A sketch of analogy as reasoning with equality hypotheses

Abstract

We specify a form of analogical reasoning in terms of a system of hypothetical reasoning based on mathematical logic. Our primary motivation is a deeper understanding of analogical reasoning as well as its relationship to existing logical models of nonmonotonic reasoning. We begin with a brief description of a hypothetical reasoning system called Theorist. Theorist is a nonmonotonic clausal theorem prover that permits consistent instances of hypotheses to participate in a deductive derivation. Such sets are viewed as explanatory theories for goal observations, which are simply questions assumed true in the intended interpretation. Our specification of analogical reasoning assumes two relatively simple and uncontroversial properties of analogical reasoning. First, analogical reasoning is non-deductive. Second, analogical reasoning is based on similarity relationships between so-called source and target objects. We use Theorist's specification of hypothetical reasoning to provide us with the required non-deductive mechanism, and interpret similarity relationships as hypotheses about various kinds of equality between source and target objects.