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A Deep Inference System for the Modal Logic S5

Phiniki Stouppa
Studia Logica: An International Journal for Symbolic Logic
Vol. 85, No. 2 (Mar., 2007), pp. 199-214
Published by: Springer
Stable URL: http://www.jstor.org/stable/40210767
Page Count: 16
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A Deep Inference System for the Modal Logic S5
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Abstract

We present a cut-admissible system for the modal logic S5 in a formalism that makes explicit and intensive use of deep inference. Deep inference is induced by the methods applied so far in conceptually pure systems for this logic. The system enjoys systematicity and modularity, two important properties that should be satisfied by modal systems. Furthermore, it enjoys a simple and direct design: the rules are few and the modal rules are in exact correspondence to the modal axioms.

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