Reasoning with three Types of Conditional: Biases and Mental Models

Two experiments are reported which compare conditional reasoning with three types of rule. These consist of two types of rule that have been widely studied previously, if p then q and p only if q, together with a third type, q if p. In both experiments, the p only if q type of rule yields a different pattern of performance from the two other types of rule. Experiment 1 is an abstract rule-evaluation task and demonstrates differential effects of temporal order and of suppositional bias. Experiment 2 investigates rule generation, rephrasing, and comparison, and demonstrates differential effects of temporal order and of thematic content. An analysis of the results is offered in terms of biases and mental models. Effects of rule form and context can be explained as reflecting the different sequences in which mental models are created for each rule form. However, it is necessary to consider the internal structure of individual mental models to account for effects arising from temporal ordering of rules.

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Dual processes and mental models in the development of conditional reasoning

The Development of Thinking and Reasoning ◽

10.4324/9780203068748-13 ◽

2013 ◽

pp. 107-133

Keyword(s):

Mental Models ◽

Conditional Reasoning ◽

Dual Processes

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On the Mental Representation of Conditional Sentences

The Quarterly Journal of Experimental Psychology Section A ◽

10.1080/713755667 ◽

1996 ◽

Vol 49 (4) ◽

pp. 1086-1114 ◽

Cited By ~ 10

Author(s):

Jonathan St. B. T. Evans ◽

Charles E. Ellis ◽

Stephen E. Newstead

Keyword(s):

Mental Models ◽

Research Methods ◽

Mental Representation ◽

Conditional Reasoning ◽

Strong Tendency ◽

Inference Rules ◽

Counter Example ◽

First Finding ◽

Blue Triangle ◽

Conditional Statements

Four experiments are reported which attempt to externalize subjects’ mental representation of conditional sentences, using novel research methods. In Experiment 1, subjects were shown arrays of coloured shapes and asked to rate the degree to which they appeared to be true of conditional statements such as “If the figure is green then it is a triangle”. The arrays contained different distributions of the four logically possible cases in which the antecedent or consequent is true or false: TT, TF, FT, and FF. For example, a blue triangle would be FT for the conditional quoted above. In Experiments 2 to 4, subjects were able to construct their own arrays to make conditionals either true or false with any distribution of the four cases they wished to choose. The presence and absence of negative components was varied, as was the form of the conditional, being either “if then” as above or “only if”: “The figure is green only if it is a triangle”. The first finding was that subjects represent conditionals in fuzzy way: conditionals that include some counter-example TF cases (Experiment 1) may be rated as true, and such cases are often included when subjects construct an array to make the rule true (Experiments 2 to 4). Other findings included a strong tendency to include psychologically irrelevant FT and FF cases in constructed arrays, presumably to show that conditional statements only apply some of the time. A tendency to construct cases in line with the “matching bias” reported on analogous tasks in the literature was found, but only in Experiment 4, where the number of symbols available to construct each case was controlled. The findings are discussed in relation to the major contemporary theories of conditional reasoning based upon inference rules and mental models, neither of which can account for all the results.

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