A Sequent Calculus for First-Order Logic

Abstract

This article is part of a series of Mizar articles which constitute a formal proof (of a basic version) of Kurt Godel’s famous completeness theorem (K. Godel, “Die Vollstandigkeit der Axiome des logischen Funktionenkalkuls”, Monatshefte fur Mathematik und Physik 37 (1930), 349–360). The completeness theorem provides the theoretical basis for a uniform formalization of mathematics as in the Mizar project. We formalize first-order logic up to the completeness theorem as in H. D. Ebbinghaus, J. Flum, and W. Thomas, Mathematical Logic, 1984, Springer Verlag New York Inc. The present article introduces a sequent calculus for first-order logic. The correctness of this calculus is shown and some important inferences are derived. The contents of this article correspond to Chapter IV of Ebbinghaus, Flum, Thomas.