Transitive reasoning with imprecise probabilities

TL;DR

This paper explores weak forms of transitivity in probabilistic reasoning using imprecise probabilities, establishing coherence-based inference rules and probability propagation methods for default sequences.

Contribution

It introduces a coherence-based framework for weak transitivity with imprecise probabilities, including new inference rules and p-entailment results.

Findings

Proved probability propagation rules for Weak Transitivity.

Established p-entailment for default sequences.

Validated inference patterns in imprecise probabilistic logic.

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. Finally, we prove the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving the p-entailment for the associated knowledge bases.