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Author: Richard L Epstein Publisher: Advanced Reasoning Forum ISBN: 0983452172 Category : Philosophy Languages : en Pages : 509
Book Description
This book presents the history, philosophy, and mathematics of the major systems of propositional logic. Classical logic, modal logics, many-valued logics, intuitionism, paraconsistent logics, and dependent implication are examined in separate chapters. Each begins with a motivation in the originators' own terms, followed by the standard formal semantics, syntax, and completeness theorem. The chapters on the various logics are largely self-contained so that the book can be used as a reference. An appendix summarizes the formal semantics and axiomatizations of the logics. The view that unifies the exposition is that propositional logics comprise a spectrum: as the aspect of propositions under consideration varies, the logic varies. Each logic is shown to fall naturally within a general framework for semantics. A theory of translations between logics is presented that allows for further comparisons, and necessary conditions are given for a translation to preserve meaning. For this third edition the material has been re-organized to make the text easier to study, and a new section on paraconsistent logics with simple semantics has been added which challenges standard views on the nature of consequence relations. The text includes worked examples and hundreds of exercises, from routine to open problems, making the book with its clear and careful exposition ideal for courses or individual study.
Author: Richard L Epstein Publisher: Advanced Reasoning Forum ISBN: 0983452172 Category : Philosophy Languages : en Pages : 509
Book Description
This book presents the history, philosophy, and mathematics of the major systems of propositional logic. Classical logic, modal logics, many-valued logics, intuitionism, paraconsistent logics, and dependent implication are examined in separate chapters. Each begins with a motivation in the originators' own terms, followed by the standard formal semantics, syntax, and completeness theorem. The chapters on the various logics are largely self-contained so that the book can be used as a reference. An appendix summarizes the formal semantics and axiomatizations of the logics. The view that unifies the exposition is that propositional logics comprise a spectrum: as the aspect of propositions under consideration varies, the logic varies. Each logic is shown to fall naturally within a general framework for semantics. A theory of translations between logics is presented that allows for further comparisons, and necessary conditions are given for a translation to preserve meaning. For this third edition the material has been re-organized to make the text easier to study, and a new section on paraconsistent logics with simple semantics has been added which challenges standard views on the nature of consequence relations. The text includes worked examples and hundreds of exercises, from routine to open problems, making the book with its clear and careful exposition ideal for courses or individual study.
Author: Colin Allen Publisher: MIT Press ISBN: 0262543648 Category : Philosophy Languages : en Pages : 175
Book Description
The new edition of a comprehensive and rigorous but concise introduction to symbolic logic. Logic Primer offers a comprehensive and rigorous introduction to symbolic logic, providing concise definitions of key concepts, illustrative examples, and exercises. After presenting the definitions of validity and soundness, the book goes on to introduce a formal language, proof theory, and formal semantics for sentential logic (chapters 1–3) and for first-order predicate logic (chapters 4–6) with identity (chapter 7). For this third edition, the material has been reorganized from four chapters into seven, increasing the modularity of the text and enabling teachers to choose alternative paths through the book. New exercises have been added, and all exercises are now arranged to support students moving from easier to harder problems. Its spare and elegant treatment makes Logic Primer unique among textbooks. It presents the material with minimal chattiness, allowing students to proceed more directly from topic to topic and leaving instructors free to cover the subject matter in the way that best suits their students. The book includes more than thirty exercise sets, with answers to many of them provided in an appendix. The book’s website allows students to enter and check proofs, truth tables, and other exercises interactively.
Author: Mordechai Ben-Ari Publisher: Springer Science & Business Media ISBN: 1447103351 Category : Computers Languages : en Pages : 311
Book Description
This is a mathematics textbook with theorems and proofs. The choice of topics has been guided by the needs of computer science students. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and yet sufficiently elementary for undergraduates. In order to provide a balanced treatment of logic, tableaux are related to deductive proof systems. The book presents various logical systems and contains exercises. Still further, Prolog source code is available on an accompanying Web site. The author is an Associate Professor at the Department of Science Teaching, Weizmann Institute of Science.
Author: David Makinson Publisher: Springer Science & Business Media ISBN: 1447125002 Category : Computers Languages : en Pages : 302
Book Description
This easy-to-follow textbook introduces the mathematical language, knowledge and problem-solving skills that undergraduates need to study computing. The language is in part qualitative, with concepts such as set, relation, function and recursion/induction; but it is also partly quantitative, with principles of counting and finite probability. Entwined with both are the fundamental notions of logic and their use for representation and proof. Features: teaches finite math as a language for thinking, as much as knowledge and skills to be acquired; uses an intuitive approach with a focus on examples for all general concepts; brings out the interplay between the qualitative and the quantitative in all areas covered, particularly in the treatment of recursion and induction; balances carefully the abstract and concrete, principles and proofs, specific facts and general perspectives; includes highlight boxes that raise common queries and clear confusions; provides numerous exercises, with selected solutions.
Author: Howard Pospesel Publisher: Prentice Hall ISBN: Category : Logic Languages : en Pages : 260
Book Description
Designed to make logic interesting and accessible -- without sacrificing content or rigor -- this classic introduction to contemporary propositional logic explains the symbolization of English sentences and develops formal-proof, truth-table, and truth-tree techniques for evaluating arguments. Organizes content around natural-deduction formal-proof procedures, truth tables, and truth trees. Also presents logical statement connectives gradually, one per chapter, and finally, increases readers' awareness of the arguments they read and hear every day by providing examples of actual arguments to which they can readily relate.
Author: Howard Pospesel Publisher: Pearson ISBN: Category : Education Languages : en Pages : 302
Book Description
For courses in Introduction to Logic and Formal Logic. This clearly written volume covers symbolization, proofs, counterexamples, and truth trees. These topics are presented in graded steps, beginning with the symbolization of categorical propositions and concluding with the properties of relations. This new edition includes 'PredLogic, ' a CD-ROM-based tutorial for students.
Author: Oscar Levin Publisher: Createspace Independent Publishing Platform ISBN: 9781534970748 Category : Languages : en Pages : 342
Book Description
This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. The book contains over 360 exercises, including 230 with solutions and 130 more involved problems suitable for homework. There are also Investigate! activities throughout the text to support active, inquiry based learning. While there are many fine discrete math textbooks available, this text has the following advantages: It is written to be used in an inquiry rich course. It is written to be used in a course for future math teachers. It is open source, with low cost print editions and free electronic editions.
Author: Peter Smith Publisher: Cambridge University Press ISBN: 9780521008044 Category : Mathematics Languages : en Pages : 370
Book Description
Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.
Author: Genesereth Michael Publisher: Springer Nature ISBN: 303101801X Category : Mathematics Languages : en Pages : 163
Book Description
This book is a gentle but rigorous introduction to Formal Logic. It is intended primarily for use at the college level. However, it can also be used for advanced secondary school students, and it can be used at the start of graduate school for those who have not yet seen the material. The approach to teaching logic used here emerged from more than 20 years of teaching logic to students at Stanford University and from teaching logic to tens of thousands of others via online courses on the World Wide Web. The approach differs from that taken by other books in logic in two essential ways, one having to do with content, the other with form. Like many other books on logic, this one covers logical syntax and semantics and proof theory plus induction. However, unlike other books, this book begins with Herbrand semantics rather than the more traditional Tarskian semantics. This approach makes the material considerably easier for students to understand and leaves them with a deeper understanding of what logic is all about. In addition to this text, there are online exercises (with automated grading), online logic tools and applications, online videos of lectures, and an online forum for discussion. They are available at http://intrologic.stanford.edu/
Author: Richard L Epstein
Author: Richard L Epstein
Author: Colin Allen
Author: Howard Pospesel
Author: Mordechai Ben-Ari
Author: David Makinson
Author: Howard Pospesel
Author: Howard Pospesel
Author: Oscar Levin
Author: Peter Smith
Author: Genesereth Michael