Studies In Logic

Author : George Boole
Publisher : Courier Corporation
ISBN 13 : 0486488268
Total Pages : 514 pages
Book Rating : 4.64/5 ( download)

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Download or read book Studies in Logic and Probability written by George Boole and published by Courier Corporation. This book was released on 2012-01-01 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: Authoritative account of the development of Boole's ideas in logic and probability theory ranges from The Mathematical Analysis of Logic to the end of his career. The Laws of Thought formed the most systematic statement of Boole's theories; this volume contains incomplete studies intended for a follow-up volume. 1952 edition.

Author : Patrick Blackburn
Publisher : Elsevier
ISBN 13 : 9780080466668
Total Pages : 1260 pages
Book Rating : 4.64/5 ( download)

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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 : Charles Sanders Peirce
Publisher :
ISBN 13 :
Total Pages : 296 pages
Book Rating : 4.68/5 ( download)

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Download or read book Studies in Logic written by Charles Sanders Peirce and published by . This book was released on 1883 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: "These papers, the work of my students, have been so instructive to me, that I have asked and obtained permission to publish them in one volume. Two of them present new developments of the logical algebra of Boole. The volume contains two other papers relating to deductive logic and two papers upon inductive logic"--Preface. (PsycINFO Database Record (c) 2010 APA, all rights reserved)

Author : R.H. Johnson
Publisher : Elsevier
ISBN 13 : 0080532918
Total Pages : 508 pages
Book Rating : 4.12/5 ( download)

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Download or read book Handbook of the Logic of Argument and Inference written by R.H. Johnson and published by Elsevier. This book was released on 2002-09-11 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of the Logic of Argument and Inference is an authoritative reference work in a single volume, designed for the attention of senior undergraduates, graduate students and researchers in all the leading research areas concerned with the logic of practical argument and inference. After an introductory chapter, the role of standard logics is surveyed in two chapters. These chapters can serve as a mini-course for interested readers, in deductive and inductive logic, or as a refresher. Then follow two chapters of criticism; one the internal critique and the other the empirical critique. The first deals with objections to standard logics (as theories of argument and inference) arising from the research programme in philosophical logic. The second canvasses criticisms arising from work in cognitive and experimental psychology. The next five chapters deal with developments in dialogue logic, interrogative logic, informal logic, probability logic and artificial intelligence. The last chapter surveys formal approaches to practical reasoning and anticipates possible future developments. Taken as a whole the Handbook is a single-volume indication of the present state of the logic of argument and inference at its conceptual and theoretical best. Future editions will periodically incorporate significant new developments.

Author : S.R. Buss
Publisher : Elsevier
ISBN 13 : 0080533183
Total Pages : 823 pages
Book Rating : 4.86/5 ( download)

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Download or read book Handbook of Proof Theory written by S.R. Buss and published by Elsevier. This book was released on 1998-07-09 with total page 823 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth. The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.

Author : Martin Heidegger
Publisher : Indiana University Press
ISBN 13 : 0253004454
Total Pages : 348 pages
Book Rating : 4.51/5 ( download)

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Download or read book Logic written by Martin Heidegger and published by Indiana University Press. This book was released on 2010-03-22 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Heidegger’s radical thinking on the meaning of truth in a “clear and comprehensive critical edition” (Philosophy in Review). Martin Heidegger’s 1925–26 lectures on truth and time provided much of the basis for his momentous work, Being and Time. Not published until 1976—three months before Heidegger’s death—as volume 21 of his Complete Works, it is nonetheless central to Heidegger’s overall project of reinterpreting Western thought in terms of time and truth. The text shows the degree to which Aristotle underlies Heidegger’s hermeneutical theory of meaning. It also contains Heidegger’s first published critique of Husserl and takes major steps toward establishing the temporal bases of logic and truth. Thomas Sheehan’s elegant and insightful translation offers English-speaking readers access to this fundamental text for the first time.

Author : Morten Heine Sørensen
Publisher : Elsevier
ISBN 13 : 0080478921
Total Pages : 457 pages
Book Rating : 4.20/5 ( download)

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Download or read book Lectures on the Curry-Howard Isomorphism written by Morten Heine Sørensen and published by Elsevier. This book was released on 2006-07-04 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance,minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc.The isomorphism has many aspects, even at the syntactic level:formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds to term reduction, etc.But there is more to the isomorphism than this. For instance, it is an old idea---due to Brouwer, Kolmogorov, and Heyting---that a constructive proof of an implication is a procedure that transformsproofs of the antecedent into proofs of the succedent; the Curry-Howard isomorphism gives syntactic representations of such procedures. The Curry-Howard isomorphism also provides theoretical foundations for many modern proof-assistant systems (e.g. Coq).This book give an introduction to parts of proof theory and related aspects of type theory relevant for the Curry-Howard isomorphism. It can serve as an introduction to any or both of typed lambda-calculus and intuitionistic logic. Key features- The Curry-Howard Isomorphism treated as common theme- Reader-friendly introduction to two complementary subjects: Lambda-calculus and constructive logics- Thorough study of the connection between calculi and logics- Elaborate study of classical logics and control operators- Account of dialogue games for classical and intuitionistic logic- Theoretical foundations of computer-assisted reasoning · The Curry-Howard Isomorphism treated as the common theme.· Reader-friendly introduction to two complementary subjects: lambda-calculus and constructive logics · Thorough study of the connection between calculi and logics.· Elaborate study of classical logics and control operators.· Account of dialogue games for classical and intuitionistic logic.· Theoretical foundations of computer-assisted reasoning

Author :
Publisher :
ISBN 13 : 9780720422009
Total Pages : 0 pages
Book Rating : 4.00/5 ( download)

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Download or read book Model Theory written by and published by . This book was released on 1973 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Nikolaos Galatos
Publisher : Elsevier
ISBN 13 : 0080489648
Total Pages : 532 pages
Book Rating : 4.43/5 ( download)

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Download or read book Residuated Lattices: An Algebraic Glimpse at Substructural Logics written by Nikolaos Galatos and published by Elsevier. This book was released on 2007-04-25 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is meant to serve two purposes. The first and more obvious one is to present state of the art results in algebraic research into residuated structures related to substructural logics. The second, less obvious but equally important, is to provide a reasonably gentle introduction to algebraic logic. At the beginning, the second objective is predominant. Thus, in the first few chapters the reader will find a primer of universal algebra for logicians, a crash course in nonclassical logics for algebraists, an introduction to residuated structures, an outline of Gentzen-style calculi as well as some titbits of proof theory - the celebrated Hauptsatz, or cut elimination theorem, among them. These lead naturally to a discussion of interconnections between logic and algebra, where we try to demonstrate how they form two sides of the same coin. We envisage that the initial chapters could be used as a textbook for a graduate course, perhaps entitled Algebra and Substructural Logics. As the book progresses the first objective gains predominance over the second. Although the precise point of equilibrium would be difficult to specify, it is safe to say that we enter the technical part with the discussion of various completions of residuated structures. These include Dedekind-McNeille completions and canonical extensions. Completions are used later in investigating several finiteness properties such as the finite model property, generation of varieties by their finite members, and finite embeddability. The algebraic analysis of cut elimination that follows, also takes recourse to completions. Decidability of logics, equational and quasi-equational theories comes next, where we show how proof theoretical methods like cut elimination are preferable for small logics/theories, but semantic tools like Rabin's theorem work better for big ones. Then we turn to Glivenko's theorem, which says that a formula is an intuitionistic tautology if and only if its double negation is a classical one. We generalise it to the substructural setting, identifying for each substructural logic its Glivenko equivalence class with smallest and largest element. This is also where we begin investigating lattices of logics and varieties, rather than particular examples. We continue in this vein by presenting a number of results concerning minimal varieties/maximal logics. A typical theorem there says that for some given well-known variety its subvariety lattice has precisely such-and-such number of minimal members (where values for such-and-such include, but are not limited to, continuum, countably many and two). In the last two chapters we focus on the lattice of varieties corresponding to logics without contraction. In one we prove a negative result: that there are no nontrivial splittings in that variety. In the other, we prove a positive one: that semisimple varieties coincide with discriminator ones. Within the second, more technical part of the book another transition process may be traced. Namely, we begin with logically inclined technicalities and end with algebraically inclined ones. Here, perhaps, algebraic rendering of Glivenko theorems marks the equilibrium point, at least in the sense that finiteness properties, decidability and Glivenko theorems are of clear interest to logicians, whereas semisimplicity and discriminator varieties are universal algebra par exellence. It is for the reader to judge whether we succeeded in weaving these threads into a seamless fabric.

Author : Alfred Tarski
Publisher : Dover Books on Mathematics
ISBN 13 : 9780486477039
Total Pages : 0 pages
Book Rating : 4.37/5 ( download)

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Download or read book Undecidable Theories written by Alfred Tarski and published by Dover Books on Mathematics. This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This well-known book by the famed logician consists of three treatises: A General Method in Proofs of Undecidability, Undecidability and Essential Undecidability in Mathematics, and Undecidability of the Elementary Theory of Groups. 1953 edition.