Probabilistic squares and hexagons of opposition under coherence

Abstract

Various semantics for studying the square of opposition and the hexagon of opposition have been proposed recently. We interpret sentences by imprecise (set-valued) probability assessments on a finite sequence of conditional events. We introduce the acceptability of a sentence within coherence-based probability theory. We analyze the relations of the square and of the hexagon in terms of acceptability. Then, we show how to construct probabilistic versions of the square and of the hexagon of opposition by forming suitable tripartitions of the set of all coherent assessments. Finally, as an application, we present new versions of the square and of the hexagon involving generalized quantifiers.

References in corpus (4)

• Probabilistic entailment in the setting of coherence: The role of quasi conjunction and inclusion relation
• Reassessing Accuracy Rates of Median Decisions
• 2-coherent and 2-convex Conditional Lower Previsions
• Transitive reasoning with imprecise probabilities

Cited by in corpus (6)

• Probabilities of conditionals and previsions of iterated conditionals
• Probabilistic inferences from conjoined to iterated conditionals
• Compound conditionals, Fréchet-Hoeffding bounds, and Frank t-norms
• Algebraic aspects and coherence conditions for conjoined and disjoined conditionals
• Interpreting connexive principles in coherence-based probability logic
• On Trivalent Logics, Compound Conditionals, and Probabilistic Deduction Theorems