Logic, Language and Reasoning

This book is dedicated to Dov Gabbay, one of the most outstanding and most productive researchers in the area of logic, language and reasoning. He has exerted a profound influence in the major fields of logic, linguistics and computer science. Most of the chapters included, therefore, build on his work and present results or summarize areas where Dov has made major contributions. In particular his work on Labelled Deductive Systems is addressed in most of the contributions. The chapters on computational linguistics address logical and deductive aspects of linguistic problems. The papers by van Benthem Lambek and Moortgat investigate categorial considerations and the use of labels within the "parsing as deduction" approach. Analyses of particular linguistic problems are given in the remaining papers by Kamp, Kempson, Moravcsik, Konig and Reyle. They address the logic of generalized quantifiers, the treatment of cross-over phenomena and temporal/aspectual interpretation, as well as applicability of underspecified deduction in linguistic formalisms. The more logic-oriented chapters address philosophical and proof-theoretic problems and give algorithmic solutions for most of them.The spectrum ranges from K. Segerberg's contribution which brings together the two traditions of epistemic and doxastic logics of belief, to M. Finger and M. Reynold's chapter on two-dimensional executable logics with applications to temporal databases. The book demonstrates that a relatively small number of basic techniques and ideas, in particular the idea of labelled deductive systems, can be successfully applied in many different areas.