Chapter

Around and Beyond the Square of Opposition

Part of the series Studies in Universal Logic pp 201-217

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

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Abstract

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.

Keywords

Square of opposition Linear logic Intuitionistic logic

Mathematics Subject Classification

03F52 03B47 03B20