Buch, Englisch, 233 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 376 g
Reihe: Trends in Logic
Buch, Englisch, 233 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 376 g
Reihe: Trends in Logic
ISBN: 978-90-481-5336-7
Verlag: Springer Netherlands
The aim of this book is to give self-contained proofs of all basic results concerning the infinite-valued proposition al calculus of Lukasiewicz and its algebras, Chang's MV -algebras. This book is for self-study: with the possible exception of Chapter 9 on advanced topics, the only prere quisite for the reader is some acquaintance with classical propositional logic, and elementary algebra and topology. In this book it is not our aim to give an account of Lukasiewicz's motivations for adding new truth values: readers interested in this topic will find appropriate references in Chapter 10. Also, we shall not explain why Lukasiewicz infinite-valued propositionallogic is a ba sic ingredient of any logical treatment of imprecise notions: Hajek's book in this series on Trends in Logic contains the most authorita tive explanations. However, in order to show that MV-algebras stand to infinite-valued logic as boolean algebras stand to two-valued logic, we shall devote Chapter 5 to Ulam's game of Twenty Questions with lies/errors, as a natural context where infinite-valued propositions, con nectives and inferences are used. While several other semantics for infinite-valued logic are known in the literature-notably Giles' game theoretic semantics based on subjective probabilities-still the transi tion from two-valued to many-valued propositonallogic can hardly be modelled by anything simpler than the transformation of the familiar game of Twenty Questions into Ulam game with lies/errors.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
- Technische Wissenschaften Elektronik | Nachrichtentechnik Elektronik Robotik
- Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
- Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie
- Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
- Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Wissensbasierte Systeme, Expertensysteme
Weitere Infos & Material
1 Basic notions.- 2 Chang completeness theorem.- 3 Free MV-algebras.- 4 ?ukasiewicz ?-valued calculus.- 5 Ulam’s game.- 6 Lattice-theoretical properties.- 7 MV-algebras and ?-groups.- 8 Varieties of MV-algebras.- 9 Advanced topics.- 10 Further Readings.
