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CIE
2007
Springer
13 years 8 months ago
Confluence of Cut-Elimination Procedures for the Intuitionistic Sequent Calculus
We prove confluence of two cut-elimination procedures for the implicational fragment of a standard intuitionistic sequent calculus. One of the cut-elimination procedures uses globa...
Kentaro Kikuchi
CADE
2006
Springer
14 years 5 months ago
Strong Cut-Elimination Systems for Hudelmaier's Depth-Bounded Sequent Calculus for Implicational Logic
Abstract. Inspired by the Curry-Howard correspondence, we study normalisation procedures in the depth-bounded intuitionistic sequent calculus of Hudelmaier (1988) for the implicati...
Roy Dyckhoff, Delia Kesner, Stéphane Lengra...
TLCA
2007
Springer
13 years 10 months ago
An Isomorphism Between Cut-Elimination Procedure and Proof Reduction
Abstract. This paper introduces a cut-elimination procedure of the intuitionistic sequent calculus and shows that it is isomorphic to the proof reduction of the intuitionistic natu...
Koji Nakazawa
WOLLIC
2009
Springer
13 years 11 months ago
Forcing-Based Cut-Elimination for Gentzen-Style Intuitionistic Sequent Calculus
We give a simple intuitionistic completeness proof of Kripke semantics with constant domain for intuitionistic logic with implication and universal quantification. We use a cut-fr...
Hugo Herbelin, Gyesik Lee
PADL
2004
Springer
13 years 10 months ago
Implementing Cut Elimination: A Case Study of Simulating Dependent Types in Haskell
Gentzen’s Hauptsatz – cut elimination theorem – in sequent calculi reveals a fundamental property on logic connectives in various logics such as classical logic and intuition...
Chiyan Chen, Dengping Zhu, Hongwei Xi