In M. B. Ferraro, Alessandro Giordani, B. Vantaggi, M. Gagolewski, M. Á Gil, P. Grzegorzewski & O. Hryniewicz (eds.), Soft Methods for Data Science. Cham, Switzerland: pp. 407-414 (2017)

Niki Pfeifer
Universität Regensburg
Giuseppe Sanfilippo
Università degli Studi di Palermo
Various semantics for studying the square of opposition have been proposed recently. So far, only [14] studied a probabilistic version of the square where the sentences were interpreted by (negated) defaults. We extend this work by interpreting sentences by imprecise (set-valued) probability assessments on a sequence of conditional events. We introduce the acceptability of a sentence within coherence-based probability theory. We analyze the relations of the square in terms of acceptability and show how to construct probabilistic versions of the square of opposition by forming suitable tripartitions. Finally, as an application, we present a new square involving generalized quantifiers.
Keywords Generalized Quantifier  Conditional Event  Logical Relation  Probability Assessment  Probabilistic Version
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Counterfactuals.David Lewis - 1973 - Foundations of Language 13 (1):145-151.

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