Uncertain deductive reasoning

In K. Manktelow, D. E. Over & S. Elqayam (eds.), The Science of Reason: A Festschrift for Jonathan St B.T. Evans. Psychology Press. 145--166 (2011)
Abstract
Probabilistic models have started to replace classical logic as the standard reference paradigm in human deductive reasoning. Mental probability logic emphasizes general principles where human reasoning deviates from classical logic, but agrees with a probabilistic approach (like nonmonotonicity or the conditional event interpretation of conditionals). This contribution consists of two parts. In the first part we discuss general features of reasoning systems including consequence relations, how uncertainty may enter argument forms, probability intervals, and probabilistic informativeness. These concepts are of central importance for the psychological task analysis. In the second part we report new experimental data on the paradoxes of the material conditional, the probabilistic modus ponens, the complement task, and data on the probabilistic truth table task. The results of the experiments provide evidence for the hypothesis that people represent indicative conditionals by conditional probability assertions.
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