# Logic: A Brief Course

Textbook

Part of the UNITEXT book series (UNITEXT)

Also part of the La Matematica per il 3+2 book sub series (UNITEXTMAT)

1. Front Matter
Pages I-XI
2. ### Propositional Logic

1. Front Matter
Pages 1-1
2. Daniele Mundici
Pages 3-6
3. Daniele Mundici
Pages 7-11
4. Daniele Mundici
Pages 13-17
5. Daniele Mundici
Pages 19-26
6. Daniele Mundici
Pages 27-30
7. Daniele Mundici
Pages 31-34
8. Daniele Mundici
Pages 35-39
9. Daniele Mundici
Pages 41-46
10. Daniele Mundici
Pages 47-51
11. Daniele Mundici
Pages 53-54
3. ### Predicate Logic

1. Front Matter
Pages 55-55
2. Daniele Mundici
Pages 57-61
3. Daniele Mundici
Pages 63-69
4. Daniele Mundici
Pages 71-78
5. Daniele Mundici
Pages 79-88
6. Daniele Mundici
Pages 89-93
7. Daniele Mundici
Pages 95-116
8. Daniele Mundici
Pages 117-120

### Introduction

This short book, geared towards undergraduate students of computer science and mathematics, is specifically designed for a first course in mathematical logic. A proof of Gödel's completeness theorem and its main consequences is given using Robinson's completeness theorem and Gödel's compactness theorem for propositional logic. The reader will familiarize himself with many basic ideas and artifacts of mathematical logic: a non-ambiguous syntax, logical equivalence and consequence relation, the Davis-Putnam procedure, Tarski semantics, Herbrand models, the axioms of identity, Skolem normal forms, nonstandard models and, interestingly enough, proofs and refutations viewed as graphic objects. The mathematical prerequisites are minimal: the book is accessible to anybody having some familiarity with proofs by induction. Many exercises on the relationship between natural language and formal proofs make the book also interesting to a wide range of students of philosophy and linguistics.

#### Authors and affiliations

1. 1.Department of Mathematics and Computer Science “U. Dini”University of FlorenceItaly

### Bibliographic information

• Book Title Logic: A Brief Course
• Authors Daniele Mundici
• Series Title UNITEXT
• DOI https://doi.org/10.1007/978-88-470-2361-1
• Copyright Information Springer Milan 2012
• Publisher Name Springer, Milano
• eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
• Softcover ISBN 978-88-470-2360-4
• eBook ISBN 978-88-470-2361-1
• Series ISSN 2038-5714
• Edition Number 1
• Number of Pages XI, 130
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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