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Quantifiers: Logics, Models and Computation is the first concentrated effort to give a systematic presentation of the main research results on the subject, since the modern concept was formulated in the late '50s and early '60s. The majority of the papers are in the nature of a handbook. All of them are self-contained, at various levels of difficulty. The Introduction surveys the main ideas and problems encountered in the logical investigation of quantifiers. The Prologue, written by Per Lindström, presents the early history of the concept of generalised quantifiers. The volume then continues with a series of papers surveying various research areas, particularly those that are of current interest. Together they provide introductions to the subject from the points of view of mathematics, linguistics, and theoretical computer science. The present volume has been prepared in parallel with Quantifiers: Logics, Models and Computation, Volume Two. Contributions, which contains a collection of research papers on the subject in areas that are too fresh to be summarised. The two volumes are complementary. For logicians, mathematicians, philosophers, linguists and computer scientists. Suitable as a text for advanced undergraduate and graduate specialised courses in logic.
This volume on the semantic complexity of natural language explores the question why some sentences are more difficult than others. While doing so, it lays the groundwork for extending semantic theory with computational and cognitive aspects by combining linguistics and logic with computations and cognition. Quantifier expressions occur whenever we describe the world and communicate about it. Generalized quantifier theory is therefore one of the basic tools of linguistics today, studying the possible meanings and the inferential power of quantifier expressions by logical means. The classic version was developed in the 1980s, at the interface of linguistics, mathematics and philosophy. Before this volume, advances in "classic" generalized quantifier theory mainly focused on logical questions and their applications to linguistics, this volume adds a computational component, the third pillar of language use and logical activity. This book is essential reading for researchers in linguistics, philosophy, cognitive science, logic, AI, and computer science.
Quantification is a topic which brings together linguistics, logic, and philosophy. Quantifiers are the essential tools with which, in language or logic, we refer to quantity of things or amount of stuff. In English they include such expressions as no, some, all, both, and many. Peters and Westerstahl present the definitive interdisciplinary exploration of how they work - their syntax, semantics, and inferential role.Quantifiers in Language and Logic is intended for everyone with a scholarly interest in the exact treatment of meaning. It presents a broad view of the semantics and logic of quantifier expressions in natural languages and, to a slightly lesser extent, in logical languages. The authors progress carefully from a fairly elementary level to considerable depth over the course of sixteen chapters; their book will be invaluable to a broad spectrum of readers, from those with a basicknowledge of linguistic semantics and of first-order logic to those with advanced knowledge of semantics, logic, philosophy of language, and knowledge representation in artificial intelligence.
Quantification is a topic which brings together linguistics, logic, and philosophy. Quantifiers are the essential tools with which, in language or logic, we refer to quantity of things or amount of stuff. In English they include such expressions as no, some, all, both, many. Peters and Westerstahl present the definitive interdisciplinary exploration of how they work - their syntax, semantics, and inferential role.
Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the refereed proceedings of the 7th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2007, held in Tbilisi, Georgia, in October 2007. The 22 revised full papers included in the book were carefully reviewed and selected from numerous presentations given at the symposium. The focus of the papers is on the following topics: conceptual modeling of spatial relations, pragmatics and game theory, atypical valency phenomena, lexical typology, formal semantics and experimental evidence, exceptional quantifier scope, Georgian focussing particles, polarity and pragmatics, dynamics of belief, learning theory, inquisitive semantics, modal logic, coalgebras, computational linguistics of Georgian, type-logical grammar and cross-serial dependencies, non-monotonic logic, Japanese quantifiers, intuitionistic logic, semantics of negated nominals, word sense disambiguation, semantics of question-embedding predicates, and reciprocals and computational complexity.
It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as well as to consumers of logic in many applied areas. The main logic article in the Encyclopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good. ! The first edition was the second handbook published for the logic commu nity. It followed the North Holland one volume Handbook of Mathematical Logic, published in 1977, edited by the late Jon Barwise, The four volume Handbook of Philosophical Logic, published 1983-1989 came at a fortunate temporal junction at the evolution of logic. This was the time when logic was gaining ground in computer science and artificial intelligence circles. These areas were under increasing commercial pressure to provide devices which help and/or replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organisa tion on the one hand and to provide the theoretical basis for the computer program constructs on the other.
This book constitutes the refereed proceedings of the 18th International Workshop on Computer Science Logic, CSL 2004, held as the 13th Annual Conference of the EACSL in Karpacz, Poland, in September 2004. The 33 revised full papers presented together with 5 invited contributions were carefully reviewed and selected from 88 papers submitted. All current aspects of logic in computer science are addressed ranging from mathematical logic and logical foundations to methodological issues and applications of logics in various computing contexts.
In this monograph we introduce and examine four new temporal logic formalisms that can be used as specification languages for the automated verification of the reliability of hardware and software designs with respect to a desired behavior. The work is organized in two parts. In the first part two logics for computations, the graded computation tree logic and the computation tree logic with minimal model quantifiers are discussed. These have proved to be useful in describing correct executions of monolithic closed systems. The second part focuses on logics for strategies, strategy logic and memoryful alternating-time temporal logic, which have been successfully applied to formalize several properties of interactive plays in multi-entities systems modeled as multi-agent games.
From a linguistic perspective, it is quanti?cation which makes all the di?- ence between “having no dollars” and “having a lot of dollars”. And it is the meaning of the quanti?er “most” which eventually decides if “Most Ame- cans voted Kerry” or “Most Americans voted Bush” (as it stands). Natural language(NL)quanti?erslike“all”,“almostall”,“many”etc. serveanimp- tant purpose because they permit us to speak about properties of collections, as opposed to describing speci?c individuals only; in technical terms, qu- ti?ers are a ‘second-order’ construct. Thus the quantifying statement “Most Americans voted Bush” asserts that the set of voters of George W. Bush c- prisesthemajorityofAmericans,while“Bushsneezes”onlytellsussomething about a speci?c individual. By describing collections rather than individuals, quanti?ers extend the expressive power of natural languages far beyond that of propositional logic and make them a universal communication medium. Hence language heavily depends on quantifying constructions. These often involve fuzzy concepts like “tall”, and they frequently refer to fuzzy quantities in agreement like “about ten”, “almost all”, “many” etc. In order to exploit this expressive power and make fuzzy quanti?cation available to technical applications, a number of proposals have been made how to model fuzzy quanti?ers in the framework of fuzzy set theory. These approaches usually reduce fuzzy quanti?cation to a comparison of scalar or fuzzy cardinalities [197, 132].
Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book represents the thoroughly refereed post-proceedings of the 6th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2005, held in Batumi, Georgia. The 19 revised full papers presented were carefully reviewed and selected from numerous presentations at the symposium. The papers present current research in all aspects of linguistics, logic and computation.