By Dov M. Gabbay, Dimitrij Skvortsov, Valentin Shehtman
Quantification and modalities have continually been issues of serious curiosity for logicians. those subject matters emerged from philosophy andlanguage in precedent days; they have been studied via conventional informalmethods until eventually the 20 th century. within the final century the instruments becamehighly mathematical, and either modal common sense and quantification came across a number of purposes in laptop technological know-how. whilst many other forms of nonclassical logics have been investigated and utilized to machine technological know-how. even if there exist a number of reliable books in propositional modal logics, this booklet is the 1st specific monograph in nonclassical first-order quantification. It contains effects received in past times thirty years. the sphere is huge, so we confine ourselves with simply types of logics: modal and superintuitionistic. the most emphasis of quantity 1 is model-theoretic, and it concentrates on descriptions of alternative sound semantics and completeness challenge --- even for those probably easy questions we now have our arms complete. the most important a part of the awarded fabric hasn't ever been released prior to. a few effects are very contemporary, and for different effects we both supply new proofs or first proofs in complete element.