A first course in logic:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Florida
CRC Press
[2019]
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xv, 233 Seiten Illustrationen, Diagramme |
| ISBN: | 9780815386643 9780815386650 |
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| 245 | 1 | 0 | |a A first course in logic |c Mark V. Lawson |
| 264 | 1 | |a Boca Raton, Florida |b CRC Press |c [2019] | |
| 300 | |a xv, 233 Seiten |b Illustrationen, Diagramme | ||
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Record in the Search Index
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| adam_text | Contents Preface ix Introduction xi 1 Propositional logic 1 1.1 Informal propositional logic ...............................................; . . . 1 1.2 Syntax of propositional logic ......................... . . . ................ 9 1.3 Semantics of propositional logic ................ 16 1.4 Logical equivalence ......................· · · ..................... .. 23 1.4.1 Definition ................................................. 23 1.4.2 Logical patterns 25 1.4.3 Applications .................................. 27 1.5 PL in action .................................................. 31 1.5.1 PL as a programming language ............. 32 1.5.2 PL can be used to model some computers ... . . . . 36 1.6 Adequate sets of connectives .................. 42 1.7 Truth functions .......................................................................... 45 1.8 Normalforms ................................................... 1.8.1 Negation normal form (NNF) ............................ 48 1.8.2 Disjunctive normal form (DNF) ............. 49 1.8.3 Conjunctive normal form (CNF) ............ 50 1.8.4 Prologue to PROLOG .............................................. ,51 1.9 V = AfV? or How to win a million dollars ... .... ; . . . 56 1.10 Valid arguments .......................................................... 1.10.1 Definitions and examples ............................................... 62 1.10.2 Proof in mathematics(I) .................................... 1.11 Truth trees ................................................................................ 71 1.11.1 The truth tree
algorithm ............ ... . . ...................... 72 1.11.2 The theory of truth trees .............................................. 83 1.12 Sequent calculus.................................................. 1.12.1 Deduction trees . .................................................................. 89 1.12.2 Truth trees revisited . ...................... .............................. 94 1.12.3 Gentzen’s system LK.............................................. ... . 99 vii 6 66
Contents viii 2 Boolean algebras 2.1 2.2 More set theory ................. Boolean algebras................. 2.2.1 Motivation .................................................................... 2.2.2 Definition and examples................................................ 2.2.3 Algebra in a Boolean algebra....................................... 2.3 Combinational circuits ............................................................ 2.3.1 How gates build circuits ........................................ 2.3.2 A simple calculator ................................................... .. . 2.4 Sequential circuits................................ 3 First-order logic 3.1 , First steps ................. . . ...................................................... 3.1.1 Names and predicates . .................... 3.1.2 Relations.................... 3.1.3 Structures.............. ...................................... ............... 3.1.4 Quantification ................................... 3.1.5 Syntax ............................................... 3.1.6 Variables: their care andmaintenance . . . ............... 3.1.7 Semantics . ................................................... 3.1.8 De Morgan’s laws for quantifiers ................................. 3.1.9 Quantifier examples ........................... . .՝.................. 3.2 Gödel’s completeness theorem . ............................................. 3.2.1 An example . ................................. 3.2.2 Truth trees for FOL .......................................... .. . . . 3.2.3 The soundness
theorem................................... 3.2.4 The completeness theorem............................................. 3.3 Proof in mathematics (II)................. 3.4 Further reading ........................................................................ 103 103 110 110 112 114 120 120 127 134 145 146 146 148 150 152 154 156 160 167 168 173 173 174 180 182 188 190 Solutions to all exercises 193 Bibliography 225 Index 231
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| language | English |
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| spelling | Lawson, Mark V. (DE-588)114617134X aut A first course in logic Mark V. Lawson Boca Raton, Florida CRC Press [2019] xv, 233 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Logic, Symbolic and mathematical Problems, exercises, etc Logic Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s DE-604 Erscheint auch als Online-Ausgabe 9781351175388 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030876316&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lawson, Mark V. A first course in logic Logic, Symbolic and mathematical Problems, exercises, etc Logic Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4037951-6 |
| title | A first course in logic |
| title_auth | A first course in logic |
| title_exact_search | A first course in logic |
| title_full | A first course in logic Mark V. Lawson |
| title_fullStr | A first course in logic Mark V. Lawson |
| title_full_unstemmed | A first course in logic Mark V. Lawson |
| title_short | A first course in logic |
| title_sort | a first course in logic |
| topic | Logic, Symbolic and mathematical Problems, exercises, etc Logic Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Logic, Symbolic and mathematical Problems, exercises, etc Logic Mathematische Logik |
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