A Short Course in Predicate Logic

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180 pages
Language:
 English
Based on a one semester final year course the intention of this book is to provide a considerate yet rigorous introduction to the Predicate Calculus and the fundamental issues it aims to address.
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About the author

Jeff Paris is a Professor of Mathematics at the University of Manchester and a Fellow of the British Academy. His research and teaching have ranged over almost all areas of mathematical logic most recently Uncertain Reasoning and Inductive Logic. He is the author of two research monographs and over 10...

Description
Content

In my experience students often struggle to understand Predicate Logic: they drown in the complicated notation; they do not understand the difference between syntax and semantics, proof and truth; they do not appreciate the importance of logic within mathematics and formal methods in general. This book was written specifically to address these issues, at the same time presenting a full and rigorous treatment of the subject requiring only basic mathematics.

The presentation is based on a course for final year undergraduate students of mathematics, computer science and philosophy supplemented with additional material for masters students. Numerous problems, together with detailed solutions, are provided to consolidate the students' understanding.

  1. Introduction
  2. Motivation
  3. Formal Languages, Formulae and Sentences
  4. Truth
  5. Logical Consequence
  6. The Prenex Normal Form Theorem
  7. Formal Proofs
  8. The Completeness and Compactness Theorems
  9. Adding Constants and Functions
  10. Herbrand’s Theorem
  11. Equality
  12. Exercises
  13. Solutions to the Exercises
  14. Appendix