A Note on Rule-Finding Abduction

The rule-finding abduction is an abduction which begins with the observation of a surprising fact, finds a rule in the set of programs, and proposes a hypothesis. This paper investigates such rule-finding abduction for logic programming from two viewpoints: termination and analogical reasoning. In order to discuss the termination of rule-finding abduction, we introduce two concepts of loop-pair and loop-elimination. We show that the loop-pair is a syntactical condition to determine whether the process of rule-finding abduction is infinite. Also we show that, by using loop-elimination, we can delete all the infinite processes of rule-finding abduction. On the other hand, we discuss the relationship between analogical reasoning and rule-finding abduction. Then, we formulate rule-finding abduction with analogy, and define a deducible hypothesis. We show that a deducible hypothesis is correct in the sense of analogical reasoning. Also we show that, if a target program is empty, then a deducible hypothesis is polynomial time computable on the length of a surprising fact and the size of a proof tree. Furthermore, we realize rule-finding abduction with analogy by a Prolog program