A local system for intuitionistic logic: Preliminary results. Available on the web at http://www.loria.fr/˜tiu/localint.pdf (2005) [2 citations — 0 self]
Abstract:
Abstract. This paper presents a system for intuitionistic logic in which all the rules are local, in the sense that, in applying the rules of the system, one needs only a fixed amount of information about the logical expressions involved. The main source of non-locality is the contraction rule. We show that the contraction rule can be restricted to the atomic one, provided we employ deep-inference, i.e., to allow rules to apply anywhere inside logical expressions. However, the use of deep-inference and the asymmetry of the logic give rise to the context-dependency of the rules. We further show that this context dependency can be removed by introducing polarities into logical expressions. We present the system in the calculus of structures, a proof theoretic formalism which supports deep-inference. This system is shown to be sound and complete with respect to Gentzen’s LJ and an equivalent notion of cut-elimination is proved.
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