Setsuo Arikawa

Elementary formal system as a unifying framework for language learning

This paper presents a unifying framework for language learning, especially for inductive inference of various classes of languages. The elementary formal systems (EFS for short), Smullyan invented to develop his recursive function theory, are proved suitable to generate languages.

Reasoning by Analogy as a Partial Identity Between Models

We present in this paper a formal theory of analogical reasoning. We are mainly concerned with three subjects: a formal definition of analogy, a formalization of the reasoning in terms of deduction, and a method for realizing the reasoning in a logic programming system. First we assume that each domain for the reasoning is the least model for logic program. Then we consider an analogy as a partial identity between the models. Secondly we introduce a notion of rule transformation which transforms rules in one domain into those in the other. Then we can formalize the reasoning as a system with three inference rules: instantiation of rules, modus ponens, and the rule transformation. Finally, based on the formalization, we present an extended pure-Prolog interpreter which performs the detection of analogy and the reasoning by the partial identity at the same time.

A foundation of reasoning by analogy: analogical union of logic programs

This paper presents a theoretical foundation of reasoning by analogy between logic programs. We give a formal definition of reasoning by analogy in terms of logic programming. We also introduce a notion of analogical union of logic programs by which we characterize the reasoning. Then we can regard the reasoning as a deduction from the analogical union. Based on this characterization, we present a general framework which is useful for discussing various requirements of analogies.

Time-bounded reasoning in first order knowledge base systems

In first order predicate logic, it is undecidable whether a formula is deducible from a set of axioms. In order to realize a practical knowledge base system in the framework of the first order logic, we must overcome this problem.

Pseudo Extension in Default Reasoning and Belief Revision by Model Inference

This paper is concerned with extension and belief revision in Reiters default reasoning. First we introduce a new notion of pseudo extension which is successively constructed from a given default theory. We show that the set of pseudo extensions contains the set of extensions, so that we can get some reasonable candidates of extension in a constructive way. This should be a first step towards computerization of the default reasoning. We also discuss the belief revision problem from the viewpoint of Shapiros inductive inference of models.