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2021•Unpublished venueRequires access

The sequent calculus

Pietro Mancosu, Sergio Galvan, Richard Zach

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Abstract

Abstract In addition to natural deduction, Gentzen developed a different calculus, called the sequent calculus. A sequent is a configuration presenting an arrow symbol (⇒) flanked on the left and on the right by finite sequences of formulas, possibly empty. The sequent calculus is developed, with examples of how to prove statements in the calculus, and a few results about transforming proofs through variable replacements are proved. Proofs in the intuitionistic sequent calculus can be translated into natural deductions, and vice versa (this system is obtained by restricting sequents to those that have at most one formula on the right hand side of the arrow).

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Abstract In addition to natural deduction, Gentzen developed a different calculus, called the sequent calculus. A sequent is a configuration presenting an arrow symbol (⇒) flanked on the left and on the right by finite sequences of formulas, possibly empty. The sequent calculus is developed, with examples of how to prove statements in the calculus, and a few results about transforming proofs through variable replacements are proved. Proofs in the intuitionistic sequent calculus can be translated into natural deductions, and vice versa (this system is obtained by restricting sequents to those that have at most one formula on the right hand side of the arrow).

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Available abstract

Abstract In addition to natural deduction, Gentzen developed a different calculus, called the sequent calculus. A sequent is a configuration presenting an arrow symbol (⇒) flanked on the left and on the right by finite sequences of formulas, possibly empty. The sequent calculus is developed, with examples of how to prove statements in the calculus, and a few results about transforming proofs through variable replacements are proved. Proofs in the intuitionistic sequent calculus can be translated into natural deductions, and vice versa (this system is obtained by restricting sequents to those that have at most one formula on the right hand side of the arrow).

Key concepts: Natural deduction, Sequent, Sequent calculus, Cut-elimination theorem, Calculus (dental), Mathematics, Mathematical proof, Curry–Howard correspondence

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