Quantification in Nonclassical Logic

Quantification and modalities have a 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
high mathematical, and both logical and quantitative computational computer Science. At the same time were investigated and applied to Computer Science.

Although there are several good books in this category, this book is the first detailed monograph in a nonclassical first-order quantification. It includes results during the past thirty years. The field is very large, so we do not have to be able to communicate with us: modal and superintuitionistic. The main emphasis of Volume 1 is model-theoretic, and it is the problem of the sound and the semblance of the problem --- even for these seemingly simple questions. The major part of the material has never been published before. Some results are very recent, and for other results.

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