Search results for "t-coherence"

Square of Opposition Under Coherence

2016

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 qu…

Imprecise probability assessments and the Square of Opposition

There is a long history of investigations on the square of opposition spanning over two millenia. A square of opposition represents logical relations among basic sentence types in a diagrammatic way. The basic sentence types, traditionally denoted by A (universal affirmative: ''Every S is P''), E (universal negative: ''No S is P''), I (particular affirmative: ''Some S are P''), and O (particular negative: ''Some S are not P''), constitute the corners of the square, and the logical relations--contradiction, contrarity, subalternation, and sub-contrarity--form the diagonals and the sides of the square. We investigate the square of opposition from a probabilistic point of view. To manage impre…