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Start Over Subject BL-algebra

1. A duality between algebras of basic logic and bounded representable DRl-monoids

Creator:
Rachůnek, Jiří
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
BL-algebra, MV -algebra, bounded DRl-monoid, representable DRl-monoid, and prime spectrum
Language:
English
Description:
BL-algebras, introduced by P. Hájek, form an algebraic counterpart of the basic fuzzy logic. In the paper it is shown that BL-algebras are the duals of bounded representable DRl-monoids. This duality enables us to describe some structure properties of BL-algebras.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Classes of fuzzy filters of residuated lattice ordered monoids

Creator:
Rachůnek, Jiří and Šalounová, Dana
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
residuated l-monoid, non-classical logics, basic fuzzy logic, intuitionistic logic, filter, fuzzy filter, BL-algebra, MV-algebra, and Heyting algebra
Language:
English
Description:
The logical foundations of processes handling uncertainty in information use some classes of algebras as algebraic semantics. Bounded residuated lattice ordered monoids (Rl-monoids) are common generalizations of BL-algebras, i.e., algebras of the propositional basic fuzzy logic, and Heyting algebras, i.e., algebras of the propositional intuitionistic logic. From the point of view of uncertain information, sets of provable formulas in inference systems could be described by fuzzy filters of the corresponding algebras. In the paper we investigate implicative, positive implicative, Boolean and fantastic fuzzy filters of bounded Rl-monoids.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Pure filters and stable topology on BL-algebra

Creator:
Eslami, Esfandiar and Haghani, Farhad Kh.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
BL-algebra, prime filters, maximal filters, pure filters, and stable topology
Language:
English
Description:
In this paper we introduce stable topology and F-topology on the set of all prime filters of a BL-algebra A and show that the set of all prime filters of A, namely Spec(A) with the stable topology is a compact space but not T0. Then by means of stable topology, we define and study pure filters of a BL-algebra A and obtain a one to one correspondence between pure filters of A and closed subsets of Max(A), the set of all maximal filters of A, as a subspace of Spec(A). We also show that for any filter F of BL-algebra A if σ(F)=F then U(F) is stable and F is a pure filter of A, where σ(F)={a∈A|y∧z=0 for some z∈F and y∈a⊥} and U(F)={P∈ Spec(A) |F⊈P}.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public