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A Proof Theory For General Unification
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Book Synopsis A Proof Theory for General Unification by : Wayne Snyder
Download or read book A Proof Theory for General Unification written by Wayne Snyder and published by Birkhäuser. This book was released on 2012-09-30 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph we study two generalizations of standard unification, E-unification and higher-order unification, using an abstract approach orig inated by Herbrand and developed in the case of standard first-order unifi cation by Martelli and Montanari. The formalism presents the unification computation as a set of non-deterministic transformation rules for con verting a set of equations to be unified into an explicit representation of a unifier (if such exists). This provides an abstract and mathematically elegant means of analysing the properties of unification in various settings by providing a clean separation of the logical issues from the specification of procedural information, and amounts to a set of 'inference rules' for unification, hence the title of this book. We derive the set of transformations for general E-unification and higher order unification from an analysis of the sense in which terms are 'the same' after application of a unifying substitution. In both cases, this results in a simple extension of the set of basic transformations given by Herbrand Martelli-Montanari for standard unification, and shows clearly the basic relationships of the fundamental operations necessary in each case, and thus the underlying structure of the most important classes of term unifi cation problems.
Book Synopsis A Proof Theory for General Unification by : W. Snyder
Download or read book A Proof Theory for General Unification written by W. Snyder and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph we study two generalizations of standard unification, E-unification and higher-order unification, using an abstract approach orig inated by Herbrand and developed in the case of standard first-order unifi cation by Martelli and Montanari. The formalism presents the unification computation as a set of non-deterministic transformation rules for con verting a set of equations to be unified into an explicit representation of a unifier (if such exists). This provides an abstract and mathematically elegant means of analysing the properties of unification in various settings by providing a clean separation of the logical issues from the specification of procedural information, and amounts to a set of 'inference rules' for unification, hence the title of this book. We derive the set of transformations for general E-unification and higher order unification from an analysis of the sense in which terms are 'the same' after application of a unifying substitution. In both cases, this results in a simple extension of the set of basic transformations given by Herbrand Martelli-Montanari for standard unification, and shows clearly the basic relationships of the fundamental operations necessary in each case, and thus the underlying structure of the most important classes of term unifi cation problems.
Book Synopsis A Proof Theory for General Unification by : Wayne Snyder
Download or read book A Proof Theory for General Unification written by Wayne Snyder and published by Birkhäuser. This book was released on 1991-11-01 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph we study two generalizations of standard unification, E-unification and higher-order unification, using an abstract approach orig inated by Herbrand and developed in the case of standard first-order unifi cation by Martelli and Montanari. The formalism presents the unification computation as a set of non-deterministic transformation rules for con verting a set of equations to be unified into an explicit representation of a unifier (if such exists). This provides an abstract and mathematically elegant means of analysing the properties of unification in various settings by providing a clean separation of the logical issues from the specification of procedural information, and amounts to a set of 'inference rules' for unification, hence the title of this book. We derive the set of transformations for general E-unification and higher order unification from an analysis of the sense in which terms are 'the same' after application of a unifying substitution. In both cases, this results in a simple extension of the set of basic transformations given by Herbrand Martelli-Montanari for standard unification, and shows clearly the basic relationships of the fundamental operations necessary in each case, and thus the underlying structure of the most important classes of term unifi cation problems.
Book Synopsis Handbook of Automated Reasoning by : Alan J.A. Robinson
Download or read book Handbook of Automated Reasoning written by Alan J.A. Robinson and published by Gulf Professional Publishing. This book was released on 2001-06-21 with total page 1004 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Automated Reasoning.
Book Synopsis Einstein's Unification by : Jeroen van Dongen
Download or read book Einstein's Unification written by Jeroen van Dongen and published by Cambridge University Press. This book was released on 2010-06-10 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why did Einstein tirelessly study unified field theory for more than thirty years? In this book, the author argues that Einstein believed he could find a unified theory of all of nature's forces by repeating the methods he thought he had used when he formulated general relativity. The book discusses Einstein's route to the general theory of relativity, focusing on the philosophical lessons that he learnt. It then addresses his quest for a unified theory for electromagnetism and gravity, discussing in detail his efforts with Kaluza-Klein and, surprisingly, the theory of spinors. From these perspectives, Einstein's critical stance towards the quantum theory comes to stand in a new light. This book will be of interest to physicists, historians and philosophers of science.
Book Synopsis Mathematical Knowledge Management by : Michael Kohlhase
Download or read book Mathematical Knowledge Management written by Michael Kohlhase and published by Springer. This book was released on 2006-01-20 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-proceedings of the 4th International Conference on Mathematical Knowledge Management. The 26 revised full papers presented were carefully selected during two rounds of reviewing and improvement from 38 submissions. The papers cover mathematical knowledge management. Topics range from foundations and the representational and document-structure aspects of mathematical knowledge, over process questions like authoring, migration, and consistency management by automated theorem proving to applications in e-learning and case studies.
Book Synopsis An Introduction to Mathematical Logic and Type Theory by : Peter B. Andrews
Download or read book An Introduction to Mathematical Logic and Type Theory written by Peter B. Andrews and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: In case you are considering to adopt this book for courses with over 50 students, please contact [email protected] for more information. This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.
Author :Jean Goubault-Larrecq Publisher :Springer Science & Business Media ISBN 13 :9781402003684 Total Pages :448 pages Book Rating :4.0/5 (36 download)
Book Synopsis Proof Theory and Automated Deduction by : Jean Goubault-Larrecq
Download or read book Proof Theory and Automated Deduction written by Jean Goubault-Larrecq and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest in computer applications has led to a new attitude to applied logic in which researchers tailor a logic in the same way they define a computer language. In response to this attitude, this text for undergraduate and graduate students discusses major algorithmic methodologies, and tableaux and resolution methods. The authors focus on first-order logic, the use of proof theory, and the computer application of automated searches for proofs of mathematical propositions. Annotation copyrighted by Book News, Inc., Portland, OR
Download or read book CSL '89 written by Egon Börger and published by Springer Science & Business Media. This book was released on 1990-07-10 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the revised versions of 28 papers presented at the third workshop on Computer Science Logic held in Kaiserslautern, FRG, October 2-6, 1989. These proceedings cover a wide range of topics both from theoretical and applied areas of computer science. More specifically, the papers deal with problems arising at the border of logic and computer science, e.g. in complexity, data base theory, logic programming, artificial intelligece, and temporal logic. The volume should be of interest to all logicians and computer scientists working in the above field.
Book Synopsis Handbook of Proof Theory by : S.R. Buss
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.
Book Synopsis Advances in Computing and Information - ICCI '90 by : Selim G. Akl
Download or read book Advances in Computing and Information - ICCI '90 written by Selim G. Akl and published by Springer Science & Business Media. This book was released on 1990 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains selected and invited papers presented at the International Conference on Computing and Information, ICCI '90, Niagara Falls, Ontario, Canada, May 23-26, 1990. ICCI conferences provide an international forum for presenting new results in research, development and applications in computing and information. Their primary goal is to promote an interchange of ideas and cooperation between practitioners and theorists in the interdisciplinary fields of computing, communication and information theory. The four main topic areas of ICCI '90 are: - Information and coding theory, statistics and probability, - Foundations of computer science, theory of algorithms and programming, - Concurrency, parallelism, communications, networking, computer architecture and VLSI, - Data and software engineering, databases, expert systems, information systems, decision making, and AI methodologies.
Book Synopsis Frontiers of Combining Systems by : Carsten Lutz
Download or read book Frontiers of Combining Systems written by Carsten Lutz and published by Springer. This book was released on 2015-09-19 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 10th International Symposium on Frontiers of Combining Systems, FroCoS 2015, held in Wroclaw, Poland, in September 2015. The 20 papers presented in this volume were carefully reviewed and selected from 34 submissions. They were organized in topical sections named: description logics; theorem proving and model building; decision procedures; decision procedures for verification; rewriting and constraint solving; transformations between symbolic systems; combination methods; and reasoning in large theories. The book also contains one invited talk in full-paper length.
Book Synopsis Computer Science Logic by : Laurent Fribourg
Download or read book Computer Science Logic written by Laurent Fribourg and published by Springer. This book was released on 2003-06-30 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 15th International Workshop on Computer Science Logic, CSL 2001, held as the 10th Annual Conerence of the EACSL in Paris, France in September 2001. The 39 revised full papers presented together with two invited papers were carefully reviewed and selected from 91 submissions. The papers are organized in topical sections on linear logic, descriptive complexity, semantics, higher-order programs, model logics, verification, automata, lambda calculus, induction, equational calculus, and constructive theory of types.
Book Synopsis Computational Logic and Proof Theory by : Georg Gottlob
Download or read book Computational Logic and Proof Theory written by Georg Gottlob and published by Springer Science & Business Media. This book was released on 1997-08-13 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 5th Kurt Gödel Colloquium on Computational Logic and Proof Theory, KGC '97, held in Vienna, Austria, in August 1997. The volume presents 20 revised full papers selected from 38 submitted papers. Also included are seven invited contributions by leading experts in the area. The book documents interdisciplinary work done in the area of computer science and mathematical logics by combining research on provability, analysis of proofs, proof search, and complexity.
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1084 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Language and Automata Theory and Applications by : Adrian-Horia Dediu
Download or read book Language and Automata Theory and Applications written by Adrian-Horia Dediu and published by Springer. This book was released on 2013-03-15 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 7th International Conference on Language and Automata Theory and Applications, LATA 2013, held in Bilbao, Spain in April 2013. The 45 revised full papers presented together with 5 invited talks were carefully reviewed and selected from 97 initial submissions. The volume features contributions from both classical theory fields and application areas (bioinformatics, systems biology, language technology, artificial intelligence, etc.). Among the topics covered are algebraic language theory; algorithms for semi-structured data mining; algorithms on automata and words; automata and logic; automata for system analysis and program verification; automata, concurrency and Petri nets; automatic structures; cellular automata; combinatorics on words; computability; computational complexity; computational linguistics; data and image compression; decidability questions on words and languages; descriptional complexity; DNA and other models of bio-inspired computing; document engineering; foundations of finite state technology; foundations of XML; fuzzy and rough languages; grammars (Chomsky hierarchy, contextual, multidimensional, unification, categorial, etc.); grammars and automata architectures; grammatical inference and algorithmic learning; graphs and graph transformation; language varieties and semigroups; language-based cryptography; language-theoretic foundations of artificial intelligence and artificial life; parallel and regulated rewriting; parsing; pattern recognition; patterns and codes; power series; quantum, chemical and optical computing; semantics; string and combinatorial issues in computational biology and bioinformatics; string processing algorithms; symbolic dynamics; symbolic neural networks; term rewriting; transducers; trees, tree languages and tree automata; weighted automata.
Book Synopsis An Introduction to Mathematical Logic and Type Theory by : Peter B. Andrews
Download or read book An Introduction to Mathematical Logic and Type Theory written by Peter B. Andrews and published by Springer Science & Business Media. This book was released on 2002-07-31 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: In case you are considering to adopt this book for courses with over 50 students, please contact [email protected] for more information. This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.
