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Fuzzy Logic of Quasi-Truth: An Algebraic Treatment
This book presents the first algebraic treatment of quasi-truth fuzzy logic and covers the algebraic foundations of many-valued logic. It offers a comprehensive account of basic techniques and reports on important results showing the pivotal role played by perfect many-valued algebras (MV-algebras)...
| Main Authors: | , , |
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| Corporate Author: | |
| Format: | e-Book |
| Language: | English |
| Published: |
Cham :
Springer International Publishing : Imprint: Springer,
2016.
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| Edition: | 1st ed. 2016. |
| Series: | Studies in Fuzziness and Soft Computing,
338 |
| Subjects: | |
| Online Access: | Full-text access View in OPAC |
| Summary: | This book presents the first algebraic treatment of quasi-truth fuzzy logic and covers the algebraic foundations of many-valued logic. It offers a comprehensive account of basic techniques and reports on important results showing the pivotal role played by perfect many-valued algebras (MV-algebras). It is well known that the first-order predicate Łukasiewicz logic is not complete with respect to the canonical set of truth values. However, it is complete with respect to all linearly ordered MV -algebras. As there are no simple linearly ordered MV-algebras in this case, infinitesimal elements of an MV-algebra are allowed to be truth values. The book presents perfect algebras as an interesting subclass of local MV-algebras and provides readers with the necessary knowledge and tools for formalizing the fuzzy concept of quasi true and quasi false. All basic concepts are introduced in detail to promote a better understanding of the more complex ones. It is an advanced and inspiring reference-guide for graduate students and researchers in the field of non-classical many-valued logics. |
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| Physical Description: | VI, 116 p. 3 illus. online resource. |
| ISBN: | 9783319304069 |
| ISSN: | 1860-0808 ; |
| DOI: | 10.1007/978-3-319-30406-9 |