An agent can usually hold a very large number of beliefs. However, only a small part of these beliefs is used at a time. Efficient operations for belief change should affect the beliefs of the agent locally, that is, the changes should be performed only in the relevant part of the belief state. In this paper we define a local consequence operator that only considers the relevant part of a belief base. This operator is used to define local versions of (...) the operations for belief change. Representation theorems are given for the local operators. (shrink)

Postulational approaches attempt to understand the dynamics of belief revision by appealing to no more than the set of beliefs held by an agent and the logical relations between them. It is argued there that such an approach cannot work. A proper account of belief revision must also appeal to the arguments supporting beliefs, and recognize that those arguments can be defeasible. If we begin with a mature epistemological theory that accommodates this, it can be seen that the belief revision (...) operators on which the postulational theories are based are ill-defined. It is further argued that there is no way to repair the definitions so as to retain the spirit of those theory. Belief revision is better studied from within an independently motivated epistemological theory. (shrink)

Kernel contraction is a natural nonrelational generalization of safe contraction. All partial meet contractions are kernel contractions, but the converse relationship does not hold. Kernel contraction is axiomatically characterized. It is shown to be better suited than partial meet contraction for formal treatments of iterated belief change.

We present different constructions for nonprioritized belief revision, that is, belief changes in which the input sentences are not always accepted. First, we present the concept of explanation in a deductive way. Second, we define multiple revision operators with respect to sets of sentences (representing explanations), giving representation theorems. Finally, we relate the formulated operators with argumentative systems and default reasoning frameworks.

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)