Handbook of Modal Logic

The Handbook of Modal Logic contains 20 articles, which collectively introduce contemporary modal logic, survey current research, and indicate the way in which the field is developing.

Author: Patrick Blackburn

Publisher: Elsevier

ISBN: 0080466664

Category: Mathematics

Page: 1260

View: 170

Download →

The Handbook of Modal Logic contains 20 articles, which collectively introduce contemporary modal logic, survey current research, and indicate the way in which the field is developing. The articles survey the field from a wide variety of perspectives: the underling theory is explored in depth, modern computational approaches are treated, and six major applications areas of modal logic (in Mathematics, Computer Science, Artificial Intelligence, Linguistics, Game Theory, and Philosophy) are surveyed. The book contains both well-written expository articles, suitable for beginners approaching the subject for the first time, and advanced articles, which will help those already familiar with the field to deepen their expertise. Please visit: http://people.uleth.ca/~woods/RedSeriesPromo_WP/PubSLPR.html - Compact modal logic reference - Computational approaches fully discussed - Contemporary applications of modal logic covered in depth
Posted in:

Modal Model Theory

Abstract: "This paper contributes to the model theory of modal logic using bisimulations as the fundamental tool.

Author: Maarten de Rijke

Publisher:

ISBN: OCLC:33099191

Category: Model theory

Page: 20

View: 459

Download →

Abstract: "This paper contributes to the model theory of modal logic using bisimulations as the fundamental tool. A uniform presentation is given of modal analogues of well-known definability and preservation results from first-order logic. These results include algebraic characterizations of modal equivalence, and of the modally definable classes of models; the preservation results concern preservation of modal formulas under submodels, unions of chains, and homomorphisms."
Posted in:

A New Introduction to Modal Logic

This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic: An Introduction to Modal Logic and A Companion to Modal Logic.

Author: M.J. Cresswell

Publisher: Routledge

ISBN: 9781134800285

Category: Philosophy

Page: 432

View: 871

Download →

This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic: An Introduction to Modal Logic and A Companion to Modal Logic. A New Introduction to Modal Logic is an entirely new work, completely re-written by the authors. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing tha clarity of exposition and approachability that were essential features of their earlier works. The book takes readers from the most basic systems of modal propositional logic right up to systems of modal predicate with identity. It covers both technical developments such as completeness and incompleteness, and finite and infinite models, and their philosophical applications, especially in the area of modal predicate logic.
Posted in:

Models for Modalities

The papers collected in this volume were written over a period of some eight or nine years, with some still earlier material incorporated in one of them.

Author: Jaakko Hintikka

Publisher: Springer Science & Business Media

ISBN: 9789401017114

Category: Philosophy

Page: 222

View: 429

Download →

The papers collected in this volume were written over a period of some eight or nine years, with some still earlier material incorporated in one of them. Publishing them under the same cover does not make a con tinuous book of them. The papers are thematically connected with each other, however, in a way which has led me to think that they can naturally be grouped together. In any list of philosophically important concepts, those falling within the range of application of modal logic will rank high in interest. They include necessity, possibility, obligation, permission, knowledge, belief, perception, memory, hoping, and striving, to mention just a few of the more obvious ones. When a satisfactory semantics (in the sense of Tarski and Carnap) was first developed for modal logic, a fascinating new set of methods and ideas was thus made available for philosophical studies. The pioneers of this model theory of modality include prominently Stig Kanger and Saul Kripke. Several others were working in the same area independently and more or less concurrently. Some of the older papers in this collection, especially 'Quantification and Modality' and 'Modes of Modality', serve to clarify some of the main possibilities in the semantics of modal logics in general.
Posted in:

Bibliography of Mathematical Logic

Answering this challenge was and is the central motivation for compiling this Bibliography. The Bibliography comprises (presently) the following six volumes (listed with the corresponding Editors): I. Classical Logic W. Rautenberg 11.

Author: Heinz-Dieter Ebbinghaus

Publisher: Springer Science & Business Media

ISBN: 9783662090589

Category: Mathematics

Page: 617

View: 885

Download →

Gert H. Müller The growth of the number of publications in almost all scientific areas, as in the area of (mathematical) logic, is taken as a sign of our scientifically minded culture, but it also has a terrifying aspect. In addition, given the rapidly growing sophistica tion, specialization and hence subdivision of logic, researchers, students and teachers may have a hard time getting an overview of the existing literature, partic ularly if they do not have an extensive library available in their neighbourhood: they simply do not even know what to ask for! More specifically, if someone vaguely knows that something vaguely connected with his interests exists some where in the literature, he may not be able to find it even by searching through the publications scattered in the review journals. Answering this challenge was and is the central motivation for compiling this Bibliography. The Bibliography comprises (presently) the following six volumes (listed with the corresponding Editors): I. Classical Logic W. Rautenberg 11. Non-classical Logics W. Rautenberg 111. Model Theory H.-D. Ebbinghaus IV. Recursion Theory P.G. Hinman V. Set Theory A.R. Blass VI. ProofTheory; Constructive Mathematics J.E. Kister; D. van Dalen & A.S. Troelstra.
Posted in:

Finite Model Theory and Its Applications

This volume gives a broadoverviewof some central themes of ?nite model theory: expressive power, descriptive complexity, and zero–one laws, together with selected applications to database theory and arti?cial intelligence, es- cially ...

Author: Erich Grädel

Publisher: Springer Science & Business Media

ISBN: 9783540004288

Category: Computers

Page: 437

View: 950

Download →

Finite model theory,as understoodhere, is an areaof mathematicallogic that has developed in close connection with applications to computer science, in particular the theory of computational complexity and database theory. One of the fundamental insights of mathematical logic is that our understanding of mathematical phenomena is enriched by elevating the languages we use to describe mathematical structures to objects of explicit study. If mathematics is the science of patterns, then the media through which we discern patterns, as well as the structures in which we discern them, command our attention. It isthis aspect oflogicwhichis mostprominentin model theory,“thebranchof mathematical logic which deals with the relation between a formal language and its interpretations”. No wonder, then, that mathematical logic, and ?nite model theory in particular, should ?nd manifold applications in computer science: from specifying programs to querying databases, computer science is rife with phenomena whose understanding requires close attention to the interaction between language and structure. This volume gives a broadoverviewof some central themes of ?nite model theory: expressive power, descriptive complexity, and zero–one laws, together with selected applications to database theory and arti?cial intelligence, es- cially constraint databases and constraint satisfaction problems. The ?nal chapter provides a concise modern introduction to modal logic,which emp- sizes the continuity in spirit and technique with ?nite model theory.
Posted in:

Many Dimensional Modal Logics Theory and Applications

The intended audience of this book is logicians as well as those researchers who use logic in computer science and artificial intelligence.

Author: A. Kurucz

Publisher: Elsevier

ISBN: 9780080535784

Category: Computers

Page: 766

View: 970

Download →

Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a many-dimensional system, say, to reason about knowledge bases developing in time or moving objects. To study the computational behaviour of many-dimensional modal logics is the main aim of this book. On the one hand, it is concerned with providing a solid mathematical foundation for this discipline, while on the other hand, it shows that many seemingly different applied many-dimensional systems (e.g., multi-agent systems, description logics with epistemic, temporal and dynamic operators, spatio-temporal logics, etc.) fit in perfectly with this theoretical framework, and so their computational behaviour can be analyzed using the developed machinery. We start with concrete examples of applied one- and many-dimensional modal logics such as temporal, epistemic, dynamic, description, spatial logics, and various combinations of these. Then we develop a mathematical theory for handling a spectrum of 'abstract' combinations of modal logics - fusions and products of modal logics, fragments of first-order modal and temporal logics - focusing on three major problems: decidability, axiomatizability, and computational complexity. Besides the standard methods of modal logic, the technical toolkit includes the method of quasimodels, mosaics, tilings, reductions to monadic second-order logic, algebraic logic techniques. Finally, we apply the developed machinery and obtained results to three case studies from the field of knowledge representation and reasoning: temporal epistemic logics for reasoning about multi-agent systems, modalized description logics for dynamic ontologies, and spatio-temporal logics. The genre of the book can be defined as a research monograph. It brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). On the other hand, well-known results from modal and first-order logic are formulated without proofs and supplied with references to accessible sources. The intended audience of this book is logicians as well as those researchers who use logic in computer science and artificial intelligence. More specific application areas are, e.g., knowledge representation and reasoning, in particular, terminological, temporal and spatial reasoning, or reasoning about agents. And we also believe that researchers from certain other disciplines, say, temporal and spatial databases or geographical information systems, will benefit from this book as well. Key Features: • Integrated approach to modern modal and temporal logics and their applications in artificial intelligence and computer science • Written by internationally leading researchers in the field of pure and applied logic • Combines mathematical theory of modal logic and applications in artificial intelligence and computer science • Numerous open problems for further research • Well illustrated with pictures and tables
Posted in:

Modal Logic

A 2001 graduate text on modal logic, a field which has caught the attention of computer scientists, economists and computational linguists.

Author: Patrick Blackburn

Publisher: Cambridge University Press

ISBN: 0521527147

Category: Computers

Page: 554

View: 697

Download →

A 2001 graduate text on modal logic, a field which has caught the attention of computer scientists, economists and computational linguists.
Posted in: