General Patterns of Opposition Squares and 2n-gons

  • Ka-fat Chow
Part of the Studies in Universal Logic book series (SUL)


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.


Trichotomy Unilateral entailment General Pattern of Squares of Opposition General Pattern of 2n-gons of Opposition 

Mathematics Subject Classification



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Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.The Hong Kong Polytechnic UniversityHong KongChina

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