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Author : Anonim
Publisher : Wydawnictwo UJ
Page : 140 pages
File Size : 45,5 Mb
Release : 2011
Category : Electronic
ISBN : 9788323384083
Reports on Mathematical Logic is a journal aimed at publishing quality research papers on mathematical logic and foundations of mathematicsâ€TM.
Author : Richard L Epstein
Publisher : Advanced Reasoning Forum
Page : 509 pages
File Size : 55,5 Mb
Release : 2018-11-05
Category : Philosophy
ISBN : 9780983452171
This book presents the history, philosophy, and mathematics of the major systems of propositional logic. Classical logic, modal logics, many-valued logics, intuitionism, paraconsistent logics, and dependent implication are examined in separate chapters. Each begins with a motivation in the originators' own terms, followed by the standard formal semantics, syntax, and completeness theorem. The chapters on the various logics are largely self-contained so that the book can be used as a reference. An appendix summarizes the formal semantics and axiomatizations of the logics. The view that unifies the exposition is that propositional logics comprise a spectrum: as the aspect of propositions under consideration varies, the logic varies. Each logic is shown to fall naturally within a general framework for semantics. A theory of translations between logics is presented that allows for further comparisons, and necessary conditions are given for a translation to preserve meaning. For this third edition the material has been re-organized to make the text easier to study, and a new section on paraconsistent logics with simple semantics has been added which challenges standard views on the nature of consequence relations. The text includes worked examples and hundreds of exercises, from routine to open problems, making the book with its clear and careful exposition ideal for courses or individual study.
Author : Nikolaos Galatos,Peter Jipsen,Tomasz Kowalski,Hiroakira Ono
Publisher : Elsevier
Page : 532 pages
File Size : 54,6 Mb
Release : 2007-04-25
Category : Mathematics
ISBN : 9780080489643
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 : R.L. Epstein
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 53,8 Mb
Release : 2013-11-11
Category : Philosophy
ISBN : 9789400905252
This book grew out of my confusion. If logic is objective how can there be so many logics? Is there one right logic, or many right ones? Is there some underlying unity that connects them? What is the significance of the mathematical theorems about logic which I've learned if they have no connection to our everyday reasoning? The answers I propose revolve around the perception that what one pays attention to in reasoning determines which logic is appropriate. The act of abstracting from our reasoning in our usual language is the stepping stone from reasoned argument to logic. We cannot take this step alone, for we reason together: logic is reasoning which has some objective value. For you to understand my answers, or perhaps better, conjectures, I have retraced my steps: from the concrete to the abstract, from examples, to general theory, to further confirming examples, to reflections on the significance of the work.
Author : [Anonymus AC02315363]
Publisher : Unknown
Page : 109 pages
File Size : 52,5 Mb
Release : 1996
Category : Electronic
ISBN : 8323311013
Author : Defense Documentation Center (U.S.)
Publisher : Unknown
Page : 1746 pages
File Size : 50,5 Mb
Release : 1961-04
Category : Military art and science
ISBN : UTEXAS:059172131213010
Author : Anonim
Publisher : Unknown
Page : 636 pages
File Size : 54,6 Mb
Release : 1998
Category : Logic, Symbolic and mathematical
ISBN : UOM:39015055727344
Author : S. S. Goncharov,Rod G. Downey,H. Ono
Publisher : World Scientific
Page : 329 pages
File Size : 41,8 Mb
Release : 2006
Category : Mathematics
ISBN : 9789812772749
This volume is devoted to the main areas of mathematical logic and applications to computer science. There are articles on weakly o-minimal theories, algorithmic complexity of relations, models within the computable model theory, hierarchies of randomness tests, computable numberings, and complexity problems of minimal unsatisfiable formulas. The problems of characterization of the deduction-detachment theorem, o 1 -induction, completeness of Leoniewski''s systems, and reduction calculus for the satisfiability problem are also discussed. The coverage includes the answer to Kanovei''s question about the upper bound for the complexity of equivalence relations by convergence at infinity for continuous functions. The volume also gives some applications to computer science such as solving the problems of inductive interference of languages from the full collection of positive examples and some negative data, the effects of random negative data, methods of formal specification and verification on the basis of model theory and multiple-valued logics, interval fuzzy algebraic systems, the problems of information exchange among agents on the base topological structures, and the predictions provided by inductive theories. Sample Chapter(s). Chapter 1: Another Characterization of the Deduction-Detachment Theorem (535 KB). Contents: Another Characterization of the Deduction-Detachment Theorem (S V Babyonyshev); On Behavior of 2-Formulas in Weakly o-Minimal Theories (B S Baizhanov & B Sh Kulpeshov); Arithmetic Turing Degrees and Categorical Theories of Computable Models (E Fokina); Negative Data in Learning Languages (S Jain & E Kinber); Effective Cardinals in the Nonstandard Universe (V Kanovei & M Reeken); Model-Theoretic Methods of Analysis of Computer Arithmetic (S P Kovalyov); The Functional Completeness of Leoniewski''s Systems (F Lepage); Hierarchies of Randomness Tests (J Reimann & F Stephan); Intransitive Linear Temporal Logic Based on Integer Numbers, Decidability, Admissible Logical Consecutions (V V Rybakov); The Logic of Prediction (E Vityaev); Conceptual Semantic Systems Theory and Applications (K E Wolff); Complexity Results on Minimal Unsatisfiable Formulas (X Zhao); and other papers. Readership: Researchers in mathematical logic and algebra, computer scientists in artificial intelligence and fuzzy logic."
Author : J. N. Crossley,C.J. Ash,C.J. Brickhill,J.C. Stillwell
Publisher : Courier Corporation
Page : 96 pages
File Size : 44,9 Mb
Release : 2012-08-29
Category : Mathematics
ISBN : 9780486151526
A serious introductory treatment geared toward non-logicians, this survey traces the development of mathematical logic from ancient to modern times and discusses the work of Planck, Einstein, Bohr, Pauli, Heisenberg, Dirac, and others. 1972 edition.
Author : Elliott M. Pearl
Publisher : Elsevier
Page : 776 pages
File Size : 47,8 Mb
Release : 2011-08-11
Category : Mathematics
ISBN : 0080475299
This volume is a collection of surveys of research problems in topology and its applications. The topics covered include general topology, set-theoretic topology, continuum theory, topological algebra, dynamical systems, computational topology and functional analysis. * New surveys of research problems in topology * New perspectives on classic problems * Representative surveys of research groups from all around the world
Author : Anonim
Publisher : Unknown
Page : 2194 pages
File Size : 51,7 Mb
Release : 1964
Category : Electronic
ISBN : PSU:000047866263
Author : Alessandro Andretta,Keith Kearnes,Domenico Zambella
Publisher : Cambridge University Press
Page : 221 pages
File Size : 42,7 Mb
Release : 2008
Category : Computers
ISBN : 9780521884242
A collection of surveys, tutorials, and research papers from the 2004 Logic Colloquium.
Author : Defense Documentation Center (U.S.)
Publisher : Unknown
Page : 922 pages
File Size : 52,5 Mb
Release : 1960
Category : Industrial arts
ISBN : UOM:39015024208558
Author : Paweł M. Idziak,Jerzy Perzanowski
Publisher : Unknown
Page : 146 pages
File Size : 44,5 Mb
Release : 1995
Category : Electronic
ISBN : 8323309825
Author : René Cori,Daniel Lascar
Publisher : OUP Oxford
Page : 361 pages
File Size : 41,5 Mb
Release : 2000-09-07
Category : Mathematics
ISBN : 9780191589775
Logic forms the basis of mathematics, and is hence a fundamental part of any mathematics course. In particular, it is a major element in theoretical computer science and has undergone a huge revival with the explosion of interest in computers and computer science. This book provides students with a clear and accessible introduction to this important subject. The concept of model underlies the whole book, giving the text a theoretical coherence whilst still covering a wide area of logic.
