Mental model construction in linear reasoning: Evidence for the construction of initial annotated models

Abstract

According to the mental model theory, reasoners build an initial model representing the information given in the premises. In the context of relational reasoning, the question arises as to which kind of representation is used to cope with indeterminate or multimodel problems. The present article presents an array of possible answers arising from the initial construction of complete explicit models, partial explicit models, partial implicit models, a single "isomeric" model, or a single annotated model. Predictions generated from these views are tested in two experiments that vary the problem structure and the number of models consistent with the premises. Analyses of the premise processing times, answering times and accuracy show that the annotated model yields the best fit of the data. Implications of these findings for the mental model theory as developed for relational reasoning are discussed.In linear syllogisms such as George is heavier than Tony and Tony is heavier than Jacques, people easily infer that George is heavier than Jacques. The findings collected in numerous studies substantiate the hypothesis that people solve such problems by constructing a linear array with the largest values at the top and the smallest ones at the bottom or alternatively by constructing a left-to-right array (see, e.g., De Soto, London, & Handel, 1965;Huttenlocher, 1968;Potts, 1974). The review by Evans, Newstead, and Byrne (1993, chap. 6) shows that this view yields the best summary of the findings reported in the literature. The usage of such an integrated spatial representation seems to be independent of the relational content and works both for determinate problems (as in the example above) and for indeterminate problems as, for example, in George is heavier than Jacques and George is heavier than Tony, where the relation between Jacques and Tony remains unresolved. Support for all this has been accumulated in

Mental models and human reasoning

“…In contrast, inferences about the relation between D and E become much harder when a description is consistent with two different layouts, which call either for two models, or at least some way to keep track of the spatial indeterminacy (30)(31)(32). Yet, such descriptions can avoid the need for an initial transitive inference, and so mental logic fails to make the correct prediction.…”

Preferred mental models in reasoning about spatial relations

“…Schaeken, van der Henst, & Schroyens, 2007;Vandierendonck, Dierckx, & De Vooght, 2004). The result of chunking is to reduce the number of possibilities that need to be kept in mind.…”

Is model construction open to strategic decisions? An exploration in the field of linear reasoning

“…On average 77% of the responses of the participants in this group were in accordance with this ordering. The remaining 42% of the participants could be partitioned as follows: 13% constructed two separate models, 13% constructed an isomeric or annotated model (revealed by mentioning an "or" between the last two premise terms or by leaving some time between the encoding of the first three premise terms and the last two terms), and 16% constructed a model of the first four premise terms and added a mini-string (see Vandierendonck, Dierckx, & De Vooght, 2002) comprising the premise term that is repeated and the last term. Only in the last group did two participants consistently respond to the indeterminate conclusions as if the order was an ABCDE order.…”