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Added by: Berta GrimauPublisher's Note: Although sequent calculi constitute an important category of proof systems, they are not as well known as axiomatic and natural deduction systems. Addressing this deficiency, Proof Theory: Sequent Calculi and Related Formalisms presents a comprehensive treatment of sequent calculi, including a wide range of variations. It focuses on sequent calculi for various non-classical logics, from intuitionistic logic to relevance logic, linear logic, and modal logic. In the first chapters, the author emphasizes classical logic and a variety of different sequent calculi for classical and intuitionistic logics. She then presents other non-classical logics and meta-logical results, including decidability results obtained specifically using sequent calculus formalizations of logics.Comment: This book can be used in a variety of advanced undergraduate and postgraduate courses. Chapters 1, 2, 3 and 8 may be useful in an advanced undergraduate or beginning graduate course, where an emphasis is placed on classical logic and on a range of different proof calculi (mainly for classical logic). Chapters 4, 5 and 6 deal almost exclusively with non-classical logics. Chapters 7 and 9 are rich in meta-logical results, including results that have been obtained specifically using sequent calculus formalizations of various logics. These last five chapters might be used in a graduate course that embraces classical and nonclassical logics together with their meta-theory. To facilitate the use of the book as a text in a course, the text is peppered with exercises. In general, the starring indicates an increase in difficulty, however, sometimes an exercise is starred simply because it goes beyond the scope of the book or it is very lengthy. Solutions to selected exercises may be found on the web at the URL www.ualberta.ca/˜bimbo/ProofTheoryBook.2001, Cambridge University Press.
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Added by: Berta GrimauPublisher's Note: Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics and computer science. The book contains a wealth of results on proof-theoretical systems, including extensions of such systems from logic to mathematics, and on the connection between the two main forms of structural proof theory - natural deduction and sequent calculus. The authors emphasize the computational content of logical results. A special feature of the volume is a computerized system for developing proofs interactively, downloadable from the web and regularly updated.Comment: This book can be used both in a general course on proof theory for advanced Undergraduates or for Masters students, and for specialized courses - for example, a course on natural deduction. Chapters 1-4 can be used as background reading of a general course. Chapter 1, 5 and 8 could be used in a course on natural deduction. The presentation is self-contained and the book should be readable without any previous knowledge of logic.2021, Pimentel, E. et al. (2021) An ecumenical notion of entailment. Synthese (Dordrecht). [Online] 198 (Suppl 22), 5391–5413.
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Added by: Sophie Nagler, Contributed by: Sophie NaglerAbstract:
Much has been said about intuitionistic and classical logical systems since Gentzen’s seminal work. Recently, Prawitz and others have been discussing how to put together Gentzen’s systems for classical and intuitionistic logic in a single unified system. We call Prawitz’ proposal the Ecumenical System, following the terminology introduced by Pereira and Rodriguez. In this work we present an Ecumenical sequent calculus, as opposed to the original natural deduction version, and state some proof theoretical properties of the system. We reason that sequent calculi are more amenable to extensive investigation using the tools of proof theory, such as cut-elimination and rule invertibility, hence allowing a full analysis of the notion of Ecumenical entailment. We then present some extensions of the Ecumenical sequent system and show that interesting systems arise when restricting such calculi to specific fragments. This approach of a unified system enabling both classical and intuitionistic features sheds some light not only on the logics themselves, but also on their semantical interpretations as well as on the proof theoretical properties that can arise from combining logical systems.
Comment: A relatively light-touch and philosophically focussed introduction to ecumenical proof systems, i.e. sequent calculi that combine aspects of different logics. Suitable for discussion in a class on philosophy of logic class or on proof theory if more philosophically focussed. Also potentially usable for a class on logical pluralism.Can’t find it?Contribute the texts you think should be here and we’ll add them soon!
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Bimbo, Katalin. Proof Theory: Sequent Calculi and Related Formalisms
2015, CRC Press, Boca Raton, FL