| Description |
1 online resource (384 pages) |
| Contents |
Understanding propositional logic -- Deductive reasoning in propositional logic -- Understanding first-order logic -- Deductive reasoning in first-order logic -- Applications : mathematical proofs and automated reasoning -- Answers and solutions to selected exercises |
| Notes |
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 |
| Subject |
Logic -- Textbooks
|
|
Logic
|
| Genre/Form |
Electronic books
|
|
Textbooks
|
| Form |
Electronic book
|
| ISBN |
9781118880043 |
|
1118880048 |
|
