On a Full Meet Base Revision That Satisfies the Categorial Matching Principle

Abstract

Belief revision theory is concerned with the problem of revising a set of beliefs K with a new belief represented by a formula α. When the set K is supposed to represent the totality of the current beliefs of an agent, it is usually taken to be closed under classical consequence, since necessary consequences of beliefs are themselves beliefs. This closure assumption nevertheless leads to important problems: Hansson, for instance, invokes in [Hansson, 1996] the disadvantages of dealing with a belief set that contains “myriads of sentences that the believer has never thought of”, and also notes that the recovery postulate problem and the problem of inconsistent belief states may find solutions that are more satisfying when the revision operation is performed on belief bases than when it is performed on belief sets. Another argument in favour of the foundations theory,which focuses on belief bases rather than on belief sets, is that it conforms with the intuistic notion that a set of beliefs most commonly consists of a rough collection B of several pieces of knowledge, put together without any structure, and treated as elementary beliefs. In order to revise the resulting theory K = Cn(B) by an information α, it is therefore natural in this perspective to first try to revise the base B by α, and it is only at a second stage that the effect of this revision on the logical closure K of B should be examined (for a more detailed discussion on the difference between the justifications theory and the coherence theory, see [Gärdenfors and Rott, 1995]).