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.

Advances in Modal Logic is a unique international forum representing the latest results and new directions of research in Modal Logic broadly conceived. The topics dealt with are of interdisciplinary interest and range from mathematical, computational, and philosophical problems to applications in knowledge representation and formal linguistics. This volume contains invited and contributed papers from the eighth conference in the AiML series, held in Moscow, Russia, in August 2010. It reports on substantial advances, both in the foundations of modal logic and in a number of application areas. It includes papers on general problems in model theory, proof theory and algorithmic properties of modal logics, on systems for spatial, temporal and epistemic reasoning, on related kinds of logics - description, relevance, substructural, intuitionistic, and on related topics in algebraic logic.