Download or read book Deducibility and Decidability written by R. R. Rockingham Gill and published by Routledge. This book was released on 2002-09-11 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the results of these thinkers in a newly unified manner and displays their significance for the philosophy of mathematics.

Download or read book Automated Deduction Decidability Complexity Tractability written by Silvio Ghilardi and published by . This book was released on 2010 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Rewriting Techniques and Applications written by Ralf Treinen and published by Springer Science & Business Media. This book was released on 2009-06-09 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 20th International Conference on Rewriting Techniques and Applications, RTA 2009, held in Brasília, Brazil, during June 29 - July 1, 2009. The 22 revised full papers and four system descriptions presented were carefully reviewed and selected from 59 initial submissions. The papers cover current research on all aspects of rewriting including typical areas of interest such as applications, foundational issues, frameworks, implementations, and semantics.

Download or read book STACS 2007 written by Wolfgang Thomas and published by Springer Science & Business Media. This book was released on 2007-02-08 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 24th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2007, held in Aachen, Germany in February 2007. The 56 revised full papers presented together with 3 invited papers were carefully reviewed and selected from about 400 submissions. The papers address the whole range of theoretical computer science including algorithms and data structures, automata and formal languages, complexity theory, logic in computer science, semantics, specification, and verification of programs, rewriting and deduction, as well as current challenges like biological computing, quantum computing, and mobile and net computing.

Download or read book Dictionary of World Philosophy written by A. Pablo Iannone and published by Routledge. This book was released on 2013-04-15 with total page 894 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Dictionary of World Philosophy covers the diverse and challenging terminology, concepts, schools and traditions of the vast field of world philosophy. Providing an extremely comprehensive resource and an essential point of reference in a complex and expanding field of study the Dictionary covers all major subfields of the discipline. Key features: * Cross-references are used to highlight interconnections and the cross-cultural diffusion and adaptation of terms which has taken place over time * The user is led from specific terms to master entries which provide valuable historical and cultural context * Each master entry is followed by at least two suggestions for further reading on the subject, creating a substantial bibliography of world philosophy * References extend beyond philosophy to related areas such as cognitive science, computer science, language and physics Subdisciplines covered include:* aesthetics * ethics * sociopolitical philosophy * the philosophy of law * epistemology * logic * the philosophy of science * the philosophy of mind * the philosophy of culture and history * metaphysics * the philosophy of religion Entries are drawn from West Africa, Arabic, Chinese, Indian, Japanese, Jewish, Korean, Latin American, Maori and Native American philosophy including the important and so far largely neglected instance of Pre-Hispanic thought: Nahua philosophy.

Download or read book Enumerability Decidability Computability written by Hans Hermes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Once we have accepted a precise replacement of the concept of algo rithm, it becomes possible to attempt the problem whether there exist well-defined collections of problems which cannot be handled by algo rithms, and if that is the case, to give concrete cases of this kind. Many such investigations were carried out during the last few decades. The undecidability of arithmetic and other mathematical theories was shown, further the unsolvability of the word problem of group theory. Many mathematicians consider these results and the theory on which they are based to be the most characteristic achievements of mathe matics in the first half of the twentieth century. If we grant the legitimacy of the suggested precise replacements of the concept of algorithm and related concepts, then we can say that the mathematicians have shown by strictly mathematical methods that there exist mathematical problems which cannot be dealt with by the methods of calculating mathematics. In view of the important role which mathematics plays today in our conception of the world this fact is of great philosophical interest. Post speaks of a natural law about the "limitations of the mathematicizing power of Homo Sapiens". Here we also find a starting point for the discussion of the question, what the actual creative activity of the mathematician consists in. In this book we shall give an introduction to the theory of algorithms.

Download or read book Heinz Von Foerster 1911 2002 written by Soren Brier and published by Imprint Academic. This book was released on 2004 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dedicated to the life and work of Heinz Von Foerster, this is a double issue of the journal "Cybernetics and Human Knowing".

Download or read book Modern Logic A Survey written by E. Agazzi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logic has attained in our century a development incomparably greater than in any past age of its long history, and this has led to such an enrichment and proliferation of its aspects, that the problem of some kind of unified recom prehension of this discipline seems nowadays unavoidable. This splitting into several subdomains is the natural consequence of the fact that Logic has intended to adopt in our century the status of a science. This always implies that the general optics, under which a certain set of problems used to be con sidered, breaks into a lot of specialized sectors of inquiry, each of them being characterized by the introduction of specific viewpoints and of technical tools of its own. The first impression, that often accompanies the creation of one of such specialized branches in a diSCipline, is that one has succeeded in isolating the 'scientific core' of it, by restricting the somehow vague and redundant generality of its original 'philosophical' configuration. But, after a while, it appears that some of the discarded aspects are indeed important and a new specialized domain of investigation is created to explore them. By follOwing this procedure, one finally finds himself confronted with such a variety of independent fields of research, that one wonders whether the fact of labelling them under a common denomination be nothing but the contingent effect of a pure historical tradition.

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.

Download or read book Dictionary of Logic as Applied in the Study of Language written by W. Marciszewski and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. STRUCTURE AND REFERENCES 1.1. The main part of the dictionary consists of alphabetically arranged articles concerned with basic logical theories and some other selected topics. Within each article a set of concepts is defined in their mutual relations. This way of defining concepts in the context of a theory provides better understand ing of ideas than that provided by isolated short defmitions. A disadvantage of this method is that it takes more time to look something up inside an extensive article. To reduce this disadvantage the following measures have been adopted. Each article is divided into numbered sections, the numbers, in boldface type, being addresses to which we refer. Those sections of larger articles which are divided at the first level, i.e. numbered with single numerals, have titles. Main sections are further subdivided, the subsections being numbered by numerals added to the main section number, e.g. I, 1.1, 1.2, ... , 1.1.1, 1.1.2, and so on. A comprehensive subject index is supplied together with a glossary. The aim of the latter is to provide, if possible, short defmitions which sometimes may prove sufficient. As to the use of the glossary, see the comment preceding it.

Download or read book A Guided Tour of Artificial Intelligence Research written by Pierre Marquis and published by Springer Nature. This book was released on 2020-05-08 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to provide an overview of AI research, ranging from basic work to interfaces and applications, with as much emphasis on results as on current issues. It is aimed at an audience of master students and Ph.D. students, and can be of interest as well for researchers and engineers who want to know more about AI. The book is split into three volumes: - the first volume brings together twenty-three chapters dealing with the foundations of knowledge representation and the formalization of reasoning and learning (Volume 1. Knowledge representation, reasoning and learning) - the second volume offers a view of AI, in fourteen chapters, from the side of the algorithms (Volume 2. AI Algorithms) - the third volume, composed of sixteen chapters, describes the main interfaces and applications of AI (Volume 3. Interfaces and applications of AI). This third volume is dedicated to the interfaces of AI with various fields, with which strong links exist either at the methodological or at the applicative levels. The foreword of this volume reminds us that AI was born for a large part from cybernetics. Chapters are devoted to disciplines that are historically sisters of AI: natural language processing, pattern recognition and computer vision, and robotics. Also close and complementary to AI due to their direct links with information are databases, the semantic web, information retrieval and human-computer interaction. All these disciplines are privileged places for applications of AI methods. This is also the case for bioinformatics, biological modeling and computational neurosciences. The developments of AI have also led to a dialogue with theoretical computer science in particular regarding computability and complexity. Besides, AI research and findings have renewed philosophical and epistemological questions, while their cognitive validity raises questions to psychology. The volume also discusses some of the interactions between science and artistic creation in literature and in music. Lastly, an epilogue concludes the three volumes of this Guided Tour of AI Research by providing an overview of what has been achieved by AI, emphasizing AI as a science, and not just as an innovative technology, and trying to dispel some misunderstandings.

Download or read book Five Papers on Logic and Foundations written by V. P. Orevkov and published by American Mathematical Soc.. This book was released on 1971 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers and articles about symbolic logic.

Download or read book The Calculi of Symbolic Logic 1 written by V. P. Orevkov and published by University of Pennsylvania Press. This book was released on 1971 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Software Science And Engineering Selected Papers From The Kyoto Symposia written by Masami Hagiya and published by World Scientific. This book was released on 1991-09-30 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Twelve outstanding papers have been carefully selected from those presented at a series of symposia held at Kyoto University and the Advanced Software Technology and Mechatronics Research Institute of Kyoto during the years 1986 through 1990. Sponsored by the Research Institute of Mathematical Sciences of Kyoto University and ASTEM RI/Kyoto, the symposia covers the theoretical and practical aspects of programming languages and systems, programming styles and methodologies, design and analysis of algorithms, database systems and machine architectures. This volume fulfils in part the goal of the symposia to promote research activities in software, to encourage publication of recent works by Japanese researchers and to circulate these results to the worldwide academic community.

Download or read book Software Safety and Security written by NATO Emerging Security Challenges Division and published by IOS Press. This book was released on 2012 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent decades have seen major advances in methods and tools for checking the safety and security of software systems. Automatic tools can now detect security flaws not only in programs of the order of a million lines of code, but also in high-level protocol descriptions. There has also been something of a breakthrough in the area of operating system verification. This book presents the lectures from the NATO Advanced Study Institute on Tools for Analysis and Verification of Software Safety and Security; a summer school held at Bayrischzell, Germany, in 2011. This Advanced Study Institute was divided into three integrated modules: Foundations of Safety and Security, Applications of Safety Analysis and Security Analysis. Subjects covered include mechanized game-based proofs of security protocols, formal security proofs, model checking, using and building an automatic program verifier and a hands-on introduction to interactive proofs. Bringing together many leading international experts in the field, this NATO Advanced Study Institute once more proved invaluable in facilitating the connections which will influence the quality of future research and the potential to transfer research into practice. This book will be of interest to all those whose work depends on the safety and security of software systems.

Download or read book Studies in Constructive Mathematics and Mathematical Logic written by A. O. Slisenko and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a number of short papers reporting results presented to the Leningrad Seminar on Constructive Mathematics or to the Leningrad Seminar on Mathematical Logic. As a rule, the notes do not contain detailed proofs. Complete explanations will be printed in the Trudy (Transac tions) of the V.A. Steklov Mathematics Institute AN SSSR (in the "Problems of Constructive Direction in Mathematics" and the "Mathematical Logic and Logical Calculus" series). The papers published herein are primarily from the constructive direction in mathematics. A. Slisenko v CONTENTS 1 Method of Establishing Deducibility in Classical Predicate Calculus ... G.V. Davydov 5 On the Correction of Unprovable Formulas ... G.V. Davydov Lebesgue Integral in Constructive Analysis ... 9 O. Demuth Sufficient Conditions of Incompleteness for the Formalization of Parts of Arithmetic ... 15 N.K. Kosovskii Normal Formfor Deductions in Predicate Calculus with Equality and Functional Symbols. ... 21 V.A. Lifshits Some Reduction Classes and Undecidable Theories. ... . 24 ... V.A. Lifshits Deductive Validity and Reduction Classes. ... 26 ... V.A. Lifshits Problem of Decidability for Some Constructive Theories of Equalities. ... 29 . . V.A. Lifshits On Constructive Groups. ... . . 32 ... V.A. Lifshits Invertible Sequential Variant of Constructive Predicate Calculus. ... . 36 . S. Yu. Maslov Choice of Terms in Quantifier Rules of Constructive Predicate Calculus .. 43 G.E. Mints Analog of Herbrand's Theorem for Prenex Formulas of Constructive Predicate Calculus .. 47 G.E. Mints Variation in the Deduction Search Tactics in Sequential Calculus ... 52 ... G.E. Mints Imbedding Operations Associated with Kripke's "Semantics" ... 60 ...

Download or read book Routledge Encyclopedia of Philosophy written by Edward Craig and published by . This book was released on 1998 with total page 890 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume five of a ten volume set which provides full and detailed coverage of all aspects of philosophy, including information on how philosophy is practiced in different countries, who the most influential philosophers were, and what the basic concepts are.