Various semantics for studying the square of opposition have been proposed recently. So far, only (Gilio et al., 2016) 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.
Pfeifer, N., Sanfilippo, G. (2017). Square of Opposition Under Coherence. In Maria Brigida Ferraro, Paolo Giordani, Barbara Vantaggi, Marek Gagolewski, María Angeles Gil, Przemysław Grzegorzewski, et al. (a cura di), Soft Methods for Data Science (pp. 407-414). Springer International Publishing [10.1007/978-3-319-42972-4_50].
Square of Opposition Under Coherence
SANFILIPPO, Giuseppe
2017-01-01
Abstract
Various semantics for studying the square of opposition have been proposed recently. So far, only (Gilio et al., 2016) 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.File | Dimensione | Formato | |
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