Logic as a Tool (eBook)
John Wiley & Sons (Verlag)
978-1-118-88004-3 (ISBN)
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.
1 Understanding Propositional Logic 9
1.1 Propositions and logical connectives. Truth-tables and tautologies. 9
1.2 Propositional logical consequence. Logically correct inferences 28
1.3 Logical equivalence. Negation normal form of propositional formulae. 39
1.4 Addendum: Inductive definitions. Structural induction and recursion 46
2 Deductive Reasoning in Propositional Logic 59
2.1 Deductive systems: an overview 59
2.2 Axiomatic systems for propositional logic 65
2.3 Semantic tableaux 72
2.4 Natural deduction 83
2.5 Normal forms. Propositional resolution. 92
2.6 Addendum: The Boolean satisfiability problem and NP-completeness. 101
2.7 Addendum: Completeness of the propositional deductive systems 104
3 Understanding First-order Logic 113
3.1 First-order structures and languages. Terms and formulae of first-order logic. 114
3.2 Semantics of first-order logic 127
3.3 Basic grammar and use of first-order languages 143
3.4 Logical validity, consequence and equivalence in first-order logic 156
3.5 Syllogisms 173
4 Deductive Reasoning in First-order Logic 181
4.1 Axiomatic system for first-order logic 182
4.2 Semantic Tableaux for First-order Logic 190
4.3 Natural Deduction for first-order logic 204
4.4 Prenex and clausal normal forms 211
4.5 Resolution for first-order logic 218
4.6 Addendum: Soundness and completeness of the deductive systems for first-order logic 234
5 Applications: Mathematical Proofs and Automated Reasoning 245
5.1 Logical reasoning and mathematical proofs 246
5.2 Logical reasoning on sets, functions and relations 255
5.3 Mathematical induction and Peano Arithmetic 271
5.4 Applications: automated reasoning and logic programming 278
6 Answers and solutions to selected exercises 289
6.1 Answers and solutions: Section 1.1 289
6.2 Answers and solutions: Section 1.2 292
6.3 Answers and solutions: Section 1.3 294
6.4 Answers and solutions: Section 2.2 296
6.5 Answers and solutions: Section 2.3 298
6.6 Answers and solutions: Section 2.4 307
6.7 Answers and solutions: Section 2.5 312
6.8 Answers and solutions: Section 3.1 318
6.9 Answers and solutions: Section 3.2 321
6.10 Answers and solutions: Section 3.3 323
6.11 Answers and solutions: Section 3.4 325
6.12 Answers and solutions: Section 3.5 330
6.13 Answers and solutions: Section 4.1 331
6.14 Answers and solutions: Section 4.2 333
6.15 Answers and solutions: Section 4.3 350
6.16 Answers and solutions: Section 4.4 352
6.17 Answers and solutions: Section 4.5 354
6.18 Answers and solutions: Section 5.1 363
6.19 Answers and solutions: Section 5.2 364
6.20 Answers and solutions: Section 5.3 368
6.21 Answers and solutions: Section 5.4 371
"Classical logic is hard but rewarding--helping with clarity in programming, business decisions, and whatever life throws at you...." (MagPi, Jan 17)
Erscheint lt. Verlag | 2.9.2016 |
---|---|
Sprache | englisch |
Themenwelt | Geisteswissenschaften ► Philosophie ► Allgemeines / Lexika |
Geisteswissenschaften ► Philosophie ► Logik | |
Mathematik / Informatik ► Informatik ► Theorie / Studium | |
Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
Technik | |
Schlagworte | Classical Logic • Computer Science • Computer Science - General Interest • deductive system • First-Order Logic • Informatik • l ogical consequence • logically valid argument • Logic & Foundations • Logik • Logik u. Grundlagen der Mathematik • mathematical reasoning and proofs • Mathematics • Mathematik • Natural deduction • Philosophical Logic • Philosophie • Philosophische Logik • Philosophy • Populäre Themen i. d. Informatik • propositional logic • Resolution • semantic tableaux |
ISBN-10 | 1-118-88004-8 / 1118880048 |
ISBN-13 | 978-1-118-88004-3 / 9781118880043 |
Haben Sie eine Frage zum Produkt? |
Größe: 51,7 MB
Kopierschutz: Adobe-DRM
Adobe-DRM ist ein Kopierschutz, der das eBook vor Mißbrauch schützen soll. Dabei wird das eBook bereits beim Download auf Ihre persönliche Adobe-ID autorisiert. Lesen können Sie das eBook dann nur auf den Geräten, welche ebenfalls auf Ihre Adobe-ID registriert sind.
Details zum Adobe-DRM
Dateiformat: EPUB (Electronic Publication)
EPUB ist ein offener Standard für eBooks und eignet sich besonders zur Darstellung von Belletristik und Sachbüchern. Der Fließtext wird dynamisch an die Display- und Schriftgröße angepasst. Auch für mobile Lesegeräte ist EPUB daher gut geeignet.
Systemvoraussetzungen:
PC/Mac: Mit einem PC oder Mac können Sie dieses eBook lesen. Sie benötigen eine
eReader: Dieses eBook kann mit (fast) allen eBook-Readern gelesen werden. Mit dem amazon-Kindle ist es aber nicht kompatibel.
Smartphone/Tablet: Egal ob Apple oder Android, dieses eBook können Sie lesen. Sie benötigen eine
Geräteliste und zusätzliche Hinweise
Buying eBooks from abroad
For tax law reasons we can sell eBooks just within Germany and Switzerland. Regrettably we cannot fulfill eBook-orders from other countries.
aus dem Bereich