How to eliminate illusions in quantified reasoning

Immediate inferences from quantified assertions

We propose a theory of immediate inferences from assertions containing a single quantifier, such as: All of the artists are bakers; therefore, some of the bakers are artists. The theory is based on mental models and is implemented in a computer program, mReasoner. It predicts three main levels of increasing difficulty: (a) immediate inferences in which the premise and conclusion have identical meanings; (b) those in which the initial mental model of the premise yields the correct conclusion; and (c) those in which only an alternative to the initial model establishes the correct conclusion. These levels of difficulty were corroborated for inferences to necessary conclusions (in a reanalysis of data from Newstead, S. E., & Griggs, R. A. (1983). Drawing inferences from quantified statements: A study of the square of opposition. Journal of Verbal Learning and Verbal Behavior, 22, 535–546), for inferences to modal conclusions, such as, it is possible that all of the bakers are artists (Experiment 1), for inferences with unorthodox quantifiers, such as, most of the artists (Experiment 2), and for inferences about the consistency of pairs of quantified assertions (Experiment 3). The theory also includes three parameters in a stochastic system that predicted quantitative differences in accuracy within the three main sorts of inference.

Deductive reasoning

This article begins with an account of logic, and of how logicians formulate formal rules of inference for the sentential calculus, which hinges on analogs of negation and the connectives if, or, and and. It considers the various ways in which computer scientists have written programs to prove the validity of inferences in this and other domains. Finally, it outlines the principal psychological theories of how human reasoners carry out deductions. Copyright © 2009 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website.

Naïve deontics: a theory of meaning, representation, and reasoning

Deontic assertions concern what one ought to do, may do, and ought not to do. This paper proposes a theory of their meanings and of how these meanings are represented in mental models. The meanings of deontic assertions refer to sets of permissible and impermissible states. An experiment corroborated the ability of individuals to list these states. The most salient were those corresponding to the mental models of the assertions. When individuals reason, they rely on mental models, which do not make all states explicit. The theory predicts the most frequent conclusions drawn from deontic premises. It also predicts the occurrence of illusory inferences from assertions of permission, i.e., inferences that seem highly plausible but that are in fact invalid. Assertions of prohibitions, according to the theory, should reduce the illusions. Further experiments corroborated these predictions.