Aristotelian and Duality Relations Beyond the Square of Opposition

  • Lorenz DemeyEmail author
  • Hans Smessaert
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10871)


Nearly all squares of opposition found in the literature represent both the Aristotelian relations and the duality relations, and exhibit a very close correspondence between both types of logical relations. This paper investigates the interplay between Aristotelian and duality relations in diagrams beyond the square. In particular, we study a Buridan octagon, a Lenzen octagon, a Keynes-Johnson octagon and a Moretti octagon. Each of these octagons is a natural extension of the square, both from an Aristotelian perspective and from a duality perspective. The results of our comparative analysis turn out to be highly nuanced.


Aristotelian relations Duality relations Square of opposition Aristotelian diagram Duality diagram Logical geometry 



We would like to thank Margaux Smets and three anonymous reviewers for their valuable feedback. The first author holds a Postdoctoral Fellowship of the Research Foundation–Flanders (FWO).


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Authors and Affiliations

  1. 1.Center for Logic and Analytic PhilosophyKU LeuvenLeuvenBelgium
  2. 2.Department of LinguisticsKU LeuvenLeuvenBelgium

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