Mathematical logic through Python
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書誌事項
Mathematical logic through Python
Cambridge University Press, 2022
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注記
Includes index
内容説明・目次
内容説明
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 Goedel's completeness theorem. A sneak peek to Goedel'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.
目次
- 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.
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