Theories of categorical reasoning and extended syllogisms

Abstract

The aim of this study was to examine the predictions of three theories of human logical reasoning, (a) mental model theory, (b) formal rules theory (e.g., PSYCOP), and (c) the probability heuristics model, regarding the inferences people make for extended categorical syllogisms. Most research with extended syllogisms has been restricted to the quantifier “All” and to an asymmetrical presentation. This study used three-premise syllogisms with the additional quantifiers that are used for traditional categorical syllogisms as well as additional syllogistic figures. The predictions of the theories were examined using overall accuracy as well as a multinomial tree modelling technique. The results demonstrated that all three theories were able to predict response selections at high levels. However, the modelling analyses showed that the probability heuristics model did the best in both Experiments 1 and 2.

Notes

¹The construction of mental models can be interpreted as being much more complex than the simple idea of constructing one versus two versus three models. However, the fleshing out of the specific aspects of model construction is beyond the scope of this paper. There is a parameterised computational version of mental model theory that is currently being developed which considers the processes involved with constructing mental models in detail (see Copeland & Radvansky, 2005).

²Some people may find it confusing that for mental model theory, the P(3^rd model | 2^nd model) was larger than the P(2^nd model | 1^st model). However, as explained earlier, these are conditional probabilities, not simply the probabilities of constructing a third versus a second model. The actual probability of constructing a third model is equal to P(1^st model) ∗ P(2^nd model | 1^st model) ∗ P(3^rd model | 2^nd model).

Additional information

Notes on contributors

David E. Copeland

I would like to thank Seth Allen for his assistance in collecting the data. I also wish to thank Steve Boker, Darcia Narvaez, Mike Oaksford, Michael Wenger, two anonymous reviewers, and especially G. A. Radvansky, for their insightful comments throughout this research project. Portions of this research were supported in part by a grant from the Army Research Institute, ARMY-DASW01-99-K-0001.