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.
Author(s): Francesca Poggiolesi
Series: Trends in Logic 32
Publisher: Springer
Year: 2011
Language: English
Pages: 224
Tags: Philosophy; Mathematics, general; Computer Imaging, Vision, Pattern Recognition and Graphics; Linguistics (general)
Front Matter....Pages i-xi
Front Matter....Pages 1-1
What Is a Good Sequent Calculus?....Pages 3-35
Front Matter....Pages 37-37
Modal Logic and Ordinary Sequent Calculi....Pages 39-53
Purely Syntactic Methods....Pages 55-74
Semantic Methods....Pages 75-100
Comparing the Different Generalisations of the Sequent Calculus....Pages 101-116
Front Matter....Pages 117-117
On the Tree-Hypersequent Calculi....Pages 119-141
Syntactic Cut-Admissibility and Decidability....Pages 143-163
Semantic Adequacy....Pages 165-174
A Hypersequent Calculus for the System S5....Pages 175-186
A Tree-Hypersequent Calculus for the Modal Logic of Provability....Pages 187-201
Further Results on Tree-Hypersequent Calculi....Pages 203-207
Back Matter....Pages 209-222
