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Author: Nino B. Cocchiarella Publisher: Oxford University Press ISBN: 0190451203 Category : Philosophy Languages : en Pages : 288
Book Description
In this text, a variety of modal logics at the sentential, first-order, and second-order levels are developed with clarity, precision and philosophical insight. All of the S1-S5 modal logics of Lewis and Langford, among others, are constructed. A matrix, or many-valued semantics, for sentential modal logic is formalized, and an important result that no finite matrix can characterize any of the standard modal logics is proven. Exercises, some of which show independence results, help to develop logical skills. A separate sentential modal logic of logical necessity in logical atomism is also constructed and shown to be complete and decidable. On the first-order level of the logic of logical necessity, the modal thesis of anti-essentialism is valid and every de re sentence is provably equivalent to a de dicto sentence. An elegant extension of the standard sentential modal logics into several first-order modal logics is developed. Both a first-order modal logic for possibilism containing actualism as a proper part as well as a separate modal logic for actualism alone are constructed for a variety of modal systems. Exercises on this level show the connections between modal laws and quantifier logic regarding generalization into, or out of, modal contexts and the conditions required for the necessity of identity and non-identity. Two types of second-order modal logics, one possibilist and the other actualist, are developed based on a distinction between existence-entailing concepts and concepts in general. The result is a deeper second-order analysis of possibilism and actualism as ontological frameworks. Exercises regarding second-order predicate quantifiers clarify the distinction between existence-entailing concepts and concepts in general. Modal Logic is ideally suited as a core text for graduate and undergraduate courses in modal logic, and as supplementary reading in courses on mathematical logic, formal ontology, and artificial intelligence.
Author: Kenneth Konyndyk Publisher: ISBN: 9780268011598 Category : Modality (Logic) Languages : en Pages : 0
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.
Author: M. Fitting Publisher: Springer Science & Business Media ISBN: 9401152926 Category : Philosophy Languages : en Pages : 300
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: Timothy Williamson Publisher: Oxford University Press ISBN: 019955207X Category : Philosophy Languages : en Pages : 481
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: Johan van Benthem Publisher: ISBN: Category : Mathematics Languages : en Pages : 402
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: Eric Pacuit Publisher: Springer ISBN: 3319671499 Category : Philosophy Languages : en Pages : 165
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
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: Patrick Blackburn Publisher: Elsevier ISBN: 9780080466668 Category : Mathematics Languages : en Pages : 1260
Book Description
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: James W. Garson
Author: James W. Garson
Author: Nino B. Cocchiarella
Author: Kenneth Konyndyk
Author: M. Fitting
Author: Timothy Williamson
Author: Brian F. Chellas
Author: Johan van Benthem
Author: Eric Pacuit
Author: Craig Smorynski
Author: Patrick Blackburn