An Approach to the Semantics of Analogical Relations1

Whereas approaches for deductive and inductive reasoning are well-examined for decades, analogical reasoning seems to be a hard problem for machine intelligence. Although several models for computing analogies have been proposed, there is no uncontroversial theory of the semantics of analogies. In this paper, we will investigate semantic issues of analogical relations, in particular, we will specify a model theory of analogical transfers. The presented approach is based on Heuristic-Driven Theory Projection (HDTP) a framework that computes an analogical relation between logical theories describing a source and a target domain. HDTP establishes the analogy by an abstraction process in which formulas from both domains are generalized creating a theory that syntactically subsumes the original theories. We will show that this syntactic process can be given a sensible interpretation on the semantic level. In particular, given models of the source and the target domains, we will examine the construction of models for the generalized theory of source and target. Furthermore, we will specify some properties of both, the corresponding models and the underlying analogical relation.