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Studia Logica

, Volume 102, Issue 1, pp 185–217 | Cite as

Curry’s Paradox, Generalized Modus Ponens Axiom and Depth Relevance

  • Gemma Robles
  • José M. Méndez
Article

Abstract

“Weak relevant model structures” (wr-ms) are defined on “weak relevant matrices” by generalizing Brady’s model structure \({\mathcal{M}_{\rm CL}}\) built upon Meyer’s Crystal matrix CL. It is shown how to falsify in any wr-ms the Generalized Modus Ponens axiom and similar schemes used to derive Curry’s Paradox. In the last section of the paper we discuss how to extend this method of falsification to more general schemes that could also be used in deriving Curry’s Paradox.

Keywords

Curry’s Paradox Depth Relevance Generalized Modus Ponens axiom Generalized Contraction rule Weak relevant model structures Relevant logic 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Dpto. de Psicología, Sociología y FilosofíaUniversidad de LeónLeónSpain
  2. 2.Universidad de SalamancaSalamancaSpain

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