Evidence for the Processing of Re-representations during the mapping of Externally Represented analogies

Evidence for the processing of re-representations during the mapping of externally represented analogies Michael Ramscar michael@cogsci.ed.ac.uk Division of Informatics, University of Edinburgh 2 Buccleuch Place, Edinburgh EH8 9LW, Scotland Abstract High level descriptions of the analogical reasoning process in cognitive science have now converged t o present a relatively unified account (Hummel and Holyoak, 1997). However, the broad, consensual account of analogy is still far from complete: whilst it i s possible to give a good explanation of the mapping of larger, structured representations in analogy, accounts of the mappings of individual sub-elements in these representations are still under-specified. Here, we review some possible approaches to this problem, describe an experiment that provides some empirical support for the ‘re-representation’ approach to sub-mapping, and then identify some shortcomings in the ‘re-representation’ approach as it is currently conceived. Introduction Cognitive science has made great strides towards answering the important question of ‘How do humans reason by analogy? ’ If we take a familiar example, the analogy between the solar system and Rutherford’s model of the atom, then it is possible to explain – in broad terms – exactly how it is that two seemingly disparate objects can both remind us of one another in the first place, and then how it is that we can make meaningful correspondences between them. Studies have shown that reminding (or retrieval) is driven by a computationally inexpensive process that initially matches surface (or semantic) elements in representations (witness the frequency – and mundanity – of most similarity based remindings, such as a lamp-shade reminding a party joker of a hat; see Gentner, Ratterman and Forbus, 1993). Analogical mappings, on the other hand, are determined by a relatively more computationally expensive process. Global, systematic structural similarities between items to be matched need to be detected in order to make the kind of ‘deeper’, inference supporting correspondences that characterise analogy (Gentner, 1983; Goswami, 1992; Holyoak and Thagard, 1995; Hummel and Holyak, 1997). Whilst theories and models of analogy are very compelling at one level of abstraction, there are certain assumptions made by all analogical theories that beg interesting questions if one seeks a more detailed explanation. As one increases the resolution of the question ‘How do humans reason by analogy? ’ it appears that there are important gaps in current theories and process models. Here, we wish to consider just one aspect of one of these gaps: the problem we focus on is that of matching the ‘semantics’ of elements during the analogical mapping process. This problem can be summarised as follows: suppose that in your representation of the atom, you describe the motion of an electron in relation to the nucleus in terms of it “revolving around” the nucleus (perhaps this is how you ordinarily think about this motion). On the other hand, suppose that in your representation of the solar system you conceive the motion of the planets in terms of their “orbiting” the sun. At one level of abstraction, it may be sufficient to say that similarities in the meanings – or usage – of these words determine these mappings. However, in a more detailed account – and model – of analogy we might wish to do more than appeal to humanistic intuitions about similarities of meaning. We might wish to account for the way in which these sub-elements of our representations of the atom and the solar-system are mapped onto one another with the same level of detail with which we account for the mappings between the representations themselves. If we are to fully explain high-level mapping in analogy, we must also account for the way lexically distinct but ‘semantically’ similar items in representations are reconciled with each other in a way that allows high- level mappings to be made. Here, we review some possible approaches to this problem, and present some evidence that offers some support to a popular proposal in the literature: the re-representation hypothesis. Semantic reconciliation and the re-representation hypothesis Perhaps the most straightforward way to explain the mapping between “revolving around” and “orbiting” 1 would be in conceptual terms. If “revolving around” and “orbiting” could be shown to decompose into some canonical conceptual representation (say “circumnavigating”), then the link between them could be explained by reference to that concept, and the process by which it is made. This proposal is put forward by Gentner, Ratterman and Forbus (1993): “[the. ] constraint of matching identical predicates assumes canonical conceptual representations, not lexical strings. Two concepts that are similar but not identical (such as “bestow” and “bequeath”) are assumed to be decomposed into a canonical We shall refer to this as the problem of semantic reconciliation in analogy.