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First book to give a uniform and exhaustive presentation of both types of sequent calculus for modal logic, the purely syntactic sequent calculi as well as the semantic ones
First book that gives a complete and accurate description of the tree-hypersequent method
One of the few books based mainly on logical results accompanied by philosophical discussion
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.