By
Dov M. Gabbay, King's College London, UK
Dimitrij Skvortsov, Department of Computer Science, King's College London, UK
Valentin Shehtman, Department of Computer Science, King's College London, UK
Description
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.
Included in series
Studies in Logic and the Foundations of Mathematics
Audience:
Graduate students working in Symbolic logic, with a focus in first-order logic, modal logic, intuitionistic logic, model theory, completeness, possible worlds semantics
