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Author: James W. Garson
Publisher: Cambridge University Press
ISBN: 0521682290
Category : Mathematics
Languages : en
Pages : 429
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Book Description
This 2006 book provides an accessible, yet technically sound treatment of modal logic and its philosophical applications.
Author: James W. Garson
Publisher: Cambridge University Press
ISBN: 0521682290
Category : Mathematics
Languages : en
Pages : 429
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Book Description
This 2006 book provides an accessible, yet technically sound treatment of modal logic and its philosophical applications.
Author: Nino B. Cocchiarella
Publisher: Oxford University Press
ISBN: 0195366573
Category : Mathematics
Languages : en
Pages : 283
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Book Description
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: Timothy Williamson
Publisher: Oxford University Press
ISBN: 019955207X
Category : Philosophy
Languages : en
Pages : 481
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Book Description
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: A. Kurucz
Publisher: Elsevier
ISBN: 008053578X
Category : Computers
Languages : en
Pages : 767
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Book Description
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: M. Fitting
Publisher: Springer Science & Business Media
ISBN: 9401152926
Category : Philosophy
Languages : en
Pages : 300
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Book Description
This is a thorough treatment of first-order modal logic. The book covers such issues as quantification, equality (including a treatment of Frege's morning star/evening star puzzle), the notion of existence, non-rigid constants and function symbols, predicate abstraction, the distinction between nonexistence and nondesignation, and definite descriptions, borrowing from both Fregean and Russellian paradigms.
Author: Eric Pacuit
Publisher: Springer
ISBN: 3319671499
Category : Philosophy
Languages : en
Pages : 165
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Book Description
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: Craig Smorynski
Publisher: Springer Science & Business Media
ISBN: 1461386012
Category : Mathematics
Languages : en
Pages : 346
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Book Description
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: Johan van Benthem
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 402
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Book Description
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: Brian F. Chellas
Publisher: Cambridge University Press
ISBN: 9780521295154
Category : Mathematics
Languages : en
Pages : 316
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Book Description
An introductory textbook on modal logic the logic of necessity and possibility.
Author: Kenneth Konyndyk
Publisher:
ISBN: 9780268011598
Category : Modality (Logic)
Languages : en
Pages : 0
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Book Description
Modal logic, developed as an extension of classical propositional logic and first-order quantification theory, integrates the notions of possibility and necessity and necessary implication. Arguments whose understanding depends on some fundamental knowledge of modal logic have always been important in philosophy of religion, metaphysics, and epistemology. Moreover, modal logic has become increasingly important with the use of the concept of "possible worlds" in these areas. Introductory Modal Logic fills the need for a basic text on modal logic, accessible to students of elementary symbolic logic. Kenneth Konyndyk presents a natural deduction treatment of propositional modal logic and quantified modal logic, historical information about its development, and discussions of the philosophical issues raised by modal logic. Characterized by clear and concrete explanations, appropriate examples, and varied and challenging exercises, Introductory Modal Logic makes both modal logic and the possible-worlds metaphysics readily available to the introductory level student.
