A theory of analogical mapping between source and target analogs based upon interacting structural, semantic, and pragmatic constraints is proposed here. The structural constraint of isomorphism encourages mappings that maximize the consistency of relational corresondences between the elements of the two analogs. The constraint of semantic similarity supports mapping hypotheses to the degree that mapped predicates have similar meanings.
See Full PDF See Full PDFWhereas 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 t.
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Theories of analogical reasoning have viewed relational structure as the dominant determinant of analogical mapping and inference, while assigning lesser importance to similarity between individual objects. An experiment is reported in which these two sources of constraints on analogy are placed in competition under conditions of high relational complexity. Results demonstrate equal importance for relational structure and object similarity, both in analogical mapping and in inference generation.
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The complex structure and organization of knowledge in the human mind is one of the key facets of thought. One of the fundamental cognitive processes that operates over that structure is analogy. A typical computational model of analogy might juxtapose a source do- main and a target domain, such as the solar system and the Bohr-Rutherford (BR) model of an atom (Gentner, 1983). The goal is to find a correspondence mapping between these two domains. Determining a mapping between the source and target domains of a non-trivial size would be intractable without a set of constraints to restrict the set of correspondences that are considered by a human reasoner. Moreover, the mere presence of domains serve as a constraint on mapping. In this paper, we study an alternative problem called unsegmented mapping - correspondence without specification of domains. We show a series of three formal constraints that allow for analogical-like mappings without explicit segmentation. The result, correspondence is possible without domains, has implications for models of analogical reasoning as well as schema induction and inference.
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