Studia Logica

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

The Faithfulness of Fat: A Proof-Theoretic Proof

Article

Abstract

It is known that there is a sound and faithful translation of the full intuitionistic propositional calculus into the atomic polymorphic system Fat, 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.

Keywords

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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