The paper attacks the widely held view that belief revision theories, as they have been studied in the past two decades, are founded on the Principle of Informational Economy. The principle comes in two versions. According to the first, an agent should, when accepting a new piece of information, aim at a minimal change of his previously held beliefs. If there are different ways to effect the belief change, then the agent should, according to he second version, give up those (...) beliefs that are least entrenched. Although widely proclaimed by belief revision theorists, I argue that both versions of the principle are dogmas that are not (and perhaps should not be) adhered to. I substantiate this claim with two simple mathematical observations, and I defend it against four possible objections that involve contractions, reconstructions, dispositions, and truths. (shrink)

The paper attacks the almost universally held view that belief revison theories, as they have been studied in the literature of the past two decades, are founded on a Principle of Minimal Change, or Principle of Informational Economy. The principle comes in two versions. According to the first, an agent should, when accepting new information, aim at a posterior belief set that minimizes the items on which it disagrees with the prior belief set. If there are different ways to effect (...) the belief change, then according to the second version, the agent should give up the beliefs that are least entrenched. Although widely endorsed and advertised by belief revision theorists, the paper argues that both versions of the principle are dogmas that are not in fact (and perhaps should not be) adhered to. Two simple mathematical observations substantiate this claim, and it is defended against four possible objections that involve contractions, reconstructions, dispositions, and truths. (shrink)

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)

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)

The AGM (Alchourrón-Gärdenfors-Makinson) model of belief change is extended to cover changes on sets of beliefs that are not closed under logical consequence (belief bases). Three major types of change operations, namely contraction, internal revision, and external revision are axiomatically characterized, and their interrelations are studied. In external revision, the Levi identity is reversed in the sense that one first adds the new belief to the belief base, and afterwards contracts its negation. It is argued that external revision represents an (...) intuitively plausible way of revising one's beliefs. Since it typically involves the temporary acceptance of an inconsistent set of beliefs, it can only be used in belief representations that distinguish between different inconsistent sets of belief. (shrink)

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

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)

The paper introduces ten open problems in belief revision theory, related to the representation of the belief state, to different notions of degrees of belief, and to the nature of change operations. It is argued that these problems are all issues in philosopical logic, in the strong sense of requiring inputs from both logic and philosophy for their solution.