### A Simulation of Natural Deduction and Gentzen Sequent Calculus

DOI: http://dx.doi.org/10.12775/LLP.2017.009

#### Abstract

We consider four natural deduction systems: Fitch-style systems, Gentzen-style systems (in the form of dags), general deduction Frege systems and nested deduction Frege systems, as well as dag-like Gentzen-style sequent calculi. All these calculi soundly and completely formalize classical propositional logic.

We show that general deduction Frege systems and Gentzen-style natural calculi provide at most quadratic speedup over nested deduction Frege systems and Fitch-style natural calculi and at most cubic speedup over Gentzen-style sequent calculi.

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