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The Faithfulness of Fat: A Proof-Theoretic Proof

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Abstract

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.

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References

  1. Ferreira F.: Comments on predicative logic. Journal of Philosophical Logic 35, 1–8 (2006)

    Article  Google Scholar 

  2. Ferreira F., Ferreira G.: Commuting conversions vs. the standard conversions of the “good” connectives. Studia Logica 92, 63–84 (2009)

    Article  Google Scholar 

  3. Ferreira F., Ferreira G.: Atomic polymorphism. The Journal of Symbolic Logic 78, 260–274 (2013)

    Article  Google Scholar 

  4. Ferreira, F., and G. Ferreira, The faithfulness of atomic polymorphism, in A. Indrzejczak, J. Kaczmarek, and M. Zawidzki (eds.), Proceedings of Trends in Logic XIII, Łódź University Press, Lodz, 2014, pp. 55–65.

  5. Girard, J.-Y., Y. Lafont, and P. Taylor, Proofs and Types, Cambridge University Press, Cambridge, 1989.

  6. Prawitz, D., Natural Deduction, Almkvist & Wiksell, Stockholm, 1965. Reprinted, with a new preface, in Dover Publications, 2006.

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Authors and Affiliations

  1. Departamento de Matemática, Faculdade de Ciências da Universidade de Lisboa, Campo Grande, Ed. C6, 1749-016, Lisbon, Portugal

    Fernando Ferreira & Gilda Ferreira

  2. Departamento de Matemática, Universidade Lusófona de Humanidades e Tecnologias, Av. do Campo Grande, 376, 1749-024, Lisbon, Portugal

    Gilda Ferreira

Authors
  1. Fernando Ferreira
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  2. Gilda Ferreira
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Correspondence to Gilda Ferreira.

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Ferreira, F., Ferreira, G. The Faithfulness of Fat: A Proof-Theoretic Proof. Stud Logica 103, 1303–1311 (2015). https://doi.org/10.1007/s11225-015-9620-5

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  • DOI: https://doi.org/10.1007/s11225-015-9620-5

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