Buch, Englisch, 390 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 622 g
Reihe: Applied Logic Series
To Truth Through Proof
Buch, Englisch, 390 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 622 g
Reihe: Applied Logic Series
ISBN: 978-90-481-6079-2
Verlag: Springer Netherlands
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.
Zielgruppe
Graduate
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik EDV | Informatik Technische Informatik Systemverwaltung & Management
- Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
- Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
- Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Wissensbasierte Systeme, Expertensysteme
- Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie
- Technische Wissenschaften Elektronik | Nachrichtentechnik Elektronik Robotik
- Geisteswissenschaften Sprachwissenschaft Computerlinguistik, Korpuslinguistik
Weitere Infos & Material
0 Introduction.- 1 Propositional Calculus.- 2 First-Order Logic.- 3 Provability and Refutability.- 4 Further Topics in First-Order Logic.- 5 Type Theory.- 6 Formalized Number Theory.- 7 Incompleteness and Undecidability.- Supplementary Exercises.- Summary of Theorems.- List of Figures.
