Figure 165

The percentage of subjects making modus ponens and modus tollens inferences when given two-premise conditional or biconditional problems from Johnson-Laird, Byrne, and Schaeken (1992, Experiment 2).

explained in an alternative manner by the model theory. They have shown that the simpler problems involved inferences that could be made from initial models, whereas the difficult problems required more models to be constructed. Furthermore, they also tested a novel prediction from the model theory, that modus tollens inferences should be easier from a biconditional than a conditional interpretation of the premises, whereas the rate of modus ponens inferences should remain constant (abstract-rule theories predict no difference in either case). This result is predicted because modus ponens can be made from just one explicit model from either interpretation, whereas modus tollens requires three explicit models to be considered for the conditional and just two explicit models for the biconditional. This prediction was confirmed (see Figure 16.5).

Furthermore, Byrne and Johnson-Laird (1992) found evidence that people represent conditionals by an explicit model in which the events occur and an implicit model in which alternative events may occur. They gave subjects different versions of three assertions:

With Modal John hires a gardener. John does some gardening. John can get the grass cut.

Without Modal John hires a gardener. John does some gardening. John gets the grass cut.

in which a modal (e.g., can) was present or absent, and asked subjects to paraphrase the assertions in a single sentence. As predicted by the model theory, they found that subjects tended to use a conditional-like paraphrase to combine the three assertions when the outcome contained a modal (e.g., John can get the grass cut; 36%) rather than when it does not (e.g., John gets the grass cut, 5%). The modal cues people to think, at least implicitly, of alternative situations in which the events do not occur.

Evaluation of the model theory

The model theory is a well specified theory that has been applied to a wide range of phenomena in conditional reasoning and beyond. There have been a large number of commentaries and criticisms of the theory (see Eysenck & Keane, 1995, for an earlier summary; Andrews, 1993; Bonatti, 1994; Bundy, 1993; Evans & Over, 1996; Goldman, 1986; O'Brien, Braine, & Yang, 1994; Rips, 1984, 1986). Many of these criticisms are answered by Johnson-Laird and Byrne (1993a) in a published debate in the journal, Behavioral & Brain Sciences (see also Johnson-Laird, Byrne, & Schaeken, 1992). We will concentrate on the main outstanding theoretical and empirical criticisms.

Theoretically, Bonatti (1994) pointed out that there were several different formulations of the number of models that might be constructed for a given problem. This is a significant criticism because most of the predictions made by the model theory are based on the number of models required by a given problem (see the spatial models described earlier). If one can pick and choose the number of different models for a given problem, then the basis on which the theory makes predictions is considerably weakened. However, Johnson-Laird et al. (1994) have asserted that the number of models is based on those required to represent and evaluate the conclusion. A computer program to automatically generate the appropriate number of models for any given set of premises has also been written, which should settle this issue (Johnson-Laird & Savary, 1996).

The other main theoretical criticism is that the model theory is incomplete. First, the comprehension component of the theory is underspecified, especially with respect to the effects of background knowledge and uncertainty. Model theorists have maintained that background knowledge plays a role in constructing models of premises but they do not have a detailed account of this process. So, although they have computational models that simulate what happens in human reasoning with premises such as "if there is a circle, there is a triangle", they do not have similar models for context effects (see Byrne, 1989a). Second, they have no detailed account of how people validate models by searching for counterexamples because there is little available evidence on how people carry out this validation (see Polk, 1993; Polk & Newell, 1995; Rips, 1990). However, it should be noted that Byrne et al. (1999) have proposed that the suppression-effect experiments can be used to explore this aspect of the theory.

From an empirical perspective, the coverage of the model theory is quite good. The main outstanding criticisms seem to hinge on its ability to explain bias type effects in reasoning tasks beyond conditionals (see Evans & Over, 1996).

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