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TERMS FOR NATURAL DEDUCTION, SEQUENT CALCULUS AND CUT ELIMINATION IN CLASSICAL LOGIC

Silvia Ghilezan

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Abstract

This paper revisits the results of Barendregt and Ghilezan (3) and generalizes them for classical logic. Instead of �-calculus, we use here �µ-calculus as the basic term cal- culus. We consider two extensionally equivalent type assignment systems for �µ-calculus, one corresponding to classical natural deduction, and the other to classical sequent cal- culus. Their relations and normalisation properties are investigated. As a consequence a short proof of Cut elimination theorem is obtained.

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What this paper is about

This paper revisits the results of Barendregt and Ghilezan (3) and generalizes them for classical logic. Instead of �-calculus, we use here �µ-calculus as the basic term cal- culus. We consider two extensionally equivalent type assignment systems for �µ-calculus, one corresponding to classical natural deduction, and the other to classical sequent cal- culus. Their relations and normalisation properties are investigated. As a consequence a short proof of Cut elimination theorem is obtained.

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Available abstract

This paper revisits the results of Barendregt and Ghilezan (3) and generalizes them for classical logic. Instead of �-calculus, we use here �µ-calculus as the basic term cal- culus. We consider two extensionally equivalent type assignment systems for �µ-calculus, one corresponding to classical natural deduction, and the other to classical sequent cal- culus. Their relations and normalisation properties are investigated. As a consequence a short proof of Cut elimination theorem is obtained.

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

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