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, Citation2005).
2Some people may find it confusing that for mental model theory, the P(3rd model | 2nd model) was larger than the P(2nd model | 1st 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(1st model) ∗ P(2nd model | 1st model) ∗ P(3rd model | 2nd model).