No Group of Opposition for Constructive Logics: The Intuitionistic and Linear Cases

Part of the Studies in Universal Logic book series (SUL)


The aim of this work is to show that no group of opposition can be built for constructive logics like intuitionistic or linear logics. Moreover, the attempt to apply the square of opposition to linear logic shows that the lack of subcontrariety and the asymmetry of contradiction are not equivalent properties. The former property, not the latter, is the general reason why there can be no group of opposition for constructive logics.


Square of opposition Linear logic Intuitionistic logic 

Mathematics Subject Classification

03F52 03B47 03B20 


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Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.Université Blaise PascalClermont-FerrandFrance

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