Authors
Niki Pfeifer
Universität Regensburg
Giuseppe Sanfilippo
Università degli Studi di Palermo
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.
Keywords coherence  conditional events  hexagon of opposition  imprecise probability   square of opposition  quantified sentences  tripartition
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