Preferred Mental Models in Spatial Reasoning

Preferred Mental Models in Spatial Reasoning Georg Jahn (georg.jahn@cognition.uni-freiburg.de) Center for Cognitive Science, Friedrichstrasse 50 D-79098 Freiburg, Germany Markus Knauff (markus.knauff@cognition.iig.uni-freiburg.de) Center for Cognitive Science, Friedrichstrasse 50 D-79098 Freiburg, Germany P. N. Johnson-Laird (phil@princeton.edu) Department of Psychology, Green Hall Princeton, NJ 08544 USA Abstract The assessment of whether a statement is consistent with what has gone before is ubiquitous in discourse comprehension. One theory of the process is that individuals search for a mental model of a situation in which all the statements in the discourse are true. In the case of spatial descriptions, individuals should prefer to construct models that retain the information in the description. Hence, they should use strategies that retain information in an efficient way. If the descriptions are consistent with multiple models then they are likely to run into difficulties. We report two experiments in which the participants judged the consistency of spatial descriptions. The participants made more errors when later assertions in the description conflicted with the preferred models of earlier assertions. The results shed light on the sequential integration of relational assertions, and they show that participants exploit implicit constraints for strategical chunking. Reasoning with Relations When we think about which alternative to choose, we often integrate relational information. For example, before buying a camera you might read several published tests that each ranks cameras. One test might tell you that camera A is better than camera B, another that camera B is better than camera C. You can easily infer that camera A is also better than camera C. The predominant strategy to draw such transitive inferences is to integrate relations in a mental representation – an idea that goes back to William James and was revived by De Soto, London, and Handel (1965) and Huttenlocher (1968). Relational assertions are interpreted by constructing a spatial representation (a mental model) that serves as a structural analog of the situation under description and that supports inferences (Johnson- Laird, 1983). Neuroimaging studies (e.g., Knauff, Fangmeier, Ruff, & Johnson-Laird, 2003) have confirmed the involvement of spatial representations in relational reasoning. Verbal processes in reasoning with relational assertions (cf. Clark, 1969) may be a precursor to the construction of models. But, the use of mental logic (Rips, 1994) has received less empirical support. The difficulty of relational reasoning problems varies with the number of possible interpretations. The camera tests in the example yield a determinate ordering of the cameras: A B C. However, a third test might tell you that camera D is better than camera B and consequently, camera A or camera D might be the best. There are two possible rank orders, ADBC and DABC, but the tests are not inconsistent. Hence, the information is indeterminate. With an indeterminate set of assertions, multiple possibilities have to be considered to validate a general conclusion. Multiple model problems are reliably harder than single model problems in relational reasoning. The general fact that individuals have difficulty in keeping track of multiple possibilities holds across a range of deductive reasoning tasks (Goodwin & Johnson-Laird, 2005). The multiple models of an indeterminate set of assertions might be narrowed down by further information. Imagine that in order to arrive at a decision between camera A and camera D, you head for a shop. You ask a sales assistant and learn that they do not sell camera A, but that camera C is better than camera D in any case. This is interesting, because this assertion is inconsistent with what you have read about the tests. According to the model theory, individuals notice such inconsistencies because they sequentially integrate assertions in a mental model, searching for a possibility in which all the asserted relations are true (Johnson-Laird, Legrenzi, Girotto, & Legrenzi, Multiple possibilities are on the same footing logically, but they might not be equally obvious. In the introductory example, the information in the first two tests that yielded the ordering: A B C, can be summarized as “Camera B is between camera A and camera C,” where it is clear from the context that camera A is the best. However, in isolation such an assertion is indeterminate. For example, if a grocer gives his apprentice three crates and tells him to put the apples between the oranges and the grapes, he probably does not care whether the oranges end up to the left or to the right of the apples. If it matters, then a further assertion or the context itself may eliminate one possibility. Otherwise,