The Model Theory Of Reasoning

• Reasoning involves three processes: the comprehension of premises to form a model (or set of models); the combining and description of models to produce a conclusion; and the validation of this conclusion by eliminating alternative models of the premises that show the putative condusion to be false (i.e., the search for counterexamples).

• In comprehending premises, semantic procedures are used to construct models taking background knowledge into account; the models are specific (they do not contain variables but specific mental tokens) and can be visually imagined, although they are not necessarily visual images.

• The models of premises are combined to form an integrated model (or set of models) and then this model is described in a parsimonious fashion to arrive at a conclusion.

• The validation of this conclusion Involves a search for counterexamples or alternative models in which all the premises are true and the putative conclusion false; if there are no such models, the conclusion is valid; if a model is found that falsifies the conclusion, then the ideal reasoner should attempt to discover whether there is any conclusion that is true in all the constructed models.

• Given the limited nature of working memory, several assumptions art made : (i) an inference will be more difficult if it can only be generated using several explicit models, (ii) an inference that can be made from initial models will be easier than one that can only be made from "fleshing out" implicit models, (iii) it takes time to detect inconsistencies between elements in a model.

• Errors may arise when conclusions are made from (i) initial models that have not been rigorously evaluated, or (ii) implicit models that have not been fleshed out sufficiently.

fashion, how this theory is applied to spatial reasoning. Consider how it has been applied to conditional reasoning.

Valid inferences in the model theory

Johnson-Laird and Byrne (1991; Byrne & Johnson-Laird, 1992; Johnson-Laird, Byrne, & Schaeken, 1992) have proposed a model theory of conditional reasoning. In this theory, a conditional premise like "If there is a circle then there is a triangle" is represented explicitly by the following three models:

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