Elsevier

Journal of Applied Logic

Volume 14, March 2016, Pages 46-64
Journal of Applied Logic

Transitivity in coherence-based probability logic

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Abstract

We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent p-consistent sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Moreover, we prove the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases. Finally, we apply our results to study selected probabilistic versions of classical categorical syllogisms and construct a new version of the square of opposition in terms of defaults and negated defaults.

Keywords

Coherence
Defaults
Generalized coherence
Imprecise probability
p-Consistency
p-Entailment
Probability logic
Square of opposition
Syllogisms
Transitivity

Cited by (0)

This paper is a revised and substantially extended version of [22]. The authors are listed alphabetically.

1

Supported by the DFG grants PF 740/2-1 and PF 740/2-2 (both within the DFG Priority Programme SPP1516) and the Alexander von Humboldt Foundation.

2

Supported by the INdAM–GNAMPA Project 2015 grant U 2015/000418.

3

These authors share equal first authorship on this work (main contribution).