Algebraic Foundations of Many-Valued Reasoning:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2000
|
| Schriftenreihe: | Trends in Logic, Studia Logica Library
7 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 prerequisite 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 propositional logic is a basic ingredient of any logical treatment of imprecise notions: Hajek's book in this series on Trends in Logic contains the most authoritative 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, connectives 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 transition from two-valued to many-valued propositonal logic can hardly be modelled by anything simpler than the transformation of the familiar game of Twenty Questions into Ulam game with lies/errors |
| Beschreibung: | 1 Online-Ressource (IX, 233 p) |
| ISBN: | 9789401594806 9789048153367 |
| ISSN: | 1572-6126 |
| DOI: | 10.1007/978-94-015-9480-6 |
Internformat
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| 500 | |a 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 prerequisite 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 propositional logic is a basic ingredient of any logical treatment of imprecise notions: Hajek's book in this series on Trends in Logic contains the most authoritative 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, connectives 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 transition from two-valued to many-valued propositonal logic can hardly be modelled by anything simpler than the transformation of the familiar game of Twenty Questions into Ulam game with lies/errors | ||
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Datensatz im Suchindex
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| author | Cignoli, Roberto L. O. |
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| discipline | Mathematik Philosophie |
| doi_str_mv | 10.1007/978-94-015-9480-6 |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401594806 9789048153367 |
| issn | 1572-6126 |
| language | English |
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| series | Trends in Logic, Studia Logica Library |
| series2 | Trends in Logic, Studia Logica Library |
| spelling | Cignoli, Roberto L. O. Verfasser aut Algebraic Foundations of Many-Valued Reasoning by Roberto L. O. Cignoli, Itala M. L. D'Ottaviano, Daniele Mundici Dordrecht Springer Netherlands 2000 1 Online-Ressource (IX, 233 p) txt rdacontent c rdamedia cr rdacarrier Trends in Logic, Studia Logica Library 7 1572-6126 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 prerequisite 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 propositional logic is a basic ingredient of any logical treatment of imprecise notions: Hajek's book in this series on Trends in Logic contains the most authoritative 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, connectives 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 transition from two-valued to many-valued propositonal logic can hardly be modelled by anything simpler than the transformation of the familiar game of Twenty Questions into Ulam game with lies/errors Philosophy (General) Logic Computational complexity Artificial intelligence Algebra Logic, Symbolic and mathematical Philosophy Order, Lattices, Ordered Algebraic Structures Mathematical Logic and Foundations Discrete Mathematics in Computer Science Artificial Intelligence (incl. Robotics) Künstliche Intelligenz Philosophie Mehrwertige Logik (DE-588)4169335-8 gnd rswk-swf Mehrwertige Logik (DE-588)4169335-8 s 1\p DE-604 D'Ottaviano, Itala M. L. Sonstige oth Mundici, Daniele 1946- Sonstige (DE-588)1089443404 oth Trends in Logic, Studia Logica Library 7 (DE-604)BV011512969 7 https://doi.org/10.1007/978-94-015-9480-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cignoli, Roberto L. O. Algebraic Foundations of Many-Valued Reasoning Trends in Logic, Studia Logica Library Philosophy (General) Logic Computational complexity Artificial intelligence Algebra Logic, Symbolic and mathematical Philosophy Order, Lattices, Ordered Algebraic Structures Mathematical Logic and Foundations Discrete Mathematics in Computer Science Artificial Intelligence (incl. Robotics) Künstliche Intelligenz Philosophie Mehrwertige Logik (DE-588)4169335-8 gnd |
| subject_GND | (DE-588)4169335-8 |
| title | Algebraic Foundations of Many-Valued Reasoning |
| title_auth | Algebraic Foundations of Many-Valued Reasoning |
| title_exact_search | Algebraic Foundations of Many-Valued Reasoning |
| title_full | Algebraic Foundations of Many-Valued Reasoning by Roberto L. O. Cignoli, Itala M. L. D'Ottaviano, Daniele Mundici |
| title_fullStr | Algebraic Foundations of Many-Valued Reasoning by Roberto L. O. Cignoli, Itala M. L. D'Ottaviano, Daniele Mundici |
| title_full_unstemmed | Algebraic Foundations of Many-Valued Reasoning by Roberto L. O. Cignoli, Itala M. L. D'Ottaviano, Daniele Mundici |
| title_short | Algebraic Foundations of Many-Valued Reasoning |
| title_sort | algebraic foundations of many valued reasoning |
| topic | Philosophy (General) Logic Computational complexity Artificial intelligence Algebra Logic, Symbolic and mathematical Philosophy Order, Lattices, Ordered Algebraic Structures Mathematical Logic and Foundations Discrete Mathematics in Computer Science Artificial Intelligence (incl. Robotics) Künstliche Intelligenz Philosophie Mehrwertige Logik (DE-588)4169335-8 gnd |
| topic_facet | Philosophy (General) Logic Computational complexity Artificial intelligence Algebra Logic, Symbolic and mathematical Philosophy Order, Lattices, Ordered Algebraic Structures Mathematical Logic and Foundations Discrete Mathematics in Computer Science Artificial Intelligence (incl. Robotics) Künstliche Intelligenz Philosophie Mehrwertige Logik |
| url | https://doi.org/10.1007/978-94-015-9480-6 |
| volume_link | (DE-604)BV011512969 |
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