Haroldas Giedra
Abstract
Hilbert style, Gentzen style sequent and Kanger style sequent calculi for logic S5n(ED) are considered in this paper. Gentzen style sequent calculus is constructed and its equivalence with Hilbert style system is proved, getting soundness and completeness of Gentzen style system. Kanger style indexed sequent calculus is defined for cut elimination.
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Hilbert style, Gentzen style sequent and Kanger style sequent calculi for logic S5n(ED) are considered in this paper. Gentzen style sequent calculus is constructed and its equivalence with Hilbert style system is proved, getting soundness and completeness of Gentzen style system. Kanger style indexed sequent calculus is defined for cut elimination.
Key concepts: Sequent, Sequent calculus, Natural deduction, Soundness, Cut-elimination theorem, Mathematics, Calculus (dental), Completeness (order theory)