Titlebook: Non-Classical Logics and their Applications to Fuzzy Subsets; A Handbook of the Ma Ulrich Höhle,Erich Peter Klement Book 1995 Springer Scie

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Book 1995ical logics and fuzzy sets. Thisvolume is indispensable for all those who are interested in a deeperunderstanding of the mathematical foundations of fuzzy set theory,particularly in intuitionistic logic, Lukasiewicz logic,monoidal logic, fuzzy logic and topos-like categories. The tutorialnature of t

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Introduction1921], A Heyting [1930], G. Birkhoff and J.v. Neumann [1936]. From a syntactical point of view they are always fragments of classical logic. Disregarding for a moment quantum logic, non-classical logics can be characterized by the abandonment of the . and the maintenance of the integrality, the exporation, imporation and Duns Scotus law.

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Free and projective Heyting and monadic Heyting algebrasrojective algebras as retract of free algebras, the characteristic of finitely generated projective algebras is given in varieties of Heyting algebras and monadic Heyting algebras. By means of projective algebras, using an algebraic proof, the conditions of Friedman’s conjecture (Problem 41 [8]) are confirmed for well-known Medvedev‘s logic.

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Prolog extensions to many-valued logicsvalued logics leads to calculi with a sound and complete proof theory. In opposition to other models where generally the set of axioms as well as the deduction schemata are enriched we restrict ourselves to a simple modification of the deduction rules of classical logic without adding new axioms.

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Ultraproduct theorem and recursive properties of fuzzy logiche latter can be understood to be a sequence of inferences in a certain fuzzy theory given by a fuzzy set of special axioms. For various purposes, it may be useful to have an analogue of the famous Los‘ ultraproduct theorem also in fuzzy logic. We introduce elements of model theory for fuzzy logic and prove the ultraproduct theorem for it.

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