Strategies in Syllogistic Reasoning

Abstract

This paper is about syllogistic reasoning, i.e., reasoning from such pairs of premises as, All the chefs are musicians; some of the musicians are painters. We present a computer model that implements the latest account of syllogisms, which is based on the theory of mental models. We also report four experiments that were designed to test this account. Experiments 1 and 2 examined the strategies revealed by the participants' use of paper and pencil as aids to reasoning. Experiment 3 used a new technique to externalize thinking. The participants had to refute, if possible, putative conclusions by constructing external models that were examples of the premises but counterexamples of the conclusions. Experiment 4 used the same techniques to examine the participants' strategies as they drew their own conclusions from syllogistic premises. The results of the experiments showed that individuals not trained in logic can construct counterexamples, that they use similar operations to those implemented in the computer model, but that they rely on a much greater variety of interpretations of premises and of search strategies than the computer model does. We re-evaluates current theories of syllogistic reasoning in the light of these results.

Logic, probability, and human reasoning

“…Hence, there are 64 possible pairs of premise: 27 of them yield valid deductions interrelating the end terms and 31 yield p-valid inferences [114]. Syllogisms vary vastly in difficulty: 7-yearold children can cope with the easiest, whereas adults struggle with the hardest [88]. Given the premises above, many reasoners infer:…”

Matching bias in syllogistic reasoning: Evidence for a dual-process account from response times and confidence ratings

“…Both theories are based on the principle that the surface features of problems determine responses, with no particular expectations arsing for differential processing times for different problems. In contrast, for theories that emphasise analytic processes such as the mental models theory (e.g., Bucciarelli & Johnson-Laird, 1999) and the mental logic theory (Rips, 1994), decisions about conclusion validity are primarily made on the basis of mental representations of the underlying logical structure of problems (note, however, that mental models theory includes heuristic processes, particularly in the initial stages of model formation and, as such, can be considered a dual-process theory; see Johnson-Laird, 1983). Unlike surface feature theories, analytic theories make predictions regarding differential processing times for different problem types.…”

The role of cognitive and socio-cognitive conflict in learning to reason

“…However, think-aloud protocols suggest the use of mental models in reasoning (see also Bucciarelli and Johnson-Laird 1999).…”

“…Indirect evidence that people tend not to falsify within the syllogistic domain is that they perform better and faster in tasks requiring the construction of only one model than in tasks requiring two or more models (Bucciarelli and Johnson-Laird 1999); moreover, invalid conclusions very often correspond to those which can be inferred from the first model constructed (see Bara et al 1995Bara et al , 2001. Bucciarelli and Johnson-Laird (1999) also find that, when dealing with syllogisms, individuals not trained in logic may search for alternative models if forced to do so, though they are less likely to search for counterexamples if the task does not explicitly request them to do so. However, at least within the domain of reasoning with non-standard quantifiers, Neth and Johnson-Laird (1999) find that individuals seem to search for counterexamples spontaneously.…”