An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2002
|
| Ausgabe: | Second Edition |
| Schriftenreihe: | Applied Logic Series
27 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In case you are considering to adopt this book for courses with over 50 students, please contact ties.nijssen@springer.com for more information. This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification |
| Beschreibung: | 1 Online-Ressource (XVIII, 390 p) |
| ISBN: | 9789401599344 9789048160792 |
| ISSN: | 1386-2790 |
| DOI: | 10.1007/978-94-015-9934-4 |
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| 500 | |a In case you are considering to adopt this book for courses with over 50 students, please contact ties.nijssen@springer.com for more information. This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification | ||
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401599344 9789048160792 |
| issn | 1386-2790 |
| language | English |
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| spelling | Andrews, Peter B. Verfasser aut An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof by Peter B. Andrews Second Edition Dordrecht Springer Netherlands 2002 1 Online-Ressource (XVIII, 390 p) txt rdacontent c rdamedia cr rdacarrier Applied Logic Series 27 1386-2790 In case you are considering to adopt this book for courses with over 50 students, please contact ties.nijssen@springer.com for more information. This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification Mathematics Logic Electronic data processing Artificial intelligence Logic, Symbolic and mathematical Computational linguistics Mathematical Logic and Foundations Computing Methodologies Artificial Intelligence (incl. Robotics) Computational Linguistics Datenverarbeitung Künstliche Intelligenz Mathematik Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Beweisbarkeit (DE-588)7578966-8 gnd rswk-swf Typentheorie (DE-588)4121795-0 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s Beweisbarkeit (DE-588)7578966-8 s Typentheorie (DE-588)4121795-0 s 1\p DE-604 https://doi.org/10.1007/978-94-015-9934-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Andrews, Peter B. An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof Mathematics Logic Electronic data processing Artificial intelligence Logic, Symbolic and mathematical Computational linguistics Mathematical Logic and Foundations Computing Methodologies Artificial Intelligence (incl. Robotics) Computational Linguistics Datenverarbeitung Künstliche Intelligenz Mathematik Mathematische Logik (DE-588)4037951-6 gnd Beweisbarkeit (DE-588)7578966-8 gnd Typentheorie (DE-588)4121795-0 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)7578966-8 (DE-588)4121795-0 |
| title | An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof |
| title_auth | An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof |
| title_exact_search | An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof |
| title_full | An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof by Peter B. Andrews |
| title_fullStr | An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof by Peter B. Andrews |
| title_full_unstemmed | An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof by Peter B. Andrews |
| title_short | An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof |
| title_sort | an introduction to mathematical logic and type theory to truth through proof |
| topic | Mathematics Logic Electronic data processing Artificial intelligence Logic, Symbolic and mathematical Computational linguistics Mathematical Logic and Foundations Computing Methodologies Artificial Intelligence (incl. Robotics) Computational Linguistics Datenverarbeitung Künstliche Intelligenz Mathematik Mathematische Logik (DE-588)4037951-6 gnd Beweisbarkeit (DE-588)7578966-8 gnd Typentheorie (DE-588)4121795-0 gnd |
| topic_facet | Mathematics Logic Electronic data processing Artificial intelligence Logic, Symbolic and mathematical Computational linguistics Mathematical Logic and Foundations Computing Methodologies Artificial Intelligence (incl. Robotics) Computational Linguistics Datenverarbeitung Künstliche Intelligenz Mathematik Mathematische Logik Beweisbarkeit Typentheorie |
| url | https://doi.org/10.1007/978-94-015-9934-4 |
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