Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 47, Number 4 (2006), 557-580.
Locality for Classical Logic
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.
Notre Dame J. Formal Logic, Volume 47, Number 4 (2006), 557-580.
First available in Project Euclid: 9 January 2007
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Brünnler, Kai. Locality for Classical Logic. Notre Dame J. Formal Logic 47 (2006), no. 4, 557--580. doi:10.1305/ndjfl/1168352668. https://projecteuclid.org/euclid.ndjfl/1168352668