Probabilistic squares and hexagons of opposition under coherence

Pfeifer, Niki; Sanfilippo, Giuseppe (2017): Probabilistic squares and hexagons of opposition under coherence. In: International Journal of Approximate Reasoning, Vol. 88: pp. 282-294

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 on a finite sequence of conditional events. Finally, as an application, we present new versions of the square and of the hexagon involving generalized quantifiers.

• Item Type: Journal article
• Faculties: Philosophy, Philosophy of Science and Religious Science > Chair of Logic and Philosophy of Language
• Subjects: 100 Philosophy and Psychology > 100 Philosophy
• ISSN: 0888-613X
• Language: English