Mathematical Logic through Python

A unique approach to mathematical logic where students implement the underlying concepts and proofs in the Python programming language.

Yannai A. Gonczarowski (Author), Noam Nisan (Author)

9781108949477, Cambridge University Press

Paperback / softback, published 15 September 2022

284 pages
25.4 x 17.8 x 1.4 cm, 0.61 kg

'Mathematical Logic through Python offers a refreshingly innovative approach that makes it stand out among several excellent books on mathematical logic. By building on readers' experience and intuition through programming, it naturally provides them with a deep understanding of the fundamental concepts of mathematical logic that underly computer science.' Yoram Moses, Technion - Israel Institute of Technology

Using a unique pedagogical approach, this text introduces mathematical logic by guiding students in implementing the underlying logical concepts and mathematical proofs via Python programming. This approach, tailored to the unique intuitions and strengths of the ever-growing population of programming-savvy students, brings mathematical logic into the comfort zone of these students and provides clarity that can only be achieved by a deep hands-on understanding and the satisfaction of having created working code. While the approach is unique, the text follows the same set of topics typically covered in a one-semester undergraduate course, including propositional logic and first-order predicate logic, culminating in a proof of Gödel's completeness theorem. A sneak peek to Gödel's incompleteness theorem is also provided. The textbook is accompanied by an extensive collection of programming tasks, code skeletons, and unit tests. Familiarity with proofs and basic proficiency in Python is assumed.

Preface
Introduction and Overview
Part I. Propositional Logic: 1. Propositional Logic Syntax
2. Propositional Logic Semantics
3. Logical Operators
4. Proof by Deduction
5. Working with Proofs
6. The Tautology Theorem and the Completeness of Propositional Logic
Part II. Predicate Logic: 7. Predicate Logic Syntax and Semantics
8. Getting Rid of Functions and Equality
9. Deductive Proofs of Predicate Logic Formulas
10. Working with Predicate Logic Proofs
11. The Deduction Theorem and Prenex Normal Form
12. The Completeness Theorem
13. Sneak Peek at Mathematical Logic II: Godel's Incompleteness Theorem
Cheatsheet Axioms and Axiomatic Inference Rules Used in this Book
Notes
Index.

Subject Areas: Computer architecture & logic design [UYF], Computer programming / software development [UM], Information technology: general issues [UB], Discrete mathematics [PBD], Mathematical logic [PBCD]