Sequents And Trees
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Sequents And Trees
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Author : Andrzej Indrzejczak
language : en
Publisher: Springer Nature
Release Date : 2020-12-16
Sequents And Trees written by Andrzej Indrzejczak and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-16 with Mathematics categories.
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.
Logic And Declarative Language
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Author : M. Downward
language : en
Publisher: Routledge
Release Date : 2004-01-14
Logic And Declarative Language written by M. Downward and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-14 with Computers categories.
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.
Logical Foundations Of Computer Science In 2 Volumes
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Author : Peter A Fejer
language : en
Publisher: World Scientific
Release Date : 2024-07-30
Logical Foundations Of Computer Science In 2 Volumes written by Peter A Fejer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-30 with Computers categories.
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.
Logics For Computer Science
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Author : Anita Wasilewska
language : en
Publisher: Springer
Release Date : 2018-11-03
Logics For Computer Science written by Anita Wasilewska and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-03 with Computers categories.
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.
Handbook Of Automated Reasoning
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Author : Alan J.A. Robinson
language : en
Publisher: Elsevier
Release Date : 2001-06-22
Handbook Of Automated Reasoning written by Alan J.A. Robinson and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-22 with Computers categories.
Handbook of Automated Reasoning
Automated Deduction Cade 22
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Author : Renate Schmidt
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-07-26
Automated Deduction Cade 22 written by Renate Schmidt 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 2009-07-26 with Computers categories.
This book constitutes the refereed proceedings of the 22nd International Conference on Automated Deduction, CADE-22, held in Montreal, Canada, in August 2009. The 27 revised full papers and 5 system descriptions presented were carefully reviewed and selected from 77 submissions. Furthermore, three invited lectures by distinguished experts in the area were included. The papers are organized in topical sections on combinations and extensions, minimal unsatisfiability and automated reasoning support, system descriptions, interpolation and predicate abstraction, resolution-based systems for non-classical logics, termination analysis and constraint solving, rewriting, termination and productivity, models, modal tableaux with global caching, arithmetic.
Foundations Of Information And Knowledge Systems
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Author : Dietmar Seipel
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-02-03
Foundations Of Information And Knowledge Systems written by Dietmar Seipel 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 2004-02-03 with Computers categories.
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.
Elementary Logic
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Author : Brian Garrett
language : en
Publisher: Routledge
Release Date : 2014-09-12
Elementary Logic written by Brian Garrett and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-12 with Philosophy categories.
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.
The Structure Of Typed Programming Languages
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Author : David A. Schmidt
language : en
Publisher: MIT Press
Release Date : 1994
The Structure Of Typed Programming Languages written by David A. Schmidt and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Computers categories.
The text is unique in its tutorial presentation of higher-order lambda calculus and intuitionistic type theory.
Mathematical Logic
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Author : Wei Li
language : en
Publisher: Springer
Release Date : 2014-11-07
Mathematical Logic written by Wei Li and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-07 with Mathematics categories.
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.