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ISIPTA'07 -
FIFTH INTERNATIONAL SYMPOSIUM ON

IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS

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Charles University, Faculty of Mathematicsand Physics

Prague, Czech Republic

16-19 July 2007

## ELECTRONIC PROCEEDINGS

## Niki Pfeifer, Gernot Kleiter

# Human reasoning with imprecise probabilities: Modus ponens and Denying the antecedent

### Abstract

The 'modus ponens' is, along with 'modus tollens' and the two logically not valid counterparts 'denying the antecedent' and 'affirming the consequent', the argument form that was most often investigated in the psychology of human reasoning. The present contribution reports the results of three experiments on the probabilistic versions of 'modus ponens' and 'denying the antecedent'. In probability logic these arguments lead to conclusions with imprecise probabilities.
In the 'modus ponens' tasks the participants inferred probabilities that agreed much better with the coherent normative values than in the 'denying the antecedent' tasks, a result that mirrors results found with the classical argument versions. For 'modus ponens' a surprisingly high number of lower and upper probabilities agreed perfectly with the conjugacy property (upper probabilities equal one complements of the lower probabilities). When the probabilities of the premises are imprecise the participants do not ignore irrelevant ('silent') boundary probabilities. The results show that human mental probability logic is close to predictions derived from probability logic for the most elementary argument form, but has considerable difficulties with the more complex forms involving negations.

** Keywords. ** mental probability logic, modus ponens, coherence, imprecise probabilities

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** Authors addresses: **

Niki Pfeifer

Department of Psychology

University of Salzburg

Hellbrunnerstrasse 34

A-5020 Salzburg

Gernot Kleiter

Institut für Psychologie Universität Salzburg

Hellbrunnerstr. 34,A-5020,Salzburg,

Austria

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