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Abstract: Much of the success of modal logic can be attributed to the adoption of relational semantics. Consequently, modal logic is seen as logic of relational structures, where logical axioms correspond to structural properties. Alex Simpson, in his 1993 PhD thesis, introduced a labelled proof theory for modal logic that that allows cut-elimination for a class of modal logics, which is characterised by so called geometric theories. This includes important and well know logics such as M, B, S4 and S5.... (Update)
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Deep Inference and the Calculus of Structures - Guglielmi (2006) (Correct)
A Deep Inference System for the Modal Logic S5 - Stouppa (2005) (Correct)
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BibTeX entry: (Update)
Robert Hein. Geometric theories and modal logic in the calculus of structures. Master's thesis, Technische Universitat Dresden, 2005. URL: http://bitschnitzer.de/robert thesis.ps.gz. http://citeseer.ist.psu.edu/hein05geometric.html More
@misc{ hein05geometric,
author = "R. Hein",
title = "Geometric theories and modal logic in the calculus of structures",
text = "Robert Hein. Geometric theories and modal logic in the calculus of structures.
Master's thesis, Technische Universitat Dresden, 2005. URL: http://bitschnitzer.de/robert
thesis.ps.gz.",
year = "2005",
url = "citeseer.ist.psu.edu/hein05geometric.html" }
Citations (may not include all citations):268 Proofs and Types (context) - Girard, Taylor et al. - 1990
73 Topology via Logic (context) - Vickers - 1989
39 Deep Inference and Symmetry in Classical Proofs (context) - Brunnler - 2004
27 The method of Hypersequents in Proof Theory of Propositional.. - Avron - 1996
26 volume 52 of Cambridge Tracts in Theoretical Computer Scienc.. (context) - Troelstra, Schwichtenberg et al. - 2000
25 A systematic proof theory for several modal logics - Stewart, Stouppa - 2004
22 The Proof Theory and Semantics of Intuitionistic Modal Logic (context) - Simpson - 1993
11 An Introduction to Modal Logic (context) - Lemmon, Scott - 1977
9 and Yde Venema (context) - Blackburn, de Rijke - 2001
8 Geometric logic in computer science - Vickers - 1993
6 Accepted by ACM Transactions on Computational Logic (context) - Guglielmi, of et al. - 2002
5 Structural Proof Theory (context) - Negri, von Plato - 2001
3 Contraction-free sequent calculi for geometric theories (context) - Negri - 2001
2 Discipline as logic: Treating labels as first class citizens (context) - Blackburn - 2000
1 A local system for linear logic (context) - Straburger - 2002
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MELL in the Calculus of Structures - Straßburger (2003) (Correct)
Implementing Deep Inference in TOM - Kahramanogullari, Moreau, Reilles (2005) (Correct)
What is a Logic, and What is a Proof? - Straßburger (2005) (Correct)
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