Logics for Computer Science
Classical and Non-Classical
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Beschreibung
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.
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.
Includes links to the author's companion lecture slides for each chapter: several hundred presentations which summarize the ideas presented in the chapters for ease of comprehension.
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.
Offers a comprehensive, intuitive understanding of different logics and discusses some of their applications to Computer Science, and also makes readers understand the need of, and existence of Symbolic Logic as a scientific field Book chapters are as self-contained as possible so that they can be combined in different sequences depending of the level of a course one wants to teach it and of material one wants to teach, whether in Computer Science, Mathematics, or Artificial Intelligence Includes long intuitive introductions to each chapter, many detailed examples explaining each of the introduced notions and definitions, and well-chosen sets of exercises with carefully written solutions. It also contains samples of quizzes and tests after each chapter Includes links to the author's companion lecture slides for each chapter: several hundred presentations which summarize the ideas presented in the chapters for ease of comprehension Includes supplementary material: sn.pub/extras
Autor*in
Anita Wasilewska
Themen in »Logics for Computer Science«
Symbolic logic propositional languages predicate languages classical semantics non-classical semantics intuitionistic logic modal logics Hilbert style formalizations Gentzen style formalizations automated theorem proving Formal methods completeness theorem Godel Theorems many-valued logics Boolean algebras
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“This textbook is intended to serve as a first introduction to logic for undergraduate students, especially for those majoring in computer science or a related field. … The text is very reader-friendly, with plenty of explanations. … The problems will provide readers with ample opportunity to hone their skills.” (Katalin Bimbó, Mathematical Reviews, October, 2019)
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