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This book is about proof theory for (the main systems of) modal logic. It is the 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.
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.
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.
From the reviews:
"This book is mainly devoted to an extensive presentation of the author's original formalisation of modal logics called tree-hypersequent calculus but other approaches are also discussed at length. ... This book is a valuable contribution to the subject of proof techniques for modal logics. The presentation is clear with a detailed but readable account of technical details." (Andrzej B. Indrzejczak, Mathematical Reviews, August, 2013)
"This book is mainly devoted to an extensive presentation of the author's original formalisation of modal logics called tree-hypersequent calculus but other approaches are also discussed at length. ... This book is a valuable contribution to the subject of proof techniques for modal logics. The presentation is clear with a detailed but readable account of technical details." (Andrzej B. Indrzejczak, Mathematical Reviews, August, 2013)