David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 65 (1):53-89 (2000)
In this paper we show that, in Gentzen systems, there is a close relation between two of the main characters in algebraic logic and proof theory respectively: protoalgebraicity and the cut rule. We give certain conditions under which a Gentzen system is protoalgebraic if and only if it possesses the cut rule. To obtain this equivalence, we limit our discussion to what we call regular sequent calculi, which are those comprising some of the structural rules and some logical rules, in a sense we make precise. We note that this restricted set of rules includes all the usual rules in the literature. We also stress the difference between the case of two-sided sequents and the case of many-sided sequents, in which more conditions are needed.
|Keywords||Philosophy Logic Mathematical Logic and Foundations Computational Linguistics|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
José Gil-Férez (2011). Representations of Structural Closure Operators. Archive for Mathematical Logic 50 (1-2):45-73.
George Voutsadakis (2005). Categorical Abstract Algebraic Logic: Gentzen Π ‐Institutions and the Deduction‐Detachment Property. Mathematical Logic Quarterly 51 (6):570-578.
Similar books and articles
Steve Giambrone & Aleksandar Kron (1987). Four Relevant Gentzen Systems. Studia Logica 46 (1):55 - 71.
Steve Giambrone (1985). On Purported Gentzen Formulations of Two Positive Relevent Logics. Studia Logica 44 (3):233 - 236.
Aleksandar Kron (1981). Gentzen Formulations of Two Positive Relevance Logics. Studia Logica 40 (3):381 - 403.
Aleksandar Kron (1980). Gentzen Formulations of Two Positive Relevance Logics. Studia Logica 39 (4):381 - 403.
Uwe Egly (2001). On Different Intuitionistic Calculi and Embeddings From Int to S. Studia Logica 69 (2):249-277.
René Lavendhomme & Thierry Lucas (2000). Sequent Calculi and Decision Procedures for Weak Modal Systems. Studia Logica 66 (1):121-145.
Ryo Kashima & Norihiro Kamide (1999). Substructural Implicational Logics Including the Relevant Logic E. Studia Logica 63 (2):181-212.
Anna Zamansky & Arnon Avron (2006). Cut-Elimination and Quantification in Canonical Systems. Studia Logica 82 (1):157 - 176.
Francesco Belardinelli, Peter Jipsen & Hiroakira Ono (2004). Algebraic Aspects of Cut Elimination. Studia Logica 77 (2):209 - 240.
Added to index2009-01-28
Total downloads12 ( #272,234 of 1,790,186 )
Recent downloads (6 months)1 ( #427,637 of 1,790,186 )
How can I increase my downloads?