Structure-mapping: A theoretical framework for analogy

Subjects judged as most apt those analogies for which they produced the most relational information.

“Further, a correlation of aptness ratings and relationality ratings revealed that subjects rated as most apt those analogies for which they wrote the greatest amount of relational information.”

• cites Gentner, 1980bNot checked yet

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A model based on the degree of featural overlap gives a good account of literal similarity comparisons.

“Such a “degree of overlap” approach seems reasonably correct for literal similarity comparisons.”

• cites Tversky (1977)Not checked yet

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Changing one relation in a mappable system affects the others.

“One symptom of this systematicity is that changing one of these relations affects the others.”

Postulating that analogies select for dynamic causal knowledge would be a mistake because it unreasonably limits the scope of analogy.

“We could accomplish this by postulating that analogies select for dynamic causal knowledge, or more generally, for appropriate abstractions.Either of these would be a mistake: The former course limits the scope of analogy unreasonably,”

Research exists that supports the structure-mapping approach.

“There is research supporting the structure-mapping approach.”

If the systematicity principle is assumed, the overlapping predicates are likely to include higher-order relations such as CAUSE and IMPLIES.

“Moreover, if we assume the systematicity principle, then the set of overlapping predicates is likely to include higher-order relations such as CAUSE and IMPLIES.”

People will favor relations belonging to the deepest, most interconnected mappable system in their interpretations.

“By the systematicity principle, to the extent that people recognize (however vaguely) that the system of predicates connected with central forces is the deepest, most interconnected mappable system for this analogy, they will favor relations that belong to that system in their interpretations.”

• AssumptionThe authors state this as an assumption: Partial knowledge of a system is often sufficient for a person to gauge its interconnectedness.

The structure-mapping theory's rules distinguish analogy from other domain comparisons, including abstraction and literal similarity.

“Further, the rules are such as to distinguish analogy from other kinds of domain comparisons, such as abstraction or literal similarity.”

The same interdependencies hold for the atom under appropriate node substitutions.

“The same interdependencies hold for the atom, if we make the appropriate node substitutions:”

Object correspondences are used to generate the candidate set of inferences in the target domain.

“These object correspondences are used to generate the candidate set of inferences in the target domain.”

This sequence can be explained by differences in predicate overlap.

“This sequence can be understood in terms of the kinds of differences in predicate overlap discussed in this paper.”

The contrast between analogy and literal similarity is a continuum, not a dichotomy.

“According to this analysis, the contrast between analogy and literal similarity is a continuum, not a dichotomy.”

The mapping rules depend only on the syntax of the knowledge representation, not on its content.

“Notice that this discussion has been purely structural; the distinctions invoked rely only on the syntax of the knowledge representation, not on the content.”

Metaphors can be mixtures of relational and attribute matches.

“Moreover, metaphors can be mixtures of all of these.”

The structure-mapping theory meets the requirement that a theory of analogy specify how an analogy's interpretation is derived from the meanings of its parts.

“The structure-mapping theory satisfies the first requirement of a theory of analogy, that it describe the rules by which the interpretation of an analogy is derived from the meanings of its parts.”

Within the structure-mapping framework, a match's accessibility and its explanatory usefulness may be negatively related.

“In the structure-mapping framework, we can suggest reasons that the accessibility and the explanatory usefulness of a match may be negatively related.”

Literal similarity matches are highly accessible because they can be indexed by object descriptions, relational structures, or both.

“Literal similarity matches are highly accessible, since they can be indexed by object descriptions, by relational structures, or by both.”

Given relational overlap, two domains are more literally similar as their object attributes also overlap.

“Given that two domains overlap in relationships, they are more literally similar to the extent that their object-attributes also overlap.”

Not all relations are equally likely to be preserved in analogy.

“However, as mentioned earlier, not all relations are equally likely to be preserved.”

The mechanism that selects the initial candidate predicates for mapping considers only the structure of the two analogs' knowledge representations, not their content.

“That is, the processing mechanism that selects the initial candidate set of predicates to map attends only to the structure of the knowledge representations for the two analogs, and not to the content.”

By favoring deeply nested relational chains, the systematicity principle favors predicates that take part in causal chains and other constraint relations.

“Thus, by promoting deeply nested relational chains, the systematicity principle operates to promote predicates that participate in causal chains and in other constraint relations.”

Winston's importance-dominated matching, which counts only predicates in causal chains, is more restrictive than the structure-mapping principle that participation in any higher-order chain leads to preferential mapping.

“This requirement is somewhat more restrictive than the structure-mapping principle that participation in any higher-order chain results in preferential mapping.”

• cites Winston (1980Winston ( , 1981))Not checked yet

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A model based on the degree of featural overlap does not give a good account of analogy.

“However, although the degree-ofoverlap model appears to work well for literal similarity comparisons, it does not provide a good account of analogy.”

Once found, an analogy should be more useful for deriving key principles because its shared structure is sparse enough to analyze.

“However, once found, an analogy should be more useful in deriving the key principles, since the shared data structure is sparse enough to permit analysis.”

The order in which analogy comprehension actually proceeds is variable.

“The actual order of processing is clearly variable.”

In a complex analogy, the number of relations available for mapping is large relative to the number of object correspondences.

“This is largely because in a complex analogy, the number of mappable relations is largely compared to the number of object correspondences;”

When the assignment of objects is not specified, a hearer can use knowledge of matching relations to determine which objects correspond.

“If the object assignment is left unspecified, the hearer can use knowledge about matching relations to decide on the object correspondences.”

The other researchers' accounts are generally compatible with the structure-mapping theory across the problem domains.

“In the main, these accounts are compatible with that given by the structure-mapping theory in each of the problem domains.”

In a literal similarity comparison, all or most of the predicates shown are mapped.

“In a literal similarity comparison, all or most of the predicates shown would be mapped.”

For metaphors analyzable as analogies or combinations of analogies, the mapping rules tend to be less regular than those for analogy.

“Finally, for metaphors that are analyzable as analogies or combinations of analogies, the mapping rules tend to be less regular than those for analogy (Gentner, 1982).”

• cites Gentner, 1982Not checked yet

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Object correspondences are settled before the mapping of relations is completed.

“Therefore, it is more accurate to replace the statement that the object correspondences are decided before the relational mappings begin with the weaker statement that the object correspondences are decided before the relational mappings arefinished.”

A theory based only on the relative numbers of shared and nonshared predicates cannot adequately account for analogy or for relatedness in general.

“A theory based on the mere relative numbers of shared and non-shared predicates cannot provide an adequate account of analogy, nor, therefore, a sufficient basis for a general account of relatedness.”

Analogy is characterized by mapping relations between objects, rather than object attributes, from base to target.

“The central claims of the theory are that analogy is characterized by the mapping of relations between objects, rather than attributes of objects, from base to target;”

Relations have priority over object attributes in analogy.

“Relations have priority over object-attributes in analogy.”

Systematicity principle: a predicate that belongs to a mappable system of mutually interconnecting relationships is more likely to be imported into the target than an isolated predicate.

“To reflect this tacit preference for coherence in analogy, I propose the systematicity principle: A predicate that belongs to a mappable system of mutually interconnecting relationships is more likely to be imported into the target than is an isolated predicate.”

Higher-order relations play an important role in analogy.

“Higher-order relations play an important role in analogy, as is discussed below.”

If higher-order relations are present in the base, they can also be mapped in an analogy.

“If higher-order relations are present in the base, they can be mapped as well:”

Relations tend to be preserved across domains whose object attributes differ, as when like procedures apply to unlike sets of objects.

“Relations tend to be preserved across domains with dissimilar object-attributes: e.g., the matching of like procedures that apply to unlike sets of objects (VanLehn & Brown, 1980).”

• cites VanLehn & Brown, 1980Not checked yet

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The interpretation rules of the structure-mapping theory can be characterized purely syntactically.

“Finally, a third feature of the structure-mapping theory is that the interpretation rules are characterizable purely syntactically.”

The relations mapped in analogy are those dominated by higher-order relations that belong to the mapping, which is the systematicity claim.

“and, further, that the particular relations mapped are those that are dominated by higher-order relations that belong to the mapping (the sysfemariciry claim).”

The systematicity principle is a purely syntactic mechanism that ensures the candidate mappings are as interesting as the knowledge base permits.

“It is a purely syntactic mechanism that guarantees that the set of candidate mappings will be as interesting-in the sense that a mutually interconnected system of predicates is interesting-as the knowledge base allows.”

Winston's importance-dominated matching similarly focuses the matcher on systematic relational structures rather than on haphazard resemblances between situations.

“However, it has the similar effect of focusing the matcher on systematic relational structures rather than on haphazard resemblances between situation.”

• cites Winston (1980Winston ( , 1981))Not checked yet

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In the structure-mapping framework, the interpretation rules for analogy can be distinguished from those for other kinds of domain comparisons.

“In the structure-mapping framework, the interpretation rules for analogy can be distinguished from those for other kinds of domain comparisons.”

Stating a general law requires creating a new relational structure whose objects lack specific attributes so that the structure can apply across widely different domains.

“To state a general law requires another step beyond creating a temporary correspondence betweeen unlike domains: The person must create a new relational structure whose objects are so lacking in specific attributes that the structure can be applied across widely different domains.”

• cites Forbus & Gentner, 1983Not checked yet

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• cites Gick & Holyoak, 1980Not checked yet

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• cites Gick & Holyoak, 1983Not checked yet

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Many or most metaphors are predominantly relational comparisons and are thus essentially analogies.

“Many (perhaps most) metaphors are predominantly relational comparisons, and are thus essentially analogies.”

Additional experimental support for structure-mapping as part of interpreting complex analogies comes from developmental studies and from studies of analogy use in science learning.

“Other experimental evidence for structure-mapping as part of the psychological process of interpreting complex analogies has included developmental studies (Gentner, 1977a,b;1980b) and studies of how people use analogies in learning science (Collins & Gentner, in preparation;Gentner, 1980aGentner, , 1981;;Gentner & Gentner, 1983).”

• cites Gentner, 1977a,b;1980bNot checked yet

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• cites Collins & Gentner, in preparationNot checked yet

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• cites Gentner & Gentner, 1983Not checked yet

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The syntactic type of shared versus nonshared predicates determines whether a comparison is treated as analogy, literal similarity, or application of an abstraction.

“The syntactic type of the shared versus nonshared predicates determines whether a given comparison is thought of as analogy, as literal similarity, or as the application of an abstraction.”

Literal similarity matches are not very useful for deriving causal principles because too much overlap makes it unclear what is crucial.

“But they are not very useful in deriving causal principles, precisely because there is too much overlap to know what is crucial.”