Studia Logica

, Volume 85, Issue 2, pp 199–214

A Deep Inference System for the Modal Logic S5


    • Institut für Informatik und Angewandte MathematikUniversity of Bern

DOI: 10.1007/s11225-007-9028-y

Cite this article as:
Stouppa, P. Stud Logica (2007) 85: 199. doi:10.1007/s11225-007-9028-y


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.


modal logic S5proof theorydeep inferencecalculus of structurescutadmissibility
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© Springer Science+Business Media, Inc. 2007