Quantification in Nonclassical Logic

This book is the first detailed monograph in nonclassical first-order quantification. It includes results obtained during the past thirty years.

Dov M. Gabbay (Author), Dimitrij Skvortsov (Author), Valentin Shehtman (Author)

9780444520128, Elsevier Science

Hardback, published 9 June 2009

640 pages
22.9 x 15.1 x 3.5 cm, 1.16 kg

Quantification and modalities have always been topics of great interest for logicians. These two themes emerged from philosophy andlanguage in ancient times; they were studied by traditional informalmethods until the 20th century. In the last century the tools becamehighly 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.

1.) Basic Propositional Logic 2.) Basic Predicate Logic3.) Kripke Semantics4.) Algebraic Semantics5.) Metaframe Semantics6.) Kripke completeness for varying domains7.) Kripke completeness for constant domains

Subject Areas: Mathematical logic [PBCD]