One way to construct a contraction operator for a theory (belief set) is to assign to it a base (belief base) and an operator of partial meet contraction for that base. Axiomatic characterizations are given of the theory contractions that are generated in this way by (various types of) partial meet base contractions.

An operator of contraction for a belief set (a theory) can be obtained by assigning to it a belief base and an operator of partial meet contraction for that base. It is argued that closure of the base under disjunction is an intuitively reasonable condition. Axiomatic characterizations are given of the contractions of belief sets that can be generated by (various types of) partial meet contraction on disjunctively closed bases. The corresponding revision operators are also characterized. Finally, some results are (...) reported on operations on bases that are closed under material implication. (shrink)

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 basic assumption of repertoire contraction is that only some of the logically closed subsets of the original belief set are viable as contraction outcomes. Contraction takes the form of choosing directly among these viable outcomes, rather than among cognitively more far-fetched objects such as possible worlds or maximal consistent subsets of the original belief set. In this first investigation of repertoire contraction, postulates for various variants of the operation are introduced. Necessary and sufficient conditions are given for when repertoire (...) contraction coincides with AGM contraction or with operations generated by AGM-style contraction on a belief base. A close connection is shown to hold between repertoire contraction and specified meet contraction. (shrink)

The AGM theory of belief contraction is extended tomultiple contraction, i.e. to contraction by a set of sentences rather than by a single sentence. There are two major variants: Inpackage contraction all the sentences must be removed from the belief set, whereas inchoice contraction it is sufficient that at least one of them is removed. Constructions of both types of multiple contraction are offered and axiomatically characterized. Neither package nor choice contraction can in general be reduced to contractions by single (...) sentences; in the finite case choice contraction allows for reduction. (shrink)

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

Specified meet contraction is the operation defined by the identity where ∼ is full meet contraction and f is a sentential selector, a function from sentences to sentences. With suitable conditions on the sentential selector, specified meet contraction coincides with the partial meet contractions that yield a finite-based contraction outcome if the original belief set is finite-based. In terms of cognitive realism, specified meet contraction has an advantage over partial meet contraction in that the selection mechanism operates on sentences rather (...) than on temporary infinite structures (remainders) that are cognitively inaccessible. Specified meet contraction provides a versatile framework in which other types of contraction, such as severe withdrawal and base-generated contraction, can be expressed with suitably chosen properties of the sentential selector. (shrink)

The postulate of recovery is commonly regarded to be the intuitively least compelling of the six basic Gärdenfors postulates for belief contraction. We replace recovery by the seemingly much weaker postulate of core-retainment, which ensures that if x is excluded from K when p is contracted, then x plays some role for the fact that K implies p. Surprisingly enough, core-retainment together with four of the other Gärdenfors postulates implies recovery for logically closed belief sets. Reasonable contraction operators without recovery (...) do not seem to be possible for such sets. Instead, however, they can be obtained for non-closed belief bases. Some results on partial meet contractions on belief bases are given, including an axiomatic characterization and a non-vacuous extension of the AGM closure condition. (shrink)

The outcome set of a belief change operator is the set of outcomes that can be obtained with it. Axiomatic characterizations are reported for the outcome sets of the standard AGM contraction operators and eight types of base-generated contraction. These results throw new light on the properties of some of these operators.

Investigates the resolution of contradictions and ambiguous derogations in a code, by means of the imposition of partial orderings. Although formulated as a study in the logic of norms, it provided the initial ideas for work on the logic of theory (or belief) change, developed by the authors in a series of papers by the authors and Peter Gardenfors beginning in 1985.