Transitive reasoning with imprecise probabilities
This work addresses foundational issues in probabilistic reasoning for AI and decision-making, but it appears incremental as it builds on existing theories of coherence and imprecise probabilities.
The paper tackles the problem of reasoning with imprecise probabilities by developing a framework for probabilistically informative weak transitivity, using coherence and imprecise probabilities to represent p-consistent sequences and prove coherent probability propagation rules for Weak Transitivity and selected inference patterns.
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.