Valentin Goranko

Logic as a Tool

A Guide to Formal Logical Reasoning

• Gebundenes Buch

Produktbeschreibung

Written in a clear, precise and user-friendly style, Logic as a Tool: A Guide to Formal Logical Reasoning is intended for undergraduates in both mathematics and computer science, and will guide them to learn, understand and master the use of classical logic as a tool for doing correct reasoning. It offers a systematic and precise exposition of classical logic with many examples and exercises, and only the necessary minimum of theory.

The book explains the grammar, semantics and use of classical logical languages and teaches the reader how grasp the meaning and translate them to and from natural language. It illustrates with extensive examples the use of the most popular deductive systems -- axiomatic systems, semantic tableaux, natural deduction, and resolution -- for formalising and automating logical reasoning both on propositional and on first-order level, and provides the reader with technical skills needed for practical derivations in them. Systematic guidelines are offered on how to perform logically correct and well-structured reasoning using these deductive systems and the reasoning techniques that they employ.

_Concise and systematic exposition, with semi-formal but rigorous treatment of the minimum necessary theory, amply illustrated with examples
_Emphasis both on conceptual understanding and on developing practical skills
_Solid and balanced coverage of syntactic, semantic, and deductive aspects of logic
_Includes extensive sets of exercises, many of them provided with solutions or answers
_Supplemented by a website including detailed slides, additional exercises and solutions

For more information browse the book's website at: https://logicasatool.wordpress.com

Produktdetails

• Verlag: Wiley / Wiley & Sons
• Artikelnr. des Verlages: 1W118880000
• 1. Auflage
• Seitenzahl: 384
• Erscheinungstermin: 17. Oktober 2016
• Englisch
• Abmessung: 244mm x 168mm x 23mm
• Gewicht: 680g
• ISBN-13: 9781118880005
• ISBN-10: 1118880005
• Artikelnr.: 45075841

Autorenporträt

Valentin Goranko is an associate professor at the Department of Applied Mathematics and Computer Science of the Technical University of Denmark. He has had over 25 years of University teaching and research experience: in particular, he has taught several courses partly based on the proposed book.

Inhaltsangabe

Preface xi

Acknowledgements xv

Introduction xvii

An Appetizer: Logical Paradoxes and Self-Reference xxi

1 Understanding Propositional Logic 1

1.1 Propositions and logical connectives: truth tables and tautologies 1

1.1.1 Propositions 1

1.1.2 Propositional logical connectives 2

1.1.3 Truth tables 3

1.1.4 The meaning of the connectives in natural language and in logic 4

1.1.5 Computing truth values of propositions 5

1.1.6 Propositional formulae and their truth tables 6

1.1.7 Tautologies 11

1.2 Propositional logical consequence: logically correct inferences 18

1.2.1 Propositional logical consequence 18

1.2.2 Logically sound rules of propositional inference and logically correct propositional arguments 21

1.2.3 Fallacies of the implication 23

1.3 Logical equivalence: negation normal form of propositional formulae 28

1.3.1 Logically equivalent propositional formulae 28

1.3.2 Basic properties of logical equivalence 29

1.3.3 Some important logical equivalences 29

1.4 Supplementary: Inductive definitions and structural induction and recursion 34

1.4.1 Inductive definitions 34

1.4.2 Induction principles and proofs by induction 36

1.4.3 Basics of the general theory of inductive definitions and principles 37

1.4.4 Inductive definitions and proofs in well-founded sets 39

1.4.5 Recursive definitions on inductively definable sets 40

2 Deductive Reasoning in Propositional Logic 47

2.1 Deductive systems: an overview 47

2.1.1 The concept and purpose of deductive systems 47

2.1.2 Brief historical remarks on deductive systems 48

2.1.3 Soundness, completeness and adequacy of deductive systems 50

2.2 Axiomatic systems for propositional logic 52

2.2.1 Description 52

2.2.2 Derivations in the axiomatic system H 54

2.3 Semantic Tableaux 58

2.3.1 Description of the deductive system ST of Semantic Tableaux 59

2.3.2 Some derivations in ST 61

2.3.3 Unsigned version of the system of Semantic Tableaux 64

2.4 Natural Deduction 68

2.4.1 Description 69

2.4.2 Examples of derivations in Natural Deduction 71

2.5 Normal forms and Propositional Resolution 77

2.5.1 Conjunctive and disjunctive normal forms of propositional formulae 77

2.5.2 Clausal Resolution 79

2.5.3 Resolution-based derivations 80

2.5.4 Optimizing the method of resolution 82

2.6 Supplementary: The Boolean satisfiability problem and NP-completeness 86

2.7 Supplementary: Completeness of the propositional deductive systems 88

3 Understanding First-order Logic 96

3.1 First-order structures and languages: terms and formulae of first-order logic 97

3.1.1 First-order structures 97

3.1.2 First-order languages 99

3.1.3 Terms and formulae 100

3.2 Semantics of first-order logic 108

3.2.1 The semantics of first-order logic: an informal outline 108

3.2.2 Interpretations of first-order languages 111

3.2.3 Variable assignment and evaluation of terms 112

3.2.4 Truth of first-order formulae 112

3.2.5 Evaluation games 114

3.2.6 Translating first-order formulae to natural language 117

3.3 Basic grammar and use of first-order languages 123

3.3.1 Translation from natural language to first-order languages: warm-up 123

3.3.2 Restricted quantification 124

3.3.3 Free and bound variables, and scope of a quan

Rezensionen

"Classical logic is hard but rewarding -helping with clarity in programming, business decisions, and whatever life throws at you"- (MagPi- Jan 17)