Open Access
Translator Disclaimer
2006 Locality for Classical Logic
Kai Brünnler
Notre Dame J. Formal Logic 47(4): 557-580 (2006). DOI: 10.1305/ndjfl/1168352668


In this paper we will see deductive systems for classical propositional and predicate logic in the calculus of structures. Like sequent systems, they have a cut rule which is admissible. Unlike sequent systems, they drop the restriction that rules only apply to the main connective of a formula: their rules apply anywhere deeply inside a formula. This allows to observe very clearly the symmetry between identity axiom and the cut rule. This symmetry allows to reduce the cut rule to atomic form in a way which is dual to reducing the identity axiom to atomic form. We also reduce weakening and even contraction to atomic form. This leads to inference rules that are local: they do not require the inspection of expressions of arbitrary size.


Download Citation

Kai Brünnler. "Locality for Classical Logic." Notre Dame J. Formal Logic 47 (4) 557 - 580, 2006.


Published: 2006
First available in Project Euclid: 9 January 2007

zbMATH: 1131.03030
MathSciNet: MR2272089
Digital Object Identifier: 10.1305/ndjfl/1168352668

Primary: 03F05
Secondary: 03F07

Keywords: cut elimination , deep inference , locality

Rights: Copyright © 2006 University of Notre Dame


Vol.47 • No. 4 • 2006
Back to Top