'Just-in-Time' Analogical Reasoning: A Progressive-Deepening Model of Structure-Mapping

Structure-Mapping is a graph-theoretic process which lies at the heart of computational models of analogy, metaphor (see Veale and Keane 1997), case-base reasoning (see Kolodner 1993) and example-based machine translation (see Veale and Way 1997). In essence this problem is a variant of the provably NPHard problem of determining the largest common isomorphic pair of sub-graphs shared by two semantic structures (see Garey & Johnson 1979; Veale & Keane 1997), called the Source and Target, such that a systematic and coherent 1-to-1 mapping of elements from the Source to the Target is established. For example, Figure 1 illustrates an instance of structuremapping between two story examples that share the same narrative backbone. The suspected intractability of this process has led researchers to tame the exponentiality of structure-mapping by introducing heuristics that operate in polynomial time to produce a near-optimal mapping interpretation, making the process of structuremapping appealing for both cognitive and engineering models (see Oblinger and Forbus 1990; Veale et al. 1996a,b, 1997).