Quantification and modalities have always been topics of great interest for logicians. These two themes emerged from philosophy and language in ancient times; they were studied by traditional informal methods until the 20th century. In the last century the tools became highly mathematical, and both modal logic and quantification found numerous applications in Computer Science. At the same time many other kinds of nonclassical logics were investigated and applied to Computer Science. Although there exist several good books in propositional modal logics, this book is the first detailed monograph in nonclassical first-order quantification. It includes results obtained during the past thirty years. The field is very large, so we confine ourselves with only two kinds of logics: modal and superintuitionistic. The main emphasis of Volume 1 is model-theoretic, and it concentrates on descriptions of different sound semantics and completeness problem --- even for these seemingly simple questions we have our hands full. The major part of the presented material has never been published before. Some results are very recent, and for other results we either give new proofs or first proofs in full detail.


Graduate students working in Symbolic logic, with a focus in first-order logic, modal logic, intuitionistic logic, model theory, completeness, possible worlds semantics

Table of Contents

1.) Basic Propositional Logic 2.) Basic Predicate Logic 3.) Kripke Semantics 4.) Algebraic Semantics 5.) Metaframe Semantics 6.) Kripke completeness for varying domains 7.) Kripke completeness for constant domains


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© 2009
Elsevier Science
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About the authors

Dov M. Gabbay

Dov M. Gabbay is Augustus De Morgan Professor Emeritus of Logic at the Group of Logic, Language and Computation, Department of Computer Science, King's College London. He has authored over four hundred and fifty research papers and over thirty research monographs. He is editor of several international Journals, and many reference works and Handbooks of Logic.

Affiliations and Expertise

King's College London, UK

Dimitrij Skvortsov

Affiliations and Expertise

Department of Computer Science, King's College London, UK

Valentin Shehtman

Affiliations and Expertise

Department of Computer Science, King's College London, UK