Beyond syllogisms: new computational theory in Psych Review on how people reason about properties

Phil Johnson-Laird and I describe an advance to the theory of mental models in a new paper out in Psychological Review. The theory and its computational model explain how people reason about inferences involving properties. Aristotle analyzed a small subset of these inferences, called categorical syllogisms, and psychologists have proposed more than a dozen theories that describe that subset. But syllogisms are just one form of reasoning about properties. Reasoners untrained in logic can make immediate inferences, too, e.g., No artists are Virginian, therefore none of the Virginians are artists. Likewise, they can make inferences about set membership, e.g., Max is a Virginian. No artists are Virginian. Therefore, Max is not an artist.

The new theory and its dual-process computational model — mReasoner — explain over 200 sorts of inference about properties. mReasoner can simulate individual differences in reasoning; it can explain why reasoners make mistakes; and it can explain how they recover from those mistakes.

The abstract of the paper is available here:

We present a theory of how people reason about properties. Such inferences have been studied since Aristotle’s invention of Western logic. But, no previous psychological theory gives an adequate account of them, and most theories do not go beyond syllogistic inferences, such as: All the bankers are architects; Some of the chefs are bankers; What follows? The present theory postulates that such assertions establish relations between properties, which mental models represent in corresponding relations between sets of entities. The theory combines the construction of models with innovative heuristics that scan them to draw conclusions. It explains the processes that generate a conclusion from premises, decides if a given conclusion is necessary or possible, assesses its probability, and evaluates the consistency of a set of assertions. A computer program implementing the theory embodies an intuitive system 1 and a deliberative system 2, and it copes with quantifiers such as more than half the architects. It fit data from over 200 different sorts of inference, including those about the properties of individuals, the properties of a set of individuals, and the properties of several such sets in syllogisms. Another innovation is that the program accounts for differences in reasoning from one individual to another, and from one group of individuals to another: some tend to reason intuitively but some go beyond intuitions to search for alternative models. The theory extends to inferences about disjunctions of properties, about relations rather than properties, and about the properties of properties.

And the paper is available for download here. Its computational modeling code + data are available here.

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