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The Faithfulness of Fat: A Proof-Theoretic Proof
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Journal Article
The Faithfulness of Fat: A Proof-Theoretic Proof
2015
Overview
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.
Publisher
Springer Science+Business Media B. V,Springer Netherlands,Springer Nature B.V
