The book is about Gentzen calculi for (the main systems of)
modal logic. It is divided into three parts. In the first partwe
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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