Protoalgebraic Gentzen systems and the cut rule

Studia Logica 65 (1):53-89 (2000)
  Copy   BIBTEX

Abstract

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.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 76,391

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Analytics

Added to PP
2009-01-28

Downloads
48 (#246,317)

6 months
1 (#451,971)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

A survey of abstract algebraic logic.J. M. Font, R. Jansana & D. Pigozzi - 2003 - Studia Logica 74 (1-2):13 - 97.
Two-dimensional adventures.Lloyd Humberstone - 2004 - Philosophical Studies 118 (1-2):17--65.
Correspondences between Gentzen and Hilbert Systems.J. G. Raftery - 2006 - Journal of Symbolic Logic 71 (3):903 - 957.
Representations of structural closure operators.José Gil-Férez - 2011 - Archive for Mathematical Logic 50 (1-2):45-73.

View all 6 citations / Add more citations

References found in this work

Protoalgebraic logics.W. J. Blok & Don Pigozzi - 1986 - Studia Logica 45 (4):337 - 369.
Proof Theory of Finite-valued Logics.Richard Zach - 1993 - Dissertation, Technische Universität Wien
.Jay Zeman - unknown
Gentzen-type systems, resolution and tableaux.Arnon Avron - 1993 - Journal of Automated Reasoning 10:265-281.

View all 8 references / Add more references