In praise of full meet contraction

Abstract

Full meet contraction, that was devised by Carlos Alchourrón and David Makinson in the early 1980' s, has often been overlooked since it is not in itself a plausible contraction operator. However, it is a highly useful building-block in the construction of composite contraction operators. In particular, all plausible contraction operators can be reconstructed so that the outcome of contracting a belief set K by a sentence p is defined as K ∼ f (p), where ∼ is full meet contraction and f a sentential selector, i.e. a function to and from sentences. This paper investigates the logic of full meet contraction. Seven properties of this operation are presented that contribute to making it useful as a building-block: (1) Full meet contraction is a purely logical operation. (2) It retains finitebasedness of the belief set. (3) It is the inclusion-maximal contraction that removes all sentences that can contribute to implying the input sentence. (4) It is the inclusion-maximal contraction that removes all non-tautologous consequences of the input sentence. (5) Almost all contractions can be reconstructed as full meet contraction. (6) Full meet contraction allows for recovery of the input sentence. (7) Full meet contraction provides a unified account of multiple and singleton contraction