Structure-Mapping Theory and Lexico-Semantic Information
Daniel Yarlett, Michael Ramscar · eScholarship (California Digital Library) · 2000
Structure—Mapping Theory and Lexico-Semantic Information Daniel Yarlett & Michael Ramscar {dany ,michael}@cogsci . ed . ac . uk Division of Informatics University of Edinburgh 2 Buccleuch Place Edinburgh EH8 9LW Abstract In modelling analogy the Structure Mapping Engine (Gentner, 1983; Falkenhainer, Forbus and Gentner, 1989) can only map successfully on representations in a canonical form because it only permits mappings be- tween relations with lexically—identical functors. We ex- amine whether co-occurrence statistics can remedy this by providing an appropriate basis for modelling lexico- semantic relations. Using a co-occurrence model we reimplement SME to allow it to map between relations with functors that are lexically-distinct. Computational experiments are then reported which show that the re- sulting model, M-SME, maps successfully on representa- tions which faithfully encode lexical properties, indicat- ing that semantic constraints should only play a minimal role in the mapping process. The Structure—Mapping Theory The structure—mapping theory was originally proposed as a set of constraints defining permissible mappings between a base and target domain in analogy (Gen- tner, 1983), and implemented in the Structure—Mapping Engine (Falkenhainer, Forbus and Gentner, 1989). Structure—mapping theory constructs analogical map- pings between discrete domains (called ‘Dgroups’) of propositional statements, with the main focus being on mapping interconnected relational structure. The Lexical-Identicality Constraint In detecting shared relational structure the structure- mapping theory only permits mappings to be made between relations if, and only if, they have lexically— identical functors and the same number of arguments. Thus there are two constraints on the formation of an initial match hypothesis. We call the first constraint on match hypothesis formation the le:cical—identicality con- straint, and it is important to observe that it carries a commitment to a canonical theory of representation be- cause it requires that mappable relations are represented with identical names. For example, structure—mapping theory would not permit an alignment between the fol- lowing two relations, even though it might be appropri- ate in a wider context: (URBITS PLANET SUN) (REVULVESJ-XRUUND ELECTRON ATOM) The fact that URBITS is not lexically—identical to REVOLVES_AROUND also means that the corresponding analogical mappings between the arguments of the re- lations (PLANET with ELECTRON, and SUN with ATOM) are not made. Holyoak and Thagard (1995) have argued that this constitutes a significant weakness in structure- mapping theory: “with its emphasis on structure to the exclusion of all other constraints, SME does not simply discourage mappings between non—identical but seman- tically similar items; it does not even permit them.” Both the ACME (Holyoak and Thagard, 1989) and LISA (Hummel and Holyoak, 1997) models of analogy avoid this objection by postulating semantic links that hold between the names of relations. These links are hand-coded into the propositional representations on which the analogical mappings are generated. If a suf- ficiently strong semantic link is coded between two re- lations then a mapping can be countenanced between them. Thus, in the example above, ACME’s or LISA’s representations could incorporate a sufficiently strong se- mantic link between DRBITS and REVOLVES_ARDUND to enable a mapping to be generated from one relation to the other. The Canonical Representation Theory Holyoak and Thagard’s criticism of the structure- mapping theory is not entirely fair, however, as it ignores SME’s commitment to a canonical representation (CR) theory. The CR theory claims that relations that are suf- ficiently similar in ‘meaning’ to facilitate mappings (e.g. ‘orbits’ and ‘revolves around’) are coded with identical tokens (in this case both might be coded as ‘orbits’). This extra assumption of the structure—mapping theory would allow the intuitively correct mapping to be made in the above case. However, since the postulation of se- mantic links and the CR theory rely on human—based coding decisions — and neither subscribe to a worked out model of semantics — both are ultimately equivalent in terms of their explanatory power. The CR commitment of structure—mapping theory al- lows a modular approach to be taken to the cognitive modelling of analogy. By mapping across canonical rep- resentations questions of semantics are left outwith the scope of structure—mapping theory — SME thus remains noncommittal with respect to a theory of lexical seman- tics. In the experiments that follow we exploit SME’s modular approach to modelling by using the information provided by a co-occurrence model of lexical semantics to see if this allows SME to map successfully on non- canonical representations, and avoid the underspecifica—