have been carried out from a relevantist perspective. There the goal is to replace the background classical consequence by one or another of the various paraconsistent logics of the literature, under which inconsistent sets of statements need not imply all statements of the language. The review is clear, balanced and well-organized, making it a valuable point of entry for those wishing to take up the challenge of doing belief change non-classically, whether for computational or philosophical reasons.
scientific article; zbMATH DE number 5886898
scientific article