Di Nola, Antonio.
Fuzzy Logic of Quasi-Truth: An Algebraic Treatment [electronic resource] / by Antonio Di Nola, Revaz Grigolia, Esko Turunen. - 1st ed. 2016. - VI, 116 p. 3 illus. online resource. - Studies in Fuzziness and Soft Computing, 338 1434-9922 ; . - Studies in Fuzziness and Soft Computing, 338 .
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 �ukasiewicz 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.
9783319304069
10.1007/978-3-319-30406-9 doi
Engineering.
Computer science--Mathematics.
Algebra.
Computational intelligence.
Engineering.
Computational Intelligence.
General Algebraic Systems.
Symbolic and Algebraic Manipulation.
Q342
006.3
Fuzzy Logic of Quasi-Truth: An Algebraic Treatment [electronic resource] / by Antonio Di Nola, Revaz Grigolia, Esko Turunen. - 1st ed. 2016. - VI, 116 p. 3 illus. online resource. - Studies in Fuzziness and Soft Computing, 338 1434-9922 ; . - Studies in Fuzziness and Soft Computing, 338 .
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 �ukasiewicz 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.
9783319304069
10.1007/978-3-319-30406-9 doi
Engineering.
Computer science--Mathematics.
Algebra.
Computational intelligence.
Engineering.
Computational Intelligence.
General Algebraic Systems.
Symbolic and Algebraic Manipulation.
Q342
006.3