Analogical Mapping by Constraint Satisfaction

similarity. Units not yet reached asymptote: 0 Goodness of network: 0.61 Calculating the best mappings after 72 cycles. Best mapping of SMART is HUNGRY. 0.70 Best mapping of TALL is FRIENDLY. 0.71 Best mapping of TIMID is FRISKY. 0.54 Best mopping of TOM is BLACKIE. 0.70 Best mapping of STEVE is FIDO. 0.54 Best mopping of BILL is ROVER. 0.71 by ACME for this example. The five sentences corresponding to the five propositions in each analog (e.g., “Bill is smart”) were listed in adjacent colunms on a piece of paper. Sentences related to the same individual were listed consecutively; otherwise, the order was scrambled. Across subjects two different orders were used. The instructions simply stated, “Your task is to figure out what in the left set of sentences corresponds to what in the right set of sentences.” Subjects were also told that the meaning of the words was irrelevant. The three individuals and three attributes of the analog on the left were listed on the bottom of the page; for each element, subjects were to write down what they believed to be the corresponding element of the analog on the right. Three minutes were allowed for completion of the task. A group of 8 UCLA students in an undergraduate psychology class served as subjects. Five subjects produced the same set of six correspondences identified by ACME, 2 subjects produced four of the six, and 1 subject was unable to understand the task. These results indicate that finding the isomorphism for this example is within the capability of many college students. 344 HOLYOAK AND THAGARD Structure and Pragmatics in Metaphor To explore the performance of ACME in metaphorical mapping, the program was given predicate-calculus representations of the knowledge underlying a metaphor that has been analyzed in detail by Kittay (1987). The metaphor is derived from a passage in Plato’s Theuetetus in which Socrates declares himself to be a “midwife of ideas,” elaborating the metaphor at length. Table 19 contains predicate-calculus representations based upon Kittay’s analysis of the source analog r.?ncerning the role of a midwife and of the target analog concerning the role of a philosopher-teacher. Roughly, Socrates claims that he is like a midwife in that he introduces the student to intellectual partners, just as a midwife often serves first as a matchmaker; Socrates helps the student evaluate the truth or falsity of his ideas much as a midwife helps a mother to deliver a child. This metaphor was used to provide an illustration of the manner in which structural and pragmatic constraints interact in ACME. Table 19 presents predicate-calculus representations of two versions of the metaphor: an isomorphic version based directly upon Kittay’s analysis, and a nonisomorphic version created by adding irrelevant and misleading information to the representation of the “Socrates” target analog. The best mappings obtained for each object and predicate in the target, produced by three runs of ACME, are reported in Table 20. The asymptotic activations of the best mappings are also presented. A mapping of “none” means that no mapping unit had an asymptotic activation greater than .20. The run reported in the first column used the isomorphic version without any pragmatic weights. The network settles with a correct set of mappings after 34 cycles. Thus Socrates maps to the midwife, his student o the mother, the student’s intellectual partner to the father, and the idea to the child. (Note that there is a homomorphic mapping of the predicates thinks-about and tests-truth to in-labor-with.) The propositions expressing causal relations in the two analogs are not essential here; deletion of them still allows a complete mapping to be discovered. A very different set of mappings is reported in the middle column of Table 20 for the nonisomorphic version of the “Socrates” analog. This version provides additional knowledge about Socrates that would be expected to produce major interference with discovery of the metaphoric relation between the two analogs. The nonisomorphic version contains the information that Socrates drinks hemlock juice, which is of course irrelevant to the metaphor. Far worse, the representation encodes the information that Socrates him’self was matched to his wife by a midwife; and that Socrates’ wife had a child with the help of this midwife. Clearly, this nonisomorphic extension will cause the structural and semantic constraints on mapping to support a much more superficial set of correspondences between the two situations. And indeed, in this second run ACME finds only the barest fragments of the intended metaphoric mappings when the network settles ANALOGICAL MAPPING 345 TABLE 19 Predicate-Calculus Representatlans of Knowledge Underlying the Metaphor “Socrates is a Mldwlfe of Ideas”‘(lsamarphlc and Nanlsomorphlc Verslons)