Mathematical Logic for Computer Science

Mathematical Logic for Computer Science is a mathematics textbook with theorems and proofs, but the choice of topics has been guided by the needs of students of computer science. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and easy to understand. The uniform use of tableaux-based techniques facilitates learning advanced logical systems based on what the student has learned from elementary systems.

The logical systems presented are: propositional logic, first-order logic, resolution and its application to logic programming, Hoare logic for the verification of sequential programs, and linear temporal logic

for the verification of concurrent programs.

The third edition has been entirely rewritten and includes new chapters on central topics of modern computer science: SAT solvers and model checking.

Table of Contents

1 Introduction

2 Propositional Logic: Formulas, Models, Tableaux

3 Propositional Logic: Deductive Systems

4 Propositional Logic: Resolution

5 Propositional Logic: Binary Decision Diagrams

6 Propositional Logic: SAT Solvers

7 First-Order Logic: Formulas, Models, Tableaux

8 First-Order Logic: Deductive Systems

9 First-Order Logic: Terms and Normal Forms

10 First-Order Logic: Resolution

11 First-Order Logic: Logic Programming

12 First-Order Logic: Undecidability and Model Theory

13 Temporal Logic: Formulas, Models, Tableaux

14 Temporal Logic: A Deductive System

15 Verification of Sequential Programs

16 Verification of Concurrent Programs

Appendix: Set Theory

About the Author

Mordechai (Moti) Ben-Ari is with the Department of Science Teaching at the Weizmann Institute of Science. He is a Distinguished Educator of the ACM and has received the ACM/SIGCSE Award for Outstanding Contributions to Computer Science Education.