Reports On Mathematical Logic No 46
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Reports On Mathematical Logic No 46
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Author :
language : en
Publisher: Wydawnictwo UJ
Release Date : 2011
Reports On Mathematical Logic No 46 written by and has been published by Wydawnictwo UJ this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
Reports on Mathematical Logic is a journal aimed at publishing quality research papers on mathematical logic and foundations of mathematicsâ€TM.
Reports On Mathematical Logic
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Author :
language : en
Publisher:
Release Date : 1998
Reports On Mathematical Logic written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Logic, Symbolic and mathematical categories.
The Semantic Foundations Of Logic Volume 1 Propositional Logics
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Author : R.L. Epstein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
The Semantic Foundations Of Logic Volume 1 Propositional Logics written by R.L. Epstein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Philosophy categories.
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.
Propositional Logics 3rd Edition
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Author : Richard L Epstein
language : en
Publisher: Advanced Reasoning Forum
Release Date : 2018-11-05
Propositional Logics 3rd Edition written by Richard L Epstein and has been published by Advanced Reasoning Forum this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-05 with Philosophy categories.
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.
Residuated Lattices An Algebraic Glimpse At Substructural Logics
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Author : Nikolaos Galatos
language : en
Publisher: Elsevier
Release Date : 2007-04-25
Residuated Lattices An Algebraic Glimpse At Substructural Logics written by Nikolaos Galatos and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-25 with Mathematics categories.
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.
U S Government Research Reports
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Author :
language : en
Publisher:
Release Date : 1964
U S Government Research Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Science categories.
Technical Abstract Bulletin
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Author :
language : en
Publisher:
Release Date : 1964
Technical Abstract Bulletin written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Science categories.
Current Research And Development In Scientific Documentation
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Author : National Science Foundation (U.S.). Office of Scientific Information
language : en
Publisher:
Release Date :
Current Research And Development In Scientific Documentation written by National Science Foundation (U.S.). Office of Scientific Information and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Current Research And Development In Scientific Documentation
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Author :
language : en
Publisher:
Release Date : 1962
Current Research And Development In Scientific Documentation written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Documentation categories.
Structure Of Language And Its Mathematical Aspects
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 1961
Structure Of Language And Its Mathematical Aspects written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Language and languages categories.