This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one of (...) its axiomatic bases), that fails to imply the proposition being eliminated. In the present paper, the authors study a broader class, including contraction functions that may be less than maximal. Specifically, they investigate "partial meet contraction functions", which are defined to yield the intersection of some nonempty family of maximal subsets of the theory that fail to imply the proposition being eliminated. Basic properties of these functions are established: it is shown in particular that they satisfy the Gardenfors postulates, and moreover that they are sufficiently general to provide a representation theorem for those postulates. Some special classes of partial meet contraction functions, notably those that are "relational" and "transitively relational", are studied in detail, and their connections with certain "supplementary postulates" of Gardenfors investigated, with a further representation theorem established. (shrink)

A study in the logic of theory change, examining the properties of maxichoice contraction and revision operations.

The purpose of this note is to make quite clear the relationship between two variants of the general notion of a preferential model for nonmonotonic inference: the models of Kraus, Lehmann and Magidor (KLM models) and those of Makinson (MAK models).On the one hand, we introduce the notion of the core of a KLM model, which suffices to fully determine the associated nonmonotonic inference relation. On the other hand, we slightly amplify MAK models with a monotonic consequence operation as additional (...) ingredient. (shrink)

Theoria, Volume 88, Issue 3, Page 494-528, June 2022.

Describes and discusses the rather special behaviour of one of the postulates in the AGM account of theory change.

This paper investigates the formal relationship between two prominent approaches to the logic of belief change. The first one uses the idea of "relational partial meet contractions" as developed by Alchourrón, Gärdenfors and Makinson (Journal of Symbolic Logic 1985), the second one uses the concept of "epistemic entrenchment" as elaborated by Gärdenfors and Makinson (in Theoretical Aspects of Reasoning about Knowledge, M. Y. Vardi, Los Altos 1988). The two approaches are shown to be strictly equivalent via direct links between the (...) underlying formal relations. The paper closes with observations about the application of epistemic entrenchment to simple and iterated revisions. (shrink)