Variables in Hypotheses

Abstract

In many applications we want to build systems which must test the consistency of some theory (or set of axioms). This problem is general to many applications, for example abduction, learning, default reasoning, diagnosis, and is examined here in the context of theory formation from a fixed set of possible hypotheses [PGA87, Poole86]. There is a problem which arises when we are generating theories that contain variables. Two solutions are examined, the first where we are only allowed to have ground instances in theories formed, and the second where we may have universally quantified variables in the theory. It is shown that for the second case that the solution of reverse Skolemisation is not adequate to solve the problem, nor is any naive pattern matcher. A solution for both cases is outlined.