Gentzen Calculi for Modal Propositional Logic

Description

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. 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