Logic as a Tool, First Edition, A Concise Guide to Logical Reasoning by Goranko, Valentin -- Read -- Imperial Library of Trantor

Index

Cover Title Page Copyright Table of Contents Dedication Preface

Aims Summary of the content and main features For the instructor

Acknowledgements

Attributions for the photos used in the book

Introduction An Appetizer: Logical Paradoxes and Self-Reference Chapter 1: Understanding Propositional Logic

1.1 Propositions and logical connectives: truth tables and tautologies Exercises 1.2 Propositional logical consequence: logically correct inferences Exercises 1.3 Logical equivalence: negation normal form of propositional formulae Exercises 1.4 Supplementary: Inductive definitions and structural induction and recursion Exercises

Chapter 2: Deductive Reasoning in Propositional Logic

2.1 Deductive systems: an overview 2.2 Axiomatic systems for propositional logic Exercises 2.3 Semantic Tableaux Exercises 2.4 Natural Deduction Exercises 2.5 Normal forms and Propositional Resolution Exercises 2.6 Supplementary: The Boolean satisfiability problem and NP-completeness 2.7 Supplementary: Completeness of the propositional deductive systems Exercises

Chapter 3: Understanding First-order Logic

3.1 First-order structures and languages: terms and formulae of first-order logic Exercises 3.2 Semantics of first-order logic 3.3 Basic grammar and use of first-order languages Exercises 3.4 Logical validity, consequence, and equivalence in first-order logic Exercises 3.5 Syllogisms Exercises

Chapter 4: Deductive Reasoning in First-order Logic

4.1 Axiomatic system for first-order logic Exercises 4.2 Semantic Tableaux for first-order logic Exercises 4.3 Natural Deduction for first-order logic Exercises 4.4 Prenex and clausal normal forms Exercises 4.5 Resolution for first-order logic Exercises 4.6 Supplementary: Soundness and completeness of the deductive systems for first-order logic Exercises

Chapter 5: Applications: Mathematical Proofs and Automated Reasoning

5.1 Logical reasoning and mathematical proofs Exercises 5.2 Logical reasoning on sets, functions, and relations Exercises 5.3 Mathematical Induction and Peano Arithmetic Exercises 5.4 Applications: automated reasoning and logic programming Exercises

Chapter 6: Answers and Solutions to Selected Exercises

Section 1.1 Section 1.2 Section 1.3 Section 1.4 Section 2.2 Section 2.3 Section 2.4 Section 2.5 Section 3.1 Section 3.2 Section 3.3 Section 3.4 Section 3.5 Section 4.1 Section 4.2 Section 4.3 Section 4.4 Section 4.5 Section 4.6 Section 5.1 Section 5.2 Section 5.3 Section 5.4

References Index End User License Agreement

← Prev
Back
Next →

← Prev
Back
Next →