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Around and Beyond the Square of Opposition

Part of the series Studies in Universal Logic pp 3-19

The New Rising of the Square of Opposition

  • Jean-Yves BéziauAffiliated withCNPq – Brazilian Research Council, UFRJ – University of Brazil Email author 

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Abstract

In this paper I relate the story about the new rising of the square of opposition: how I got in touch with it and started to develop new ideas and to organize world congresses on the topic with subsequent publications. My first contact with the square was in connection with Slater’s criticisms of paraconsistent logic. Then by looking for an intuitive basis for paraconsistent negation, I was led to reconstruct S5 as a paraconsistent logic considering ¬□ as a paraconsistent negation. Making the connection between ¬□ and the O-corner of the square of opposition, I developed a paraconsistent star and hexagon of opposition and then a polyhedron of opposition, as a general framework to understand relations between modalities en negations. I also proposed the generalization of the theory of oppositions to polytomy. After having developed all this work I have begun to promote interdisciplinary world events on the square of opposition.

Keywords

Square of opposition Paraconsistent logic Negation Modal logic

Mathematics Subject Classification

03B53 03B45 03B20 03B22