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Logic: a Brief Course

  • Textbook
  • © 2012

Overview

Authors:
  1. Daniele Mundici

    1. Department of Mathematics and Computer Science “U. Dini”, University of Florence, Italy

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  • Mathematical logic
  • Mathematical minimal
  • Includes supplementary material: sn.pub/extras

Part of the book series: UNITEXT (UNITEXT)

Part of the book sub series: La Matematica per il 3+2 (UNITEXTMAT)

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Table of contents (17 chapters)

  1. Front Matter

    Pages I-XI
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  2. Propositional Logic

    1. Front Matter

      Pages 1-1
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    2. Introduction

      • Daniele Mundici
      Pages 3-6

    3. Fundamental Logical Notions

      • Daniele Mundici
      Pages 7-11

    4. The Resolution Method

      • Daniele Mundici
      Pages 13-17

    5. Robinson’s Completeness Theorem

      • Daniele Mundici
      Pages 19-26

    6. Fast Classes for DPP

      • Daniele Mundici
      Pages 27-30

    7. Gödel’s Compactness Theorem

      • Daniele Mundici
      Pages 31-34

    8. Propositional Logic: Syntax

      • Daniele Mundici
      Pages 35-39

    9. Propositional Logic: Semantics

      • Daniele Mundici
      Pages 41-46

    10. Normal Forms

      • Daniele Mundici
      Pages 47-51

    11. Recap: Expressivity and Efficiency

      • Daniele Mundici
      Pages 53-54

  3. Predicate Logic

    1. Front Matter

      Pages 55-55
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    2. The Quantifiers “There Exists” and “For All”

      • Daniele Mundici
      Pages 57-61

    3. Syntax of Predicate Logic

      • Daniele Mundici
      Pages 63-69

    4. The Meaning of Clauses

      • Daniele Mundici
      Pages 71-78

    5. Gödel’s Completeness Theorem for the Logic of Clauses

      • Daniele Mundici
      Pages 79-88

    6. Equality Axioms

      • Daniele Mundici
      Pages 89-93

    7. The Predicate Logic L

      • Daniele Mundici
      Pages 95-116

    8. Final Remarks

      • Daniele Mundici
      Pages 117-120
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About this book

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.

Reviews

From the reviews:

“This is a short introduction to mathematical logic that covers basic material in 17 chapters … . The book is interspersed with several small references to various scholars involved in the development of logic, which provides for welcome interruptions in the formal exposition. … An important aspect of the book is a veritable multitude of exercises. … it is a very nice booklet that in view of this reviewer is an attractive choice for an introductory logic course for first year computer science students.” (Krzysztof R. Apt, Theory and Practice of Logic Programming, Vol. 12 (3), 2012)

“The book contains all the necessary means to understand any advanced text in logic, including the subjects covering Gödel’s incompleteness theorems. Although brief, this course seems to be an excellent introduction to modern mathematical logic, and, as such, we recommend it firstly to students of mathematics and computer science, and also to students of philosophy and linguistics … . The author’s beautiful, clear and approachable style makes this book also recommendable to a broader range of readers who are interested in modern trends in logic.” (Branislav Boričić, Zentralblatt MATH, Vol. 1235, 2012)

Authors and Affiliations

  • Department of Mathematics and Computer Science “U. Dini”, University of Florence, Italy

    Daniele Mundici

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