12(1GentzenInt)

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

This preview shows pages 1–4. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
Axioms of LI consists of any sequent from the set ISEQ which contains a formula that appears on both sides of the sequent ar-

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 13

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online