Maps between some different kinds of contraction function: the finite case (Q1089333)

A contraction of a theory A with respect to a proposition x is a subset of A that is closed under logical consequence and does not contain x. This paper compares different kinds of contraction functions, in particular partial meet contractions and safe contractions. It is known that every safe contraction function is a partial meet contraction function. In this paper it is shown that if the theory is finite, the converse also holds. Furthermore, this result is extended to some subclasses of partial meet contractions and safe contractions.