Modalities and Multimodalities

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Springer, Nov 29, 2010 - Mathematics - 306 pages
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This book is intended to provide a philosophically- and historically-based introduction to modal logic, offering to every reader, even those with little specific background, a conceptually clear path through the labyrinth of contemporary modal logic. This is done by emphasizing the notion of multimodality while delineating the formal side of the semantics and proof theory behind the topics in a smooth and gentle pace. The conceptual thread which ties the book together passes through topics like the development of modal logic from standard logic; the syntax and semantics of normal modal systems; the seminal ideas behind completeness, incompleteness, canonicity and finite models; the temporal logics, the logics of knowledge and belief; the generalized syntactical and semantical treatment of multimodalities and finally the pleasures and difficulties of quantified modal logic. Multimodality is the notion which stands behind the most fertile investigations in modal logic, such as temporal logics, epistemic logics, dynamic logics and so on. By focusing on multimodal logic this book provides common ground for philosophers, logicians, linguists, mathematicians and computer scientists.The book is also designed to provide a repertoire of ideas and techniques for students interested in progressive inquiry in modal and multimodal logic. Each chapter is relatively independent, complemented with exercises and followed by a short bibliographical commentary intended for historically-minded readers.

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About the author (2010)

Walter Carnielli is Full Professor of Logic, Department of Philosophy, State University of Campinas, Brazil. Ex-Director of the Centre for Logic, Epistemology and the History of Science (1998-2004) and full member of the Security and Quantum Information Group-- Institute of Telecommunications, Lisbon, Portugal. Grantee of the Alexander von Humboldt Foundation, Germany, held temporary positions and research appointments in the USA (University of California, Berkeley), as well as in several institutions in Chile, Colombia, Venezuela, Italy, Germany (Münster and Bonn), France, Spain, Portugal and Luxembourg. Carnielli is known for his contribution to the proof theory and semantics for contemporary heterodox (non-classical) logics. Of special significance are his contributions to many-valued logics, paraconsistent logics and combinations of logics. With his students and collaborators Carnielli introduced the possible-translations semantics, which led to a revival in the semantic interpretation of paraconsistent logics, and the concept of logics of formal inconsistency which systematize a great number of extant paraconsistent logics, opening the way to applications of paraconsistency to computer science and to philosophical investigations around the topic. Carnielli has also worked on finite and infinite combinatorics, and shaped, with collaborators, the modulated logics, a wide class of logics dedicated to formalize quantified uncertain reasoning. He is the author or co-author of more than academic 70 publications (papers, books and monographs). Claudio Pizzi is Full Professor of Philosophy of Science at the Faculty of Letters of the University of Siena (Italy) and contract professor at the University of Milano Bicocca. His main interests are in the field of general modal logic, conditional logic, tense logic and philosophy of causality. In 1973 he translated and edited the Italian version G.E.Hughes and M.J.Cresswell's "An Introduction to Modal Logic". In the past ten years he has been at the head of a research team which organized the international conferences of the series MBR (Model-Based Reasoning). He is author or coauthor of more that 70 publications , some of which published in Topoi, Notre Dame Journal of Formal Logic, Logique et Analyse, Journal of Philosophical Logic, Studia Logica. His main theoretical contributions concern a theory of rational inference based on the consequence relation (consequential implication) and a theory of causal relations based on iterated conditionals.

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