12(1GentzenInt)

12(1GentzenInt) - Chapter 12: Gentzen Sequent Calculus for...

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Chapter 12: Gentzen Sequent Calculus for Intuitionistic Logic Part 1: LI System The proof system LI was published by Gentzen in 1935 as a particular case of his proof system LK for the classical logic. We discussed a version of the original Gentzen’s system LK in the previous chapter. We present now the proof system LI and then we show how it can be extended to the original Gentzen system LK . 1
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Language of LI We consider the set of all Gentzen sequents built out of the formulas of our language L and the additional symbol -→ , as defined in the previous section: SEQ = { Γ -→ Δ : Γ , Δ ∈ F * } . In the intuitionistic logic we deal only with sequents of the form Γ -→ Δ , where Δ consists of at most one formula. The intuitionistic sequents are elements of a following subset IS of the set SEQ of all sequents. ISEQ = { Γ -→ Δ : Δ consists of at most one formula } . 2
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Axioms of LI consists of any sequent from the set ISEQ which contains a formula that appears on both sides of the sequent ar-
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This note was uploaded on 02/12/2011 for the course CSE 541 taught by Professor Bachmair,l during the Spring '08 term at SUNY Stony Brook.

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12(1GentzenInt) - Chapter 12: Gentzen Sequent Calculus for...

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