Quantification in Nonclassical Logic

Nonfiction, Science & Nature, Mathematics, Logic
Cover of the book Quantification in Nonclassical Logic by Dov M. Gabbay, Dimitrij Skvortsov, Valentin Shehtman, Elsevier Science
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Author: Dov M. Gabbay, Dimitrij Skvortsov, Valentin Shehtman ISBN: 9780080931128
Publisher: Elsevier Science Publication: June 20, 2009
Imprint: Elsevier Science Language: English
Author: Dov M. Gabbay, Dimitrij Skvortsov, Valentin Shehtman
ISBN: 9780080931128
Publisher: Elsevier Science
Publication: June 20, 2009
Imprint: Elsevier Science
Language: English

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.

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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.

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