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Structural Completeness in Relevance Logics

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Abstract

It is proved that the relevance logic \({\mathbf{R}}\) (without sentential constants) has no structurally complete consistent axiomatic extension, except for classical propositional logic. In fact, no other such extension is even passively structurally complete.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Pretoria, Private Bag X20, Hatfield, Pretoria, 0028, South Africa

    J. G. Raftery

  2. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland

    K. Świrydowicz

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  1. J. G. Raftery
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  2. K. Świrydowicz
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Correspondence to J. G. Raftery.

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Raftery, J.G., Świrydowicz, K. Structural Completeness in Relevance Logics. Stud Logica 104, 381–387 (2016). https://doi.org/10.1007/s11225-015-9644-x

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