Natural Deduction Hybrid Systems And Modal Logics

Author : Andrzej Indrzejczak
Publisher : Springer Science & Business Media
ISBN 13 : 9048187850
Total Pages : 515 pages
Book Rating : 4.50/5 ( download)

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Download or read book Natural Deduction, Hybrid Systems and Modal Logics written by Andrzej Indrzejczak and published by Springer Science & Business Media. This book was released on 2010-07-03 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed exposition of one of the most practical and popular methods of proving theorems in logic, called Natural Deduction. It is presented both historically and systematically. Also some combinations with other known proof methods are explored. The initial part of the book deals with Classical Logic, whereas the rest is concerned with systems for several forms of Modal Logics, one of the most important branches of modern logic, which has wide applicability.

Author : Torben Braüner
Publisher : Springer Science & Business Media
ISBN 13 : 9400700024
Total Pages : 240 pages
Book Rating : 4.24/5 ( download)

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Download or read book Hybrid Logic and its Proof-Theory written by Torben Braüner and published by Springer Science & Business Media. This book was released on 2010-11-17 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book-length treatment of hybrid logic and its proof-theory. Hybrid logic is an extension of ordinary modal logic which allows explicit reference to individual points in a model (where the points represent times, possible worlds, states in a computer, or something else). This is useful for many applications, for example when reasoning about time one often wants to formulate a series of statements about what happens at specific times. There is little consensus about proof-theory for ordinary modal logic. Many modal-logical proof systems lack important properties and the relationships between proof systems for different modal logics are often unclear. In the present book we demonstrate that hybrid-logical proof-theory remedies these deficiencies by giving a spectrum of well-behaved proof systems (natural deduction, Gentzen, tableau, and axiom systems) for a spectrum of different hybrid logics (propositional, first-order, intensional first-order, and intuitionistic).

Author : M. Fitting
Publisher : Springer Science & Business Media
ISBN 13 : 9789027715739
Total Pages : 574 pages
Book Rating : 4.34/5 ( download)

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Download or read book Proof Methods for Modal and Intuitionistic Logics written by M. Fitting and published by Springer Science & Business Media. This book was released on 1983-04-30 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Necessity is the mother of invention. " Part I: What is in this book - details. There are several different types of formal proof procedures that logicians have invented. The ones we consider are: 1) tableau systems, 2) Gentzen sequent calculi, 3) natural deduction systems, and 4) axiom systems. We present proof procedures of each of these types for the most common normal modal logics: S5, S4, B, T, D, K, K4, D4, KB, DB, and also G, the logic that has become important in applications of modal logic to the proof theory of Peano arithmetic. Further, we present a similar variety of proof procedures for an even larger number of regular, non-normal modal logics (many introduced by Lemmon). We also consider some quasi-regular logics, including S2 and S3. Virtually all of these proof procedures are studied in both propositional and first-order versions (generally with and without the Barcan formula). Finally, we present the full variety of proof methods for Intuitionistic logic (and of course Classical logic too). We actually give two quite different kinds of tableau systems for the logics we consider, two kinds of Gentzen sequent calculi, and two kinds of natural deduction systems. Each of the two tableau systems has its own uses; each provides us with different information about the logics involved. They complement each other more than they overlap. Of the two Gentzen systems, one is of the conventional sort, common in the literature.

Author : Dag Prawitz
Publisher : Courier Dover Publications
ISBN 13 : 0486446557
Total Pages : 132 pages
Book Rating : 4.54/5 ( download)

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Download or read book Natural Deduction written by Dag Prawitz and published by Courier Dover Publications. This book was released on 2006-02-24 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: An innovative approach to the semantics of logic, proof-theoretic semantics seeks the meaning of propositions and logical connectives within a system of inference. Gerhard Gentzen invented proof-theoretic semantics in the early 1930s, and Dag Prawitz, the author of this study, extended its analytic proofs to systems of natural deduction. Prawitz's theories form the basis of intuitionistic type theory, and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics. The concept of natural deduction follows a truly natural progression, establishing the relationship between a noteworthy systematization and the interpretation of logical signs. As this survey explains, the deduction's principles allow it to proceed in a direct fashion — a manner that permits every natural deduction's transformation into the equivalent of normal form theorem. A basic result in proof theory, the normal form theorem was established by Gentzen for the calculi of sequents. The proof of this result for systems of natural deduction is in many ways simpler and more illuminating than alternative methods. This study offers clear illustrations of the proof and numerous examples of its advantages.

Author : James W. Garson
Publisher : Cambridge University Press
ISBN 13 : 0521682290
Total Pages : 429 pages
Book Rating : 4.99/5 ( download)

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Download or read book Modal Logic for Philosophers written by James W. Garson and published by Cambridge University Press. This book was released on 2006-08-14 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2006 book provides an accessible, yet technically sound treatment of modal logic and its philosophical applications.

Author : Ángel Garrido
Publisher : Birkhäuser
ISBN 13 : 3319654306
Total Pages : 815 pages
Book Rating : 4.00/5 ( download)

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Download or read book The Lvov-Warsaw School. Past and Present written by Ángel Garrido and published by Birkhäuser. This book was released on 2018-06-12 with total page 815 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of new investigations and discoveries on the history of a great tradition, the Lvov-Warsaw School of logic and mathematics, by the best specialists from all over the world. The papers range from historical considerations to new philosophical, logical and mathematical developments of this impressive School, including applications to Computer Science, Mathematics, Metalogic, Scientific and Analytic Philosophy, Theory of Models and Linguistics.

Author : Zuzana Rybaříková
Publisher : Vydavatelství Filozofické fakulty Univerzity Palackého v Olomouci
ISBN 13 : 8087895770
Total Pages : 134 pages
Book Rating : 4.71/5 ( download)

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Download or read book The Reconstruction of A. N. Prior's Ontology written by Zuzana Rybaříková and published by Vydavatelství Filozofické fakulty Univerzity Palackého v Olomouci. This book was released on with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the first analytic philosophers were primarily focused on the logical analysis of language, some of their initial works also contained ontological discussions. One of the most distinct ontological positions of the twentieth century was defended by Arthur Norman Prior. The unusual nature of the position could be demonstrated by the fact that he was ascribed to such divergent positions as nominalism and platonism. This might have been caused by his atypical combination of ontological views. He was, on the one hand, a nominalist in his mature works. On the other hand, he advocated intensional logic and presentism. The aim of this study is to reconstruct the ideas which influenced him as he formulated his ontological positions. Not only are Prior’s ideas introduced, but also the ideas of his precursors and contemporaries who influenced him. In contrast, the ideas of logicians and philosophers who Prior opposed are also presented. The dissertation consists of four parts which deal with Prior’s concepts of possible worlds, theories of quantifications, propositions and individuals. It is a historical study and therefore the polemics which arose after Prior’s death are not discussed.

Author : Bangs L. Tapscott
Publisher :
ISBN 13 :
Total Pages : 240 pages
Book Rating : 4.58/5 ( download)

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Download or read book Modal Deduction written by Bangs L. Tapscott and published by . This book was released on 2018 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Dov M. Gabbay
Publisher : Springer Science & Business Media
ISBN 13 : 9400766009
Total Pages : 282 pages
Book Rating : 4.06/5 ( download)

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Download or read book Handbook of Philosophical Logic written by Dov M. Gabbay and published by Springer Science & Business Media. This book was released on 2013-08-04 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition of the Handbook of Philosophical Logic reflects great changes in the landscape of philosophical logic since the first edition. It gives readers an idea of that landscape and its relation to computer science and formal language and artificial intelligence. It shows how the increased demand for philosophical logic from computer science and artificial intelligence and computational linguistics accelerated the development of the subject directly and indirectly. This development in turn, directly pushed research forward, stimulated by the needs of applications. New logic areas became established and old areas were enriched and expanded. At the same time, it socially provided employment for generations of logicians residing in computer science, linguistics and electrical engineering departments which of course helped keep the logic community to thrive. The many contributors to this Handbook are active in these application areas and are among the most famous leading figures of applied philosophical logic of our times. ​

Author : M.J. Cresswell
Publisher : Routledge
ISBN 13 : 1134800274
Total Pages : 436 pages
Book Rating : 4.78/5 ( download)

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Download or read book A New Introduction to Modal Logic written by M.J. Cresswell and published by Routledge. This book was released on 2012-08-06 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.