The Faithfulness of Fat: A Proof-Theoretic Proof
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.
KeywordsPredicative polymorphism Faithfulness Natural deduction Strong normalization Intuitionistic propositional calculus Disjunction property
Unable to display preview. Download preview PDF.
- 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.Google Scholar
- 5.Girard, J.-Y., Y. Lafont, and P. Taylor, Proofs and Types, Cambridge University Press, Cambridge, 1989.Google Scholar
- 6.Prawitz, D., Natural Deduction, Almkvist & Wiksell, Stockholm, 1965. Reprinted, with a new preface, in Dover Publications, 2006.Google Scholar