Download or read book Sequents and Trees written by Andrzej Indrzejczak and published by Springer Nature. This book was released on 2020-12-16 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a detailed introduction to the methodology and applications of sequent calculi in propositional logic. Unlike other texts concerned with proof theory, emphasis is placed on illustrating how to use sequent calculi to prove a wide range of metatheoretical results. The presentation is elementary and self-contained, with all technical details both formally stated and also informally explained. Numerous proofs are worked through to demonstrate methods of proving important results, such as the cut-elimination theorem, completeness, decidability, and interpolation. Other proofs are presented with portions left as exercises for readers, allowing them to practice techniques of sequent calculus. After a brief introduction to classical propositional logic, the text explores three variants of sequent calculus and their features and applications. The remaining chapters then show how sequent calculi can be extended, modified, and applied to non-classical logics, including modal, intuitionistic, substructural, and many-valued logics. Sequents and Trees is suitable for graduate and advanced undergraduate students in logic taking courses on proof theory and its application to non-classical logics. It will also be of interest to researchers in computer science and philosophers.

Download or read book Advances in Computing Science ASIAN 99 written by P.S. Thiagarajan and published by Springer. This book was released on 2003-07-31 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 5th Asian Computing Science Conference, ASIAN'99, held in Phuket, Thailand, in December 1999. The 28 revised full papers presented together with two invited contributions and 11 short presentations were carefully reviewed and selected from a total of 114 submissions. Among the topics addressed are programming theory, formal methods, automated reasoning, verification, embedded systems, real-time systems, distributed systems, and mobile computing.

Download or read book Systems and Computer Science written by John F Hart and published by University of Toronto Press. This book was released on 1967-12-15 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the papers delivered at the Conference on Systems and Computer Science held at the University of Western Ontario in September 1965. The primary purposes of the Conference were the promotion of research and the development of the teaching of computer science in Canadian universities. The papers focus attention on some of the concepts of Computer Science as a new field of study and at the same time provide a background for scientists looking at the subject for the first time. The chief developments in computer science have been concerned with the "applied" rather than the "pure" areas of the field: numerical analysis, applied statistics and operations research, and data processing. But there is something more to computers than the physical components and this book represents an attempt to correct the imbalance between "applied" and "pure" by drawing attention to certain theoretical aspects of computer and information science. Among the topics discussed are the theory of finite and infinite automata, aspects of formal language theory, heuristic and non-heuristic approaches to theorem proving and the mathematical formulation of the theory of general systems. There are also references to the problems of machine design, to software systems including higher-level languages, to multiple control computer models and to applied systems. This collection of papers will appeal first to graduate students and professors in Computer Science. It will also be of interest to computer scientists in industry and in government and university research groups and to the scientific public interested in discovering some of the principal ingredients and directions of the computer and information sciences.

Download or read book Natural Language Semantics written by Brendan S. Gillon and published by MIT Press. This book was released on 2019-03-12 with total page 731 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to natural language semantics that offers an overview of the empirical domain and an explanation of the mathematical concepts that underpin the discipline. This textbook offers a comprehensive introduction to the fundamentals of those approaches to natural language semantics that use the insights of logic. Many other texts on the subject focus on presenting a particular theory of natural language semantics. This text instead offers an overview of the empirical domain (drawn largely from standard descriptive grammars of English) as well as the mathematical tools that are applied to it. Readers are shown where the concepts of logic apply, where they fail to apply, and where they might apply, if suitably adjusted. The presentation of logic is completely self-contained, with concepts of logic used in the book presented in all the necessary detail. This includes propositional logic, first order predicate logic, generalized quantifier theory, and the Lambek and Lambda calculi. The chapters on logic are paired with chapters on English grammar. For example, the chapter on propositional logic is paired with a chapter on the grammar of coordination and subordination of English clauses; the chapter on predicate logic is paired with a chapter on the grammar of simple, independent English clauses; and so on. The book includes more than five hundred exercises, not only for the mathematical concepts introduced, but also for their application to the analysis of natural language. The latter exercises include some aimed at helping the reader to understand how to formulate and test hypotheses.

Download or read book Current Approaches in Applied Artificial Intelligence written by Moonis Ali and published by Springer. This book was released on 2015-04-30 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed conference proceedings of the 28th International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems, IEA/AIE 2015, held in Seoul, South Korea, in June 2015. The 73 revised full papers presented were carefully reviewed and selected from 105 submissions. The papers cover a wide range of topics in applied artificial intelligence including reasoning, robotics, cognitive modeling, machine learning, pattern recognition, optimization, text mining, social network analysis, and evolutionary algorithms. They are organized in the following topical sections: theoretical AI, knowledge-based systems, optimization, Web and social networks, machine learning, classification, unsupervised learning, vision, image and text processing, and intelligent systems applications.

Download or read book Dag Prawitz on Proofs and Meaning written by Heinrich Wansing and published by Springer. This book was released on 2014-11-27 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an introductory paper that surveys Prawitz's numerous contributions to proof theory and proof-theoretic semantics and puts his work into a somewhat broader perspective, both historically and systematically. Chapters include either in-depth studies of certain aspects of Dag Prawitz's work or address open research problems that are concerned with core issues in structural proof theory and range from philosophical essays to papers of a mathematical nature. Investigations into the necessity of thought and the theory of grounds and computational justifications as well as an examination of Prawitz's conception of the validity of inferences in the light of three “dogmas of proof-theoretic semantics” are included. More formal papers deal with the constructive behaviour of fragments of classical logic and fragments of the modal logic S4 among other topics. In addition, there are chapters about inversion principles, normalization of p roofs, and the notion of proof-theoretic harmony and other areas of a more mathematical persuasion. Dag Prawitz also writes a chapter in which he explains his current views on the epistemic dimension of proofs and addresses the question why some inferences succeed in conferring evidence on their conclusions when applied to premises for which one already possesses evidence.

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.

Download or read book Automated Reasoning with Analytic Tableaux and Related Methods written by Didier Galmiche and published by Springer. This book was released on 2013-09-11 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 22th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2013, held in Nancy, France, in September 2013. The 20 revised research papers presented together with 4 system descriptions were carefully reviewed and selected from 38 submissions. The papers cover many topics as proof-theory in classical and non-classical logics, analytic tableaux for various logics, related techniques and concepts, e.g., model checking and BDDs, related methods (model elimination, sequent calculi, resolution, and connection method), new calculi and methods for theorem proving and verification in classical and non-classical logics, systems, tools, implementations and applications as well as automated deduction and formal methods applied to logic, mathematics, software development, protocol verification, and security.

Download or read book Logics in Artificial Intelligence written by Farinas Luis Del Cerro and published by Springer. This book was released on 2003-05-20 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the papers selected for presentation at the conference and two abstracts from invited speakers. The programme committee selected these 25 papers from 12 countries out of 65 submissions from 17 countries. The rst JELIA meeting was in Rosco , France, ten years ago. Afterwards, it took place in the Netherlands, Germany, United Kingdom, Portugal, and now again in Germany. The proceedings of the last four meetings appeared in the Springer-Verlag LNCS series, and a selected series of papers of the English and the Portuguese meeting appeared as special issues in the Journal of Applied Non-Classical Logics and in the Journal of Automated Reasoning, respectively. The aim of JELIA was and still is to provide a forum for the exchange of ideas and results in the domain of foundations of AI, focusing on rigorous descriptions of some aspects of intelligence. These descriptions are promoted by applications, and produced by logical tools and methods. The papers contained in this volume cover the following topics: 1. Logic programming 2. Epistemic logics 3. Theorem proving 4. Non-monotonic reasoning 5. Non-standard logics 6. Knowledge representation 7. Higher order logics We would like to warmly thank the authors, the invited speakers, the m- bers of the program committee, and the additional reviewers listed below. They all have made these proceedings possible and ensured their quality.

Download or read book Logic And Declarative Language written by M. Downward and published by Routledge. This book was released on 2004-01-14 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logic has acquired a reputation for difficulty, perhaps because many of the approaches adopted have been more suitable for mathematicians than computer scientists. This book shows that the subject is not inherently difficult and that the connections between logic and declarative language are straightforward. Many exercises have been included in the hope that these will lead to a much greater confidence in manual proofs, therefore leading to a greater confidence in automated proofs.

Download or read book Logics for Computer Science written by Anita Wasilewska and published by Springer. This book was released on 2018-11-03 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an in-depth introduction to fundamental classical and non-classical logics, this textbook offers a comprehensive survey of logics for computer scientists. Logics for Computer Science contains intuitive introductory chapters explaining the need for logical investigations, motivations for different types of logics and some of their history. They are followed by strict formal approach chapters. All chapters contain many detailed examples explaining each of the introduced notions and definitions, well chosen sets of exercises with carefully written solutions, and sets of homework. While many logic books are available, they were written by logicians for logicians, not for computer scientists. They usually choose one particular way of presenting the material and use a specialized language. Logics for Computer Science discusses Gentzen as well as Hilbert formalizations, first order theories, the Hilbert Program, Godel's first and second incompleteness theorems and their proofs. It also introduces and discusses some many valued logics, modal logics and introduces algebraic models for classical, intuitionistic, and modal S4 and S5 logics. The theory of computation is based on concepts defined by logicians and mathematicians. Logic plays a fundamental role in computer science, and this book explains the basic theorems, as well as different techniques of proving them in classical and some non-classical logics. Important applications derived from concepts of logic for computer technology include Artificial Intelligence and Software Engineering. In addition to Computer Science, this book may also find an audience in mathematics and philosophy courses, and some of the chapters are also useful for a course in Artificial Intelligence.

Download or read book Logical Foundations Of Computer Science In 2 Volumes written by Peter A Fejer and published by World Scientific. This book was released on 2024-07-30 with total page 1336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logic is a foundational mathematical discipline for Computer Science. This unique compendium provides the main ideas and techniques originating from logic. It is divided into two volumes — propositional logic and predicate logic. The volume presents some of the most important concepts starting with a variety of logic formalisms — Hilbert/Frege systems, tableaux, sequents, and natural deduction in both propositional and first-order logic, as well as transformations between these formalisms. Topics like circuit design, resolution, cutting planes, Hintikka sets, paramodulation, and program verification, which do not appear frequently in logic books are discussed in detail.The useful reference text has close to 800 exercises and supplements to deepen understanding of the subject. It emphasizes proofs and overcomes technical difficulties by providing detailed arguments. Computer scientists and mathematicians will benefit from this volume.

Download or read book Theorem Proving in Higher Order Logics written by Victor A. Carreno and published by Springer Science & Business Media. This book was released on 2002-08-07 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Felty PuzzleTool:AnExampleofProgrammingComputationandDeduction . . 214 MichaelJ. C. Gordon AFormalApproachtoProbabilisticTermination. ... ... 230 JoeHurd UsingTheoremProvingforNumericalAnalysis. ... ... . 246 MicaelaMayero QuotientTypes:AModularApproach. ... ... ... 263 AlekseyNogin SequentSchemaforDerivedRules ... ... ... . 281 AlekseyNogin, JasonHickey AlgebraicStructuresandDependentRecords ... ... . 298 VirgilePrevosto, DamienDoligez, Thþ er` eseHardin ProvingtheEquivalenceofMicrostepandMacrostepSemantics. ... 314 KlausSchneider WeakestPreconditionforGeneralRecursiveProgramsFormalizedinCoq.

Download or read book Foundations of Information and Knowledge Systems written by Dietmar Seipel and published by Springer Science & Business Media. This book was released on 2004-02-03 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Third International Symposium on Foundations of Information and Knowledge Systems, FoIKS 2004 held at Wilheminenburg Castle, Austria in February 2004. The 18 revised full papers presented together with 2 invited papers were carefully reviewed and selected from 64 submissions. Among the topics covered are data integration, data security, logic programming and databases, relational reasoning, database queries, higher-order data models, updates, database views, OLAP, belief modeling, fixpoint computations, interaction schemes, plan databases, etc.

Download or read book Mathematical Logic written by Wei Li and published by Springer. This book was released on 2014-11-07 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical logic is a branch of mathematics that takes axiom systems and mathematical proofs as its objects of study. This book shows how it can also provide a foundation for the development of information science and technology. The first five chapters systematically present the core topics of classical mathematical logic, including the syntax and models of first-order languages, formal inference systems, computability and representability, and Gödel’s theorems. The last five chapters present extensions and developments of classical mathematical logic, particularly the concepts of version sequences of formal theories and their limits, the system of revision calculus, proschemes (formal descriptions of proof methods and strategies) and their properties, and the theory of inductive inference. All of these themes contribute to a formal theory of axiomatization and its application to the process of developing information technology and scientific theories. The book also describes the paradigm of three kinds of language environments for theories and it presents the basic properties required of a meta-language environment. Finally, the book brings these themes together by describing a workflow for scientific research in the information era in which formal methods, interactive software and human invention are all used to their advantage. The second edition of the book includes major revisions on the proof of the completeness theorem of the Gentzen system and new contents on the logic of scientific discovery, R-calculus without cut, and the operational semantics of program debugging. This book represents a valuable reference for graduate and undergraduate students and researchers in mathematics, information science and technology, and other relevant areas of natural sciences. Its first five chapters serve as an undergraduate text in mathematical logic and the last five chapters are addressed to graduate students in relevant disciplines.

Download or read book Elementary Logic written by Brian Garrett and published by Routledge. This book was released on 2014-09-12 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary Logic explains what logic is, how it is done, and why it can be exciting. The book covers the central part of logic that all students have to learn: propositional logic. It aims to provide a crystal-clear introduction to what is often regarded as the most technically difficult area in philosophy. The book opens with an explanation of what logic is and how it is constructed. Subsequent chapters take the reader step-by-step through all aspects of elementary logic. Throughout, ideas are explained simply and directly, with the chapters packed with overviews, illustrative examples, and summaries. Each chapter builds on previous explanation and example, with the final chapters presenting more advanced methods. After a discussion of meta-logic and logical systems, the book closes with an exploration of how paradoxes can exist in the world of logic. Elementary Logic's clarity and engagement make it ideal for any reader studying logic for the first time.

Download or read book Deduction Systems written by Rolf Socher-Ambrosius and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea of mechanizing deductive reasoning can be traced all the way back to Leibniz, who proposed the development of a rational calculus for this purpose. But it was not until the appearance of Frege's 1879 Begriffsschrift-"not only the direct ancestor of contemporary systems of mathematical logic, but also the ancestor of all formal languages, including computer programming languages" ([Dav83])-that the fundamental concepts of modern mathematical logic were developed. Whitehead and Russell showed in their Principia Mathematica that the entirety of classical mathematics can be developed within the framework of a formal calculus, and in 1930, Skolem, Herbrand, and Godel demonstrated that the first-order predicate calculus (which is such a calculus) is complete, i. e. , that every valid formula in the language of the predicate calculus is derivable from its axioms. Skolem, Herbrand, and GOdel further proved that in order to mechanize reasoning within the predicate calculus, it suffices to Herbrand consider only interpretations of formulae over their associated universes. We will see that the upshot of this discovery is that the validity of a formula in the predicate calculus can be deduced from the structure of its constituents, so that a machine might perform the logical inferences required to determine its validity. With the advent of computers in the 1950s there developed an interest in automatic theorem proving.