Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/69576
Title: General patterns of opposition squares and 2n-gons
Authors: Chow, KF 
Keywords: Trichotomy
Unilateral entailment
General Pattern of Squares of Opposition
General Pattern of 2n-gons of Opposition
Issue Date: 2012
Publisher: Birkhäuser
Source: In JY Béziau & D Jacquette (Eds.), Around and beyond the square of opposition, p. 263-275. Basel: Birkhäuser, 2012 How to cite?
Abstract: In the first part of this paper we formulate the General Pattern of Squares of Opposition (GPSO), which comes in two forms. The first form is based on trichotomies whereas the second form is based on unilateral entailments. We then apply the two forms of GPSO to construct some new squares of opposition (SOs) not known to traditional logicians. In the second part of this paper we discuss the hexagons of opposition (6Os) as an alternative representation of trichotomies. We then generalize GPSO to the General Pattern of 2n-gons of Opposition (GP2nO), which also comes in two forms. The first form is based on n-chotomies whereas the second form is based on co-antecedent unilateral entailments. We finally introduce the notion of perfection associated with 2n-gons of opposition (2nOs) and point out that the fundamental difference between a SO and a 6O is that the former is imperfect while the latter is perfect. We also discuss how imperfect 2nOs can be perfected at different fine-grainedness.
URI: http://hdl.handle.net/10397/69576
ISBN: 9783034803793 (electronic bk.)
3034803796 (electronic bk.)
9783034803786
DOI: 10.1007/978-3-0348-0379-3_18
Appears in Collections:Book Chapter

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