Probabilistic squares and hexagons of opposition under coherence
Probability
2017-10-13 v1 Logic
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
Cite
@article{arxiv.1701.07306,
title = {Probabilistic squares and hexagons of opposition under coherence},
author = {Niki Pfeifer and Giuseppe Sanfilippo},
journal= {arXiv preprint arXiv:1701.07306},
year = {2017}
}