Studia Logica

, Volume 103, Issue 6, pp 1303–1311 | Cite as

The Faithfulness of Fat: A Proof-Theoretic Proof

  • Fernando Ferreira
  • Gilda FerreiraEmail author


It is known that there is a sound and faithful translation of the full intuitionistic propositional calculus into the atomic polymorphic system F at, a predicative calculus with only two connectives: the conditional and the second-order universal quantifier. The faithfulness of the embedding was established quite recently via a model-theoretic argument based in Kripke structures. In this paper we present a purely proof-theoretic proof of faithfulness. As an application, we give a purely proof-theoretic proof of the disjunction property of the intuitionistic propositional logic in which commuting conversions are not needed.


Predicative polymorphism Faithfulness Natural deduction Strong normalization Intuitionistic propositional calculus Disjunction property 


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Departamento de MatemáticaFaculdade de Ciências da Universidade de LisboaLisbonPortugal
  2. 2.Departamento de MatemáticaUniversidade Lusófona de Humanidades e TecnologiasLisbonPortugal

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