Square of Opposition Under Coherence

Pfeifer, Niki and Sanfilippo, Giuseppe (2017): Square of Opposition Under Coherence. In: Soft Methods for Data Science, Vol. 456: pp. 407-414

Abstract

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.

• Item Type: Journal article
• Faculties: Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP)
• Subjects: 100 Philosophy and Psychology > 100 Philosophy; 500 Science > 510 Mathematics
• ISSN: 2194-5357
• Language: English