Gentzen Calculi for Modal Propositional Logic

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Springer Science & Business Media, Nov 19, 2010 - Philosophy - 224 pages
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The book is about Gentzen calculi for (the main systems of) modal logic. It is divided into three parts. In the first part we introduce and discuss the main philosophical ideas related to proof theory, and we try to identify criteria for distinguishing good sequent calculi. In the second part we present the several attempts made from the 50’s until today to provide modal logic with Gentzen calculi. In the third and and final part we analyse new calculi for modal logics, called tree-hypersequent calculi, which were recently introduced by the author. We show in a precise and clear way the main results that can be proved with and about them.

 

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Contents

Part I An Overview of the Sequent Calculus
2
Part II Sequent Calculi for Modal Logic
38
Part III TreeHypersequent Calculi
117
References
209
Symbols and Notations
215
Index
219
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