A mental model theory of set membership

Sangeet KhemlaniNaval Research Laboratory, Washington, DC, USA
Max LotsteinUniversity of Freiburg
Phil Johnson-LairdPrinceton University / New York University

Abstract

Assertions of set membership, such as "Amy is an artist", should not be confused with those of set inclusion, such as "All artists are bohemians." Membership is not a transitive relation, whereas inclusion is. Cognitive scientists have neglected the topic, and so we developed a theory of inferences yielding conclusions about membership, e.g., "Amy is a bohemian," and about non-membership, "Abbie is not an artist." The theory is implemented in a computer program, mReasoner, and it is based on mental models. The theory predicts that inferences that depend on a search for alternative models should be more difficult than those that do not. An experiment corroborated this prediction. The program contains a parameter, σ, which determines the probability of searching for alternative models. A search showed that its optimal value of .58 yielded a simulation that matched the participant's accuracy in making inferences. We discuss the results as a step towards a unified theory of reasoning about sets.

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