6533b858fe1ef96bd12b593d

RESEARCH PRODUCT

Transitivity in coherence-based probability logic

Angelo GilioGiuseppe SanfilippoNiki Pfeifer

subject

Square of oppositionSettore MAT/06 - Probabilita' E Statistica MatematicaTheoretical computer scienceLogicInferenceSquare of oppositionProbability logicSettore M-FIL/02 - Logica E Filosofia Della Scienza02 engineering and technologyComputer Science::Artificial Intelligence0603 philosophy ethics and religion0202 electrical engineering electronic engineering information engineeringGeneralized coherenceCategorical variableMathematicsTransitivityTransitive relationApplied MathematicsDefaultProbabilistic logicSyllogism06 humanities and the artsCoherence (statistics)Settore MAT/01 - Logica MatematicaImprecise probabilityp-EntailmentSyllogism060302 philosophyImprecise probabilityp-Consistency020201 artificial intelligence & image processingCoherenceAlgorithm

description

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.

yearjournalcountryeditionlanguage
2016-03-01Journal of Applied Logic
https://doi.org/10.1016/j.jal.2015.09.012