On a General Bayesian Pattern Logic of Frequency-Based Logical Inclusion Fallacies

Abstract

Bayesian logic provides a rational model of probability judgments deviating from the standard extensional norm of extensional probability. It formalizes the general idea of an inductive pattern logic that may resolve paradoxes of inclusion. Bayesian logic predicts that it should be possible to generalize the phenomenon of frequency-based logical conjunction fallacies to a system of logical inclusion fallacies. In Experiment 1 quantitative conditions for conjunction fallacies and the role of negations are investigated. Experiment 2 provides a first test of the postulated more general system of logical inclusion fallacies. The results of both experiments confirmed the proposed pattern logic and its formalization as Bayesian logic. Other theories of the conjunction fallacy cannot readily explain this class of frequency-based and pattern-based inclusion fallacies. Whether there are simpler heuristics that may perhaps explain these data as well should be investigated in the future.

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