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Author : K.A. Bowen
Publisher : Springer Science & Business Media
ISBN 13 : 9401576424
Total Pages : 147 pages
Book Rating : 4.4/5 (15 download)
Download or read book Model Theory for Modal Logic written by K.A. Bowen and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A. Kurucz
Publisher : Elsevier
ISBN 13 : 008053578X
Total Pages : 767 pages
Book Rating : 4.0/5 (85 download)
Download or read book Many-Dimensional Modal Logics: Theory and Applications written by A. Kurucz and published by Elsevier. This book was released on 2003-10-21 with total page 767 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Author : K. A. Bowen
Publisher :
ISBN 13 : 9789401576437
Total Pages : 152 pages
Book Rating : 4.5/5 (764 download)
Download or read book Model Theory for Modal Logic written by K. A. Bowen and published by . This book was released on 2014-01-15 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Timothy Williamson
Publisher : Oxford University Press
ISBN 13 : 019955207X
Total Pages : 481 pages
Book Rating : 4.1/5 (995 download)
Download or read book Modal Logic as Metaphysics written by Timothy Williamson and published by Oxford University Press. This book was released on 2013-03-28 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: Timothy Williamson gives an original and provocative treatment of deep metaphysical questions about existence, contingency, and change, using the latest resources of quantified modal logic. Contrary to the widespread assumption that logic and metaphysics are disjoint, he argues that modal logic provides a structural core for metaphysics.
Author : Heinrich Wansing
Publisher : Springer Science & Business Media
ISBN 13 : 9401727988
Total Pages : 317 pages
Book Rating : 4.4/5 (17 download)
Download or read book Proof Theory of Modal Logic written by Heinrich Wansing and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof procedures. The volume is of immense importance for the interdisciplinary fields of logic, knowledge representation, and automated deduction.
Author : Patrick Blackburn
Publisher : Elsevier
ISBN 13 : 9780080466668
Total Pages : 1260 pages
Book Rating : 4.4/5 (666 download)
Download or read book Handbook of Modal Logic written by Patrick Blackburn and published by Elsevier. This book was released on 2006-11-03 with total page 1260 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Author : Johan van Benthem
Publisher :
ISBN 13 :
Total Pages : 402 pages
Book Rating : 4.3/5 (555 download)
Download or read book Modal Logic for Open Minds written by Johan van Benthem and published by . This book was released on 2010 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work, the author provides an introduction to the field of modal logic, outlining its major ideas and emploring the numerous ways in which various academic fields have adopted it.
Author : Eric Pacuit
Publisher : Springer
ISBN 13 : 3319671499
Total Pages : 165 pages
Book Rating : 4.3/5 (196 download)
Download or read book Neighborhood Semantics for Modal Logic written by Eric Pacuit and published by Springer. This book was released on 2017-11-15 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a state-of-the-art introduction to the basic techniques and results of neighborhood semantics for modal logic. In addition to presenting the relevant technical background, it highlights both the pitfalls and potential uses of neighborhood models – an interesting class of mathematical structures that were originally introduced to provide a semantics for weak systems of modal logic (the so-called non-normal modal logics). In addition, the book discusses a broad range of topics, including standard modal logic results (i.e., completeness, decidability and definability); bisimulations for neighborhood models and other model-theoretic constructions; comparisons with other semantics for modal logic (e.g., relational models, topological models, plausibility models); neighborhood semantics for first-order modal logic, applications in game theory (coalitional logic and game logic); applications in epistemic logic (logics of evidence and belief); and non-normal modal logics with dynamic modalities. The book can be used as the primary text for seminars on philosophical logic focused on non-normal modal logics; as a supplemental text for courses on modal logic, logic in AI, or philosophical logic (either at the undergraduate or graduate level); or as the primary source for researchers interested in learning about the uses of neighborhood semantics in philosophical logic and game theory.
Author : Bruno Courcelle
Publisher : Cambridge University Press
ISBN 13 : 1139644009
Total Pages : 743 pages
Book Rating : 4.1/5 (396 download)
Download or read book Graph Structure and Monadic Second-Order Logic written by Bruno Courcelle and published by Cambridge University Press. This book was released on 2012-06-14 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The authors not only provide a thorough description of the theory, but also detail its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.
Author : K.A. Bowen
Publisher : Springer
ISBN 13 : 9789027709295
Total Pages : 139 pages
Book Rating : 4.7/5 (92 download)
Download or read book Model Theory for Modal Logic written by K.A. Bowen and published by Springer. This book was released on 1978-12-31 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Craig Smorynski
Publisher : Springer Science & Business Media
ISBN 13 : 1461386012
Total Pages : 346 pages
Book Rating : 4.4/5 (613 download)
Download or read book Self-Reference and Modal Logic written by Craig Smorynski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is Sunday, the 7th of September 1930. The place is Konigsberg and the occasion is a small conference on the foundations of mathematics. Arend Heyting, the foremost disciple of L. E. J. Brouwer, has spoken on intuitionism; Rudolf Carnap of the Vienna Circle has expounded on logicism; Johann (formerly Janos and in a few years to be Johnny) von Neumann has explained Hilbert's proof theory-- the so-called formalism; and Hans Hahn has just propounded his own empiricist views of mathematics. The floor is open for general discussion, in the midst of which Heyting announces his satisfaction with the meeting. For him, the relationship between formalism and intuitionism has been clarified: There need be no war between the intuitionist and the formalist. Once the formalist has successfully completed Hilbert's programme and shown "finitely" that the "idealised" mathematics objected to by Brouwer proves no new "meaningful" statements, even the intuitionist will fondly embrace the infinite. To this euphoric revelation, a shy young man cautions~ "According to the formalist conception one adjoins to the meaningful statements of mathematics transfinite (pseudo-')statements which in themselves have no meaning but only serve to make the system a well-rounded one just as in geometry one achieves a well rounded system by the introduction of points at infinity.
Author : Daniel Gallin
Publisher : Elsevier
ISBN 13 : 148327473X
Total Pages : 159 pages
Book Rating : 4.4/5 (832 download)
Download or read book Intensional and Higher-Order Modal Logic written by Daniel Gallin and published by Elsevier. This book was released on 2016-06-03 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: North-Holland Mathematics Studies, 19: Intensional and Higher-Order Modal Logic: With Applications to Montague Semantics focuses on an approach to the problem of providing a precise account of natural language syntax and semantics, including the set-theoretic semantical methods, Boolean models, and two-sorted type theory. The book first offers information on intensional logic and alternative formulations of intensional logic. Topics include two-sorted type theory, normal forms, extensions and intensional logic, modal T-logic, persistence in intensional logic, generalized completeness of intensional logic, and natural language and intensional logic. The text then examines higher-order modal logic and algebraic semantics. Discussions focus on Cohen's independence results, topological models of MLp, modal independence results, Boolean models of MLp, relative strength of intensional logic and MLp, propositional operators, modal predicate logic, and propositions in MLp. The monograph is a valuable reference for mathematicians and researchers interested in intensional and higher-order modal logic.
Author : Patrick Blackburn
Publisher : Cambridge University Press
ISBN 13 : 1316101959
Total Pages : 574 pages
Book Rating : 4.3/5 (161 download)
Download or read book Modal Logic written by Patrick Blackburn and published by Cambridge University Press. This book was released on 2002-08-22 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an advanced 2001 textbook on modal logic, a field which caught the attention of computer scientists in the late 1970s. Researchers in areas ranging from economics to computational linguistics have since realised its worth. The book is for novices and for more experienced readers, with two distinct tracks clearly signposted at the start of each chapter. The development is mathematical; prior acquaintance with first-order logic and its semantics is assumed, and familiarity with the basic mathematical notions of set theory is required. The authors focus on the use of modal languages as tools to analyze the properties of relational structures, including their algorithmic and algebraic aspects, and applications to issues in logic and computer science such as completeness, computability and complexity are considered. Three appendices supply basic background information and numerous exercises are provided. Ideal for anyone wanting to learn modern modal logic.
Author : Nino B. Cocchiarella
Publisher : Oxford University Press
ISBN 13 : 0195366573
Total Pages : 283 pages
Book Rating : 4.1/5 (953 download)
Download or read book Modal Logic written by Nino B. Cocchiarella and published by Oxford University Press. This book was released on 2008 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Introduction. 2. The Syntax of Modal Sentential Calculi. 4. Semantics for Logical Necessity. 5. Semantics for S5. 6. Relational World Systems. 7. Quantified Modal Logic. 8. The Semantics of Quantified Modal Logic. 9. Second-Order Modal Logic. 10. Semantics of Second-Order Modal Logic. Afterword. Bibliography. Index.
Author : James W. Garson
Publisher : Cambridge University Press
ISBN 13 : 1107512301
Total Pages : 505 pages
Book Rating : 4.1/5 (75 download)
Download or read book Modal Logic for Philosophers written by James W. Garson and published by Cambridge University Press. This book was released on 2013-11-25 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on modal logic is especially designed for philosophy students. It provides an accessible yet technically sound treatment of modal logic and its philosophical applications. Every effort is made to simplify the presentation by using diagrams instead of more complex mathematical apparatus. These and other innovations provide philosophers with easy access to a rich variety of topics in modal logic, including a full coverage of quantified modal logic, non-rigid designators, definite descriptions, and the de-re de-dicto distinction. Discussion of philosophical issues concerning the development of modal logic is woven into the text. The book uses natural deduction systems, which are widely regarded as the easiest to teach and use. It also includes a diagram technique that extends the method of truth trees to modal logic. This provides a foundation for a novel method for showing completeness that is easy to extend to quantifiers. This second edition contains a new chapter on logics of conditionals, an updated and expanded bibliography, and is updated throughout.
Author : Maarten Marx
Publisher : Springer Science & Business Media
ISBN 13 : 9401156948
Total Pages : 242 pages
Book Rating : 4.4/5 (11 download)
Download or read book Multi-Dimensional Modal Logic written by Maarten Marx and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modal Logic is a branch of logic with applications in many related disciplines such as computer science, philosophy, linguistics and artificial intelligence. Over the last twenty years, in all of these neighbouring fields, modal systems have been developed that we call multi-dimensional. (Our definition of multi-dimensionality in modal logic is a technical one: we call a modal formalism multi-dimensional if, in its intended semantics, the universe of a model consists of states that are tuples over some more basic set.) This book treats such multi-dimensional modal logics in a uniform way, linking their mathematical theory to the research tradition in algebraic logic. We will define and discuss a number of systems in detail, focusing on such aspects as expressiveness, definability, axiomatics, decidability and interpolation. Although the book will be mathematical in spirit, we take care to give motivations from the disciplines mentioned earlier on.
Author : Katrin Tent
Publisher : Cambridge University Press
ISBN 13 : 052176324X
Total Pages : 259 pages
Book Rating : 4.5/5 (217 download)
Download or read book A Course in Model Theory written by Katrin Tent and published by Cambridge University Press. This book was released on 2012-03-08 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise introduction to current topics in model theory, including simple and stable theories.
