Automated Hypothesis Generation Using Extended Inductive Resolution

We report on a method of automated hypothesis generation, called f-resolution, which is derived from deductive resolution techniques. The method is inductive in character, in the sense that given input statement E, it generates hypotheses H, such that E is a deductive consequence of E. The method is extended by a generalized unification algorithm which introduces appropriate identity assumptions needed to unify a pair of literals. The f-resolution technique is shown to embody a version of Ockham's raror as a pruning heuristic. Some promising experimental results are also presented. In [5] we discussed a general method for transforrairg deductive consequence generators into inductive consequence generators. In this paper we wish to report on a general mechanised inductive method, to be called f-resolution, which was derived from normal resolution procedures. The f-reeolution procedure was not designed as a special purpose routine only applicable to certain problems (like the routine described in [2]), but rather it is applicable to any problem in any context suitably descrlb-able in the syntax of first-order predicate calculus with identity. The potential range of applicability of the method is thus extremely broad. Our routine appears to deal with a more general class of hypotheses than previously reported efforts in this area; in particular, We assume familiarity with the usual terminology and theory of resolution. For any expression E, we represent the set of clauses obtained from the clause form of E by C(E). For a set C of clauses, we represent the set of all pairwise resolvents of members of C by R(C). We then define R0(C) = C and R n+1 (C) = R(R n (C)) U R n (C). For our purposes, we will consider resolution as a consequence generator. As such, resolution ie not complete. That is, for any expression E, there are expressions E' such that E entails E' but for nc n is it the case that C(E') c Rn(c(E)). For just one type of example, consider the case in which E' contains predicates which do not occur in E, and note that resolution introduces no new predicates. The basic f-resolution principle is very similar to the basic resolution principle. The principle appears to be, in essential respects, the same as the basic inverse method of [3], apparently developed by Maslov as early as 1964. However, our development was independent of Maslov's. work, and our routine is used induc-tively rather than deductively. …