Rule-Generating Abduction for Recursive Prolog

Proc. 5th Intern. Workshop on Analogical and Inductive Inference for Program SynthesisThe rule-generating abduction is a kind of abduction which generates a rule and proposes a hypothesis from a surprising fact. In general, there may exist infinitely many rules and hypotheses to explain such a surprising fact. Hence, we need to put some restriction on the class of rules. In rule-generating abduction, only one surprising fact is given. Hence, we also need to generalize the concept of a surprising fact. When we deal with such generalizations, we must avoid overgeneralization. It should be determined whether or not a generalization is overgeneral by an intended model. However, it is hard to give in advance such an intended model in our rule-generating abduction. Hence, in this paper we introduce a syntactical formulation of generalization, in which it can be determined whether or not a generalization is overgeneral by the forms of atoms and substitutions. On the other hand, by the restriction of rules, it suffices to consider only two types of terms, constants and lists, and two types of substitutions with these two terms. By using the above generalizations and substitutions, we design an algorithm for rule-generating abduction, which generates rules and proposes hypotheses in polynomial time with respect to the length of a surprising fact. The number of rules and hypotheses is at most the number of common terms in a surprising fact. Furthermore, we show that a common term in some argument of a surprising fact also appears in the same argument of the proposed hypothesis by this algorithm