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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Ulrich Höhle; E P Klement |

ISBN: | 9789401102155 9401102155 |

OCLC Number: | 851370642 |

Description: | 1 online resource (viii, 392 pages). |

Contents: | A Algebraic Foundations of Non-Classical Logics -- I?-Complete MV-algebras -- II On MV-algebras of continuous functions -- III Free and projective Heyting and monadic Heyting algebras -- IV Commutative, residuated 1 -- monoids -- V A Proof of the completeness of the infinite-valued calculus of Lukasiewicz with one varibale -- B Non-Classical Models and Topos-Like Categories -- VI Presheaves Over GL-monoide -- VII Quantales: Quantal sets -- VIII Categories of fuzzy sets with values in a quantale or project ale -- IX Fuzzy logic and categories of fuzzy sets -- C General Aspects of Non-Classical Logics 269 -- X Prolog extensions to many-valued logics -- XI Epistemological aspects of many-valued logics and fuzzy structures -- XII Ultraproduct theorem and recursive properties of fuzzy logic. |

Series Title: | Theory and decision library., Series B,, Mathematical and statistical methods ;, 32. |

Responsibility: | edited by Ulrich Höhle, Erich Peter Klement. |

### Abstract:

Non-Classical Logics and their Applications to Fuzzy Subsets is the first major work devoted to a careful study of various relations between non-classical logics and fuzzy sets. This volume is indispensable for all those who are interested in a deeper understanding of the mathematical foundations of fuzzy set theory, particularly in intuitionistic logic, Lukasiewicz logic, monoidal logic, fuzzy logic and topos-like categories. The tutorial nature of the longer chapters, the comprehensive bibliography and index make it suitable as a valuable and important reference for graduate students as well as research workers in the field of non-classical logics. The book is arranged in three parts: Part A presents the most recent developments in the theory of Heyting algebras, MV-algebras, quantales and GL-monoids. Part B gives a coherent and current account of topos-like categories for fuzzy set theory based on Heyting algebra valued sets, quantal sets of M-valued sets. Part C addresses general aspects of non-classical logics including epistemological problems as well as recursive properties of fuzzy logic.

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