Soft Computing, ISSN 1432-7643, 7/2008, Volume 12, Issue 9, pp. 835 - 856

Since all the algebras connected to logic have, more or less explicitly, an associated order relation, it follows, by duality principle, that they have two...

IMTL algebra | Hájek(P) algebra | Divisible BCK(P) lattice | Engineering | Weak-BL algebra | Artificial Intelligence (incl. Robotics) | BL algebra | Wajsberg algebra | Generalized-MV algebra | Heyting algebra | BCK(P) lattice | R 0 algebra | WNM algebra | Generalized-Wajsberg algebra | t-norm | MV algebra | BCK algebra | MTL algebra | Generalized-BL algebra | Residuated lattice | NM algebra | Control Engineering | Numerical and Computational Methods in Engineering | Pocrim | Mathematical Logic and Foundations | MTLalgebra | algebra | RESIDUATED LATTICES | Haijek(P) algebra | FUZZY-LOGIC | PROPOSITIONAL CALCULUS | VARIETIES | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SYSTEMS | R-0 algebra

IMTL algebra | Hájek(P) algebra | Divisible BCK(P) lattice | Engineering | Weak-BL algebra | Artificial Intelligence (incl. Robotics) | BL algebra | Wajsberg algebra | Generalized-MV algebra | Heyting algebra | BCK(P) lattice | R 0 algebra | WNM algebra | Generalized-Wajsberg algebra | t-norm | MV algebra | BCK algebra | MTL algebra | Generalized-BL algebra | Residuated lattice | NM algebra | Control Engineering | Numerical and Computational Methods in Engineering | Pocrim | Mathematical Logic and Foundations | MTLalgebra | algebra | RESIDUATED LATTICES | Haijek(P) algebra | FUZZY-LOGIC | PROPOSITIONAL CALCULUS | VARIETIES | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SYSTEMS | R-0 algebra

Journal Article

Algebra universalis, ISSN 0002-5240, 12/2018, Volume 79, Issue 4, pp. 1 - 30

Although there have been repeated attempts to define the concept of an Archimedean algebra for individual classes of residuated lattices, there is no...

Substructural logic | Archimedean property | Generalized BL-algebra | Mathematics | Conrad’s program | Algebra | Generalized MV-algebra | Residuated lattice | Lattice-ordered group | 06F15 | 06F05 | 06D35 | 03B47 | 03G10 | MATHEMATICS | PSEUDO MV-ALGEBRAS | VARIETIES | BL-ALGEBRAS | Conrad's program

Substructural logic | Archimedean property | Generalized BL-algebra | Mathematics | Conrad’s program | Algebra | Generalized MV-algebra | Residuated lattice | Lattice-ordered group | 06F15 | 06F05 | 06D35 | 03B47 | 03G10 | MATHEMATICS | PSEUDO MV-ALGEBRAS | VARIETIES | BL-ALGEBRAS | Conrad's program

Journal Article

Algebra universalis, ISSN 0002-5240, 05/2009, Volume 60, Issue 4, pp. 381 - 404

Generalized basic logic algebras (GBL-algebras for short) have been introduced in [JT02] as a generalization of Hájek’s BL-algebras, and constitute a bridge...

residuated lattices | lattice-ordered groups | Algebra | generalized MV-algebras | hoops | generalized BL-algebras | Mathematics | Secondary: 06F15, 06D35, 03G25 | Primary: 06F05 | basic logic | Generalized BL-algebras | Basic logic | Hoops | Residuated lattices | Lattice-ordered groups | Generalized MV-algebras | MATHEMATICS | WORD PROBLEM | Computer science

residuated lattices | lattice-ordered groups | Algebra | generalized MV-algebras | hoops | generalized BL-algebras | Mathematics | Secondary: 06F15, 06D35, 03G25 | Primary: 06F05 | basic logic | Generalized BL-algebras | Basic logic | Hoops | Residuated lattices | Lattice-ordered groups | Generalized MV-algebras | MATHEMATICS | WORD PROBLEM | Computer science

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 04/2012, Volume 62, Issue 2, pp. 157 - 168

Banaschewski's theorem concerns subdirect product decompositions of lattice ordered groups. In the present paper we deal with the analogous investigation for...

congruence relation | GMV-algebra | subdirect product | lattice ordered group | MATHEMATICS | RESIDUATED LATTICES | GENERALIZED MV-ALGEBRAS | MAPPINGS | Public contracts | Algebra

congruence relation | GMV-algebra | subdirect product | lattice ordered group | MATHEMATICS | RESIDUATED LATTICES | GENERALIZED MV-ALGEBRAS | MAPPINGS | Public contracts | Algebra

Journal Article

Algebra universalis, ISSN 0002-5240, 8/2006, Volume 55, Issue 2, pp. 227 - 238

A generalized BL - algebra (or GBL-algebra for short) is a residuated lattice that satisfies the identities $$ x\Lambda y = ((x\Lambda y)/y)y = y(y\backslash...

residuated lattices | Algebra | generalized MV-algebras | Generalized BL-algebras | Mathematics | 06F05 | 03G25 | 06D35 | 03G10 | basic logic | Basic logic | Residuated lattices | Generalized MV-algebras | MATHEMATICS | MV-ALGEBRAS | generalized BL-algebras

residuated lattices | Algebra | generalized MV-algebras | Generalized BL-algebras | Mathematics | 06F05 | 03G25 | 06D35 | 03G10 | basic logic | Basic logic | Residuated lattices | Generalized MV-algebras | MATHEMATICS | MV-ALGEBRAS | generalized BL-algebras

Journal Article

Annals of Pure and Applied Logic, ISSN 0168-0072, 2009, Volume 161, Issue 2, pp. 228 - 234

It is shown that the Boolean center of complemented elements in a bounded integral residuated lattice characterizes direct decompositions. Generalizing both...

Generalized BL-algebras | Basic logic | Residuated lattices | Posets | Generalized MV-algebras | MATHEMATICS | MATHEMATICS, APPLIED | LOGIC

Generalized BL-algebras | Basic logic | Residuated lattices | Posets | Generalized MV-algebras | MATHEMATICS | MATHEMATICS, APPLIED | LOGIC

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 4/2010, Volume 60, Issue 2, pp. 179 - 188

The notion of idempotent modification of an algebra was introduced by Ježek; he proved that the idempotent modification of a group is always subdirectly...

Algebra | generalized MV -algebra | Secondary 06F20 | Mathematics, general | direct irreducibility | subdirect irreducibility | Mathematics | Primary 06D35 | boolean element | lattice ordered group | generalized MV-algebra | Boolean element | Subdirect irreducibility | Generalized MV-algebra | Lattice ordered group | Direct irreducibility | MATHEMATICS | Public contracts | Web services

Algebra | generalized MV -algebra | Secondary 06F20 | Mathematics, general | direct irreducibility | subdirect irreducibility | Mathematics | Primary 06D35 | boolean element | lattice ordered group | generalized MV-algebra | Boolean element | Subdirect irreducibility | Generalized MV-algebra | Lattice ordered group | Direct irreducibility | MATHEMATICS | Public contracts | Web services

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 6/2011, Volume 61, Issue 3, pp. 341 - 354

We apply the notion of generalized MV-algebra (GMV-algebra, in short) in the sense of Galatos and Tsinakis. Let M be a complete GMV-algebra and let α be a...

Secondary 06F15 | Algebra | higher degrees of distributivity | generalized MV -algebra | Mathematics, general | Mathematics | completeness | direct product | Primary 06D35 | generalized MV-algebra | MATHEMATICS | LATTICE-ORDERED GROUPS | MAPPINGS | Public contracts

Secondary 06F15 | Algebra | higher degrees of distributivity | generalized MV -algebra | Mathematics, general | Mathematics | completeness | direct product | Primary 06D35 | generalized MV-algebra | MATHEMATICS | LATTICE-ORDERED GROUPS | MAPPINGS | Public contracts

Journal Article

JOURNAL OF UNIVERSAL COMPUTER SCIENCE, ISSN 0948-695X, 2008, Volume 14, Issue 22, pp. 3686 - 3715

Since all the algebras connected to logic have, more or less explicitely, an associated order relation, it follows that they have two presentations, dual to...

IMTL algebra | Heyting algebra | BCK(P) lattice | weak-BL algebra | WNM algebra | t-norm | generalized-Wajsberg algebra | Hajek(P) algebra | MV algebra | generalized-BL algebra | COMPUTER SCIENCE, SOFTWARE ENGINEERING | BCK algebra | MTL algebra | residuated lattice | divisible BCK(P) lattice | Hilbert algebra | Hertz algebra | NM algebra | BL algebra | R-0 algebra | COMPUTER SCIENCE, THEORY & METHODS | Wajsberg algebra | generalized-MV algebra | pocrim

IMTL algebra | Heyting algebra | BCK(P) lattice | weak-BL algebra | WNM algebra | t-norm | generalized-Wajsberg algebra | Hajek(P) algebra | MV algebra | generalized-BL algebra | COMPUTER SCIENCE, SOFTWARE ENGINEERING | BCK algebra | MTL algebra | residuated lattice | divisible BCK(P) lattice | Hilbert algebra | Hertz algebra | NM algebra | BL algebra | R-0 algebra | COMPUTER SCIENCE, THEORY & METHODS | Wajsberg algebra | generalized-MV algebra | pocrim

Journal Article

Communications in Algebra, ISSN 0092-7872, 10/2007, Volume 35, Issue 11, pp. 3370 - 3390

In spite of the well-know fact that the system of ℓ-groups with strong unit (unital ℓ-groups) does not form a variety, there is a categorical connection...

Top component | 03B50 | Completeness Theorem State | Extremal state | Infinitesimal | Top variety | MV-algebra | Normal valued variety | Generalized MV-algebra | 03G12 | 06F15 | Variety | 06D35 | Unital ℓ-group | Unital α-group | Completeness theorem state | MATHEMATICS | normal valued variety | top variety | unital l-group | PSEUDOEFFECT ALGEBRAS | extremal state | top component | completeness theorem state | variety | infinitesimal | generalized MV-algebra

Top component | 03B50 | Completeness Theorem State | Extremal state | Infinitesimal | Top variety | MV-algebra | Normal valued variety | Generalized MV-algebra | 03G12 | 06F15 | Variety | 06D35 | Unital ℓ-group | Unital α-group | Completeness theorem state | MATHEMATICS | normal valued variety | top variety | unital l-group | PSEUDOEFFECT ALGEBRAS | extremal state | top component | completeness theorem state | variety | infinitesimal | generalized MV-algebra

Journal Article

Journal of Universal Computer Science, ISSN 0958-695X, 2008, Volume 14, Issue 22, pp. 3686 - 3715

Generalized-MV algebra | IMTL algebra | Hájek(P) algebra | Divisible BCK(P) lattice | Heyting algebra | BCK(P) lattice | WNM algebra | Generalized-Wajsberg algebra | MV algebra | BCK algebra | MTL algebra | T-norm | Weak-BL algebra | Generalized-BL algebra | Residuated lattice | Hertz algebra | Hilbert algebra | NM algebra | BL algebra | Wajsberg algebra | Pocrim | Ro algebra

Journal Article

Czechoslovak Mathematical Journal, ISSN 0011-4642, 3/2007, Volume 57, Issue 1, pp. 161 - 171

In this paper we investigate the relations between isometries and direct product decompositions of generalized MV-algebras.

Ordinary Differential Equations | direct product decomposition | Analysis | Convex and Discrete Geometry | generalized MV -algebra | Mathematics, general | Mathematics | Mathematical Modeling and Industrial Mathematics | isometry | Generalized MV-algebra | Direct product decomposition | Isometry | MATHEMATICS | INTERVALS | generalized MV-algebra

Ordinary Differential Equations | direct product decomposition | Analysis | Convex and Discrete Geometry | generalized MV -algebra | Mathematics, general | Mathematics | Mathematical Modeling and Industrial Mathematics | isometry | Generalized MV-algebra | Direct product decomposition | Isometry | MATHEMATICS | INTERVALS | generalized MV-algebra

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 10/2010, Volume 60, Issue 5, pp. 591 - 606

We apply the concept of generalized MV-algebra (GMV-algebra, for short) in the sense defined and studied by Galatos and Tsinakis. We introduce the notion of...

GMV-algebra | Algebra | Mathematics, general | Mathematics | Primary 06D35 | internal direct product decomposition | isometry | MATHEMATICS | GENERALIZED MV-ALGEBRAS | ORDERED-GROUPS | Public contracts

GMV-algebra | Algebra | Mathematics, general | Mathematics | Primary 06D35 | internal direct product decomposition | isometry | MATHEMATICS | GENERALIZED MV-ALGEBRAS | ORDERED-GROUPS | Public contracts

Journal Article

Kybernetika, ISSN 0023-5954, 2005, Volume 41, Issue 2, pp. 129 - 142

We study unbounded versions of effect algebras. We show a necessary and sufficient condition, when lattice operations of a such generalized effect algebra P...

Prelattice and homogeneous generalized effect algebra | Generalized MV-effect algebra | Effect algebra | Generalized effect algebra | generalized effect algebra | effect algebra | BLOCKS | generalized MV-effect algebra | COMPUTER SCIENCE, CYBERNETICS | prelattice and homogeneous generalized effect algebra

Prelattice and homogeneous generalized effect algebra | Generalized MV-effect algebra | Effect algebra | Generalized effect algebra | generalized effect algebra | effect algebra | BLOCKS | generalized MV-effect algebra | COMPUTER SCIENCE, CYBERNETICS | prelattice and homogeneous generalized effect algebra

Journal Article

Czechoslovak Mathematical Journal, ISSN 0011-4642, 12/2007, Volume 57, Issue 4, pp. 1099 - 1105

A generalized MV-algebra A is called representable if it is a subdirect product of linearly ordered generalized MV-algebras. Let S be the system of all...

Congruence relation | Unital lattice ordered group | Representability | Generalized MV-algebra | MATHEMATICS | congruence relation | generalized MV-algebra | unital lattice ordered group | represent ability

Congruence relation | Unital lattice ordered group | Representability | Generalized MV-algebra | MATHEMATICS | congruence relation | generalized MV-algebra | unital lattice ordered group | represent ability

Journal Article

JOURNAL OF UNIVERSAL COMPUTER SCIENCE, ISSN 0948-695X, 2007, Volume 13, Issue 11, pp. 1628 - 1654

Since all the algebras connected to logic have, more or less explicitely, an associated order relation, it follows that they have two presentations, dual to...

IMTL algebra | Hajek(P) algebra | generalized-BL algebra | residuated lattice | divisible BCK(P) lattice | RESIDUATED LATTICES | Hilbert algebra | FUZZY-LOGIC | BL algebra | COMPUTER SCIENCE, THEORY & METHODS | Wajsberg algebra | LUKASIEWICZ-MOISIL ALGEBRAS | Heyting algebra | BCK(P) lattice | weak-BL algebra | PROPOSITIONAL CALCULUS | WNM algebra | VARIETIES | t-norm | generalized-Wajsberg algebra | CONNECTIONS | MV algebra | COMPUTER SCIENCE, SOFTWARE ENGINEERING | BCK algebra | MTL algebra | Hertz algebra | NM algebra | SYSTEMS | R-0 algebra | generalized-MV algebra | pocrim

IMTL algebra | Hajek(P) algebra | generalized-BL algebra | residuated lattice | divisible BCK(P) lattice | RESIDUATED LATTICES | Hilbert algebra | FUZZY-LOGIC | BL algebra | COMPUTER SCIENCE, THEORY & METHODS | Wajsberg algebra | LUKASIEWICZ-MOISIL ALGEBRAS | Heyting algebra | BCK(P) lattice | weak-BL algebra | PROPOSITIONAL CALCULUS | WNM algebra | VARIETIES | t-norm | generalized-Wajsberg algebra | CONNECTIONS | MV algebra | COMPUTER SCIENCE, SOFTWARE ENGINEERING | BCK algebra | MTL algebra | Hertz algebra | NM algebra | SYSTEMS | R-0 algebra | generalized-MV algebra | pocrim

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 12/2008, Volume 58, Issue 6, pp. 719 - 738

We use the concept of generalized MV-algebra (GMV-algebra, in short) in the sense of Galatos and Tsinakis; the main tool in their investigation was a...

Secondary 06F15 | Algebra | generalized MV -algebra | Mathematics, general | Mathematics | radical class | Primary 06D35 | lattice ordered group | generalized MV-algebra | Generalized MV-algebra | Radical class | Lattice ordered gropu | LATTICE-ORDERED-GROUPS | MATHEMATICS | GENERALIZED MV-ALGEBRAS | Public contracts

Secondary 06F15 | Algebra | generalized MV -algebra | Mathematics, general | Mathematics | radical class | Primary 06D35 | lattice ordered group | generalized MV-algebra | Generalized MV-algebra | Radical class | Lattice ordered gropu | LATTICE-ORDERED-GROUPS | MATHEMATICS | GENERALIZED MV-ALGEBRAS | Public contracts

Journal Article

Algebra Universalis, ISSN 0002-5240, 02/2009, Volume 60, Issue 1, pp. 37 - 62

We generalize Komori's characterization of the proper subvarieties of MV-algebras. Namely, within the variety of generalized MV-algebras (GMV-algebras) such...

GMV-algebra | Unital ℓ-group, representation | N-perfect GMV-algebra | State | Categorical equivalence | Komori's characterization | Top variety | Variety | MATHEMATICS | unital l-group | top variety | n-perfect GMV-algebra | variety | GENERALIZED MV-ALGEBRAS | categorical equivalence | state | representation | Public contracts | Printing industry

GMV-algebra | Unital ℓ-group, representation | N-perfect GMV-algebra | State | Categorical equivalence | Komori's characterization | Top variety | Variety | MATHEMATICS | unital l-group | top variety | n-perfect GMV-algebra | variety | GENERALIZED MV-ALGEBRAS | categorical equivalence | state | representation | Public contracts | Printing industry

Journal Article

Czechoslovak Mathematical Journal, ISSN 0011-4642, 12/2007, Volume 57, Issue 4, pp. 1099 - 1105

A generalized MV-algebra A is called representable if it is a subdirect product of linearly ordered generalized MV-algebras. Let S be the system of all...

congruence relation | Ordinary Differential Equations | Analysis | Convex and Discrete Geometry | representability | generalized MV -algebra | Mathematics, general | Mathematics | Mathematical Modeling and Industrial Mathematics | unital lattice ordered group

congruence relation | Ordinary Differential Equations | Analysis | Convex and Discrete Geometry | representability | generalized MV -algebra | Mathematics, general | Mathematics | Mathematical Modeling and Industrial Mathematics | unital lattice ordered group

Journal Article

Czechoslovak Mathematical Journal, ISSN 0011-4642, 3/2008, Volume 58, Issue 1, pp. 183 - 202

In the present paper we deal with generalized MV-algebras (GMV-algebras, in short) in the sense of Galatos and Tsinakis. According to a result of the mentioned...

residuated lattice | Ordinary Differential Equations | direct summand | Convex and Discrete Geometry | Analysis | generalized MV -algebra | Mathematics, general | Mathematics | Mathematical Modeling and Industrial Mathematics | lattice ordered group | Generalized MV-algebra | Direct summand | Lattice ordered group | Residuated lattice | LATTICE-ORDERED-GROUPS | MATHEMATICS | generalized MV-algebra

residuated lattice | Ordinary Differential Equations | direct summand | Convex and Discrete Geometry | Analysis | generalized MV -algebra | Mathematics, general | Mathematics | Mathematical Modeling and Industrial Mathematics | lattice ordered group | Generalized MV-algebra | Direct summand | Lattice ordered group | Residuated lattice | LATTICE-ORDERED-GROUPS | MATHEMATICS | generalized MV-algebra

Journal Article

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