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2019, Trends in Logic, Studia Logica Library, ISBN 3030120953, Volume 50, 107

This book presents an English translation of a classic Russian text on duality theoryfor Heyting algebras...

Duality theory (Mathematics)

Duality theory (Mathematics)

eBook

Soft computing (Berlin, Germany), ISSN 1432-7643, 11/2018, Volume 22, Issue 21, pp. 7119 - 7128

Hoop algebras or hoops are naturally ordered commutative residuated integral monoids, introduced by Bosbach (Fundam Math 64:257...

Heyting algebra | Node | Kleene algebra | Semi-De Morgan algebra | Hoop | Engineering | Computational Intelligence | Control, Robotics, Mechatronics | Hertz algebra | Hilbert algebra | BCK-algebra | Artificial Intelligence (incl. Robotics) | Nodal filter | Mathematical Logic and Foundations | Computer Science, Artificial Intelligence | Computer Science, Interdisciplinary Applications | Technology | Computer Science | Science & Technology | Algebra | Hoops | Monoids

Heyting algebra | Node | Kleene algebra | Semi-De Morgan algebra | Hoop | Engineering | Computational Intelligence | Control, Robotics, Mechatronics | Hertz algebra | Hilbert algebra | BCK-algebra | Artificial Intelligence (incl. Robotics) | Nodal filter | Mathematical Logic and Foundations | Computer Science, Artificial Intelligence | Computer Science, Interdisciplinary Applications | Technology | Computer Science | Science & Technology | Algebra | Hoops | Monoids

Journal Article

Order, ISSN 0167-8094, 3/2018, Volume 35, Issue 1, pp. 23 - 45

Generalizing the well known and exploited relation between Heyting and Nelson algebras to semi-Heyting algebras, we introduce the variety of semi-Nelson algebras...

Geometry | Twist structures | Nelson algebras | Semi-Heyting algebras | Semi-Nelson algebras | Mathematics | Number Theory | Heyting algebras | Physical Sciences | Science & Technology | Algebra | Congruences

Geometry | Twist structures | Nelson algebras | Semi-Heyting algebras | Semi-Nelson algebras | Mathematics | Number Theory | Heyting algebras | Physical Sciences | Science & Technology | Algebra | Congruences

Journal Article

2005, 3rd ed., Oxford logic guides, ISBN 9780198568520, Volume 47., xxii, 191

.... In this edition, the background material has been augmented to include an introduction to Heyting algebras...

Set theory | Algebra, Boolean | Proof theory | Logic | Heyting algebra | Ultrailter | Category | Generic | Boolean algebra | Boolean-valued model | Forcing | Axiom of choice | Continuum hypothesis | Lattice

Set theory | Algebra, Boolean | Proof theory | Logic | Heyting algebra | Ultrailter | Category | Generic | Boolean algebra | Boolean-valued model | Forcing | Axiom of choice | Continuum hypothesis | Lattice

Book

Soft computing (Berlin, Germany), 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 presentations, dual to each...

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 | Computer Science, Artificial Intelligence | Computer Science, Interdisciplinary Applications | Technology | Computer Science | Science & Technology

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 | Computer Science, Artificial Intelligence | Computer Science, Interdisciplinary Applications | Technology | Computer Science | Science & Technology

Journal Article

International journal of theoretical physics, ISSN 0020-7748, 10/2014, Volume 53, Issue 10, pp. 3409 - 3422

Heyting effect algebras are lattice-ordered pseudoboolean effect algebras endowed with a pseudocomplementation that maps on the center (i.e. Boolean elements...

Deduction-detachment theorem | Heyting algebra | Pseudoboolean effect algebra | Decidability | Heyting-Wajsberg algebra | Strong completeness | Theoretical, Mathematical and Computational Physics | Quantum Physics | Physics | Heyting effect algebra | Elementary Particles, Quantum Field Theory | MV-algebra | Lattice-ordered effect algebra | Effect algebra | Physics, general | Stonean MV-algebra | Algebra

Deduction-detachment theorem | Heyting algebra | Pseudoboolean effect algebra | Decidability | Heyting-Wajsberg algebra | Strong completeness | Theoretical, Mathematical and Computational Physics | Quantum Physics | Physics | Heyting effect algebra | Elementary Particles, Quantum Field Theory | MV-algebra | Lattice-ordered effect algebra | Effect algebra | Physics, general | Stonean MV-algebra | Algebra

Journal Article

Order, ISSN 0167-8094, 7/2017, Volume 34, Issue 2, pp. 327 - 348

In this article we investigate the lattices of Dyck paths of type A and B under dominance order, and explicitly describe their Heyting algebra structure...

Geometry | Heyting algebra | Distributive lattice | Discrete Mathematics in Computer Science | Symmetric group | Mathematics | Theory of Computation | Dyck path | Dominance order | Catalan numbers | Hyperoctahedral group | Physical Sciences | Science & Technology | Algebra | Dominance | Lattices | Combinatorial analysis | Proving | Mathematics - Combinatorics

Geometry | Heyting algebra | Distributive lattice | Discrete Mathematics in Computer Science | Symmetric group | Mathematics | Theory of Computation | Dyck path | Dominance order | Catalan numbers | Hyperoctahedral group | Physical Sciences | Science & Technology | Algebra | Dominance | Lattices | Combinatorial analysis | Proving | Mathematics - Combinatorics

Journal Article

Information sciences, ISSN 0020-0255, 03/2017, Volume 381, pp. 270 - 282

In this paper, by considering the notion of equality algebra, which is introduced by Jenei in [18...

BL-algebra | Hoop-algebra | Hertz-algebra | Equality algebra | Residuated lattice | Boolean-algebra | Heyting-algebra | MTL-algebra | EQ-algebra | MV-algebra | Computer Science, Information Systems | Technology | Computer Science | Science & Technology | Algebra | Equality | Fuzzy logic | Equivalence | Semantics | Lattices

BL-algebra | Hoop-algebra | Hertz-algebra | Equality algebra | Residuated lattice | Boolean-algebra | Heyting-algebra | MTL-algebra | EQ-algebra | MV-algebra | Computer Science, Information Systems | Technology | Computer Science | Science & Technology | Algebra | Equality | Fuzzy logic | Equivalence | Semantics | Lattices

Journal Article

2016, ISBN 9781498735278, 254

.... Computations with these truth values are governed by the truth value algebra of type-2 fuzzy sets...

Set Theory | Applied Mathematics | Algebra | laws | STMnetBASE | SCI-TECHnetBASE | MATHnetBASE | type-2 | operations | lattice | binary | join | distributive | partial | order | subsets | Heyting algebras

Set Theory | Applied Mathematics | Algebra | laws | STMnetBASE | SCI-TECHnetBASE | MATHnetBASE | type-2 | operations | lattice | binary | join | distributive | partial | order | subsets | Heyting algebras

eBook

03/2016, Monographs and research notes in mathematics, ISBN 9781498735278, Volume 22, 221

.... It will be of interest to mathematicians who work in fields related to fuzzy sets as well as those who work with universal algebra...

Fuzzy sets | Algebra

Fuzzy sets | Algebra

eBook

Synthese (Dordrecht), ISSN 0039-7857, 6/2012, Volume 186, Issue 3, pp. 719 - 752

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hubert space, or, more generally, on the lattice of projections in a von Neumann algebra...

Von Neumann algebra | Algebra | Boolean data | Quantum mechanics | Mathematical lattices | Mathematical topoi | Quantum logic | Hilbert spaces | Heyting algebras | Boolean algebras | Philosophy of Science | Philosophy of Language | Intuitionistic logic | Epistemology | C-algebras | Bohrification | Metaphysics | Logic | Locales | Philosophy | Arts & Humanities | History & Philosophy Of Science | Computer science | Valuation | Distributivity | Handbooks | Realism | Families & family life | Mathematics | Quantum physics | Physics | Function words | Semantics | Hilbert space | Philosophy of science | Quantum theory

Von Neumann algebra | Algebra | Boolean data | Quantum mechanics | Mathematical lattices | Mathematical topoi | Quantum logic | Hilbert spaces | Heyting algebras | Boolean algebras | Philosophy of Science | Philosophy of Language | Intuitionistic logic | Epistemology | C-algebras | Bohrification | Metaphysics | Logic | Locales | Philosophy | Arts & Humanities | History & Philosophy Of Science | Computer science | Valuation | Distributivity | Handbooks | Realism | Families & family life | Mathematics | Quantum physics | Physics | Function words | Semantics | Hilbert space | Philosophy of science | Quantum theory

Journal Article

Order, ISSN 0167-8094, 3/2017, Volume 34, Issue 1, pp. 23 - 35

In a pseudocomplemented de Morgan algebra, it is shown that the set of kernel ideals is a complete Heyting lattice, and a necessary and sufficient condition that the set of kernel ideals is boolean (resp. Stone) is derived...

Geometry | Heyting algebra | Distributive p -algebra | Congruence | Discrete Mathematics in Computer Science | Kernel ideal | Mathematics | Theory of Computation | De Morgan algebra | Stone lattice | Distributive p-algebra | Physical Sciences | Science & Technology | Algebra | Kernels

Geometry | Heyting algebra | Distributive p -algebra | Congruence | Discrete Mathematics in Computer Science | Kernel ideal | Mathematics | Theory of Computation | De Morgan algebra | Stone lattice | Distributive p-algebra | Physical Sciences | Science & Technology | Algebra | Kernels

Journal Article

Studia logica, ISSN 0039-3215, 8/2015, Volume 103, Issue 4, pp. 713 - 731

In this note, it is shown that the set of kernel ideals of a Kn,0-algebra L is a complete Heyting algebra, and the largest congruence on L such that the given kernel ideal as its congruence class...

Ockham algebra | Heyting algebra | Congruence | Computational Linguistics | 06D30 | Kernel ideal | Logic | Philosophy | Mathematical Logic and Foundations | Physical Sciences | Science & Technology - Other Topics | Mathematics | Arts & Humanities | Science & Technology | Algebra

Ockham algebra | Heyting algebra | Congruence | Computational Linguistics | 06D30 | Kernel ideal | Logic | Philosophy | Mathematical Logic and Foundations | Physical Sciences | Science & Technology - Other Topics | Mathematics | Arts & Humanities | Science & Technology | Algebra

Journal Article

Studia logica, ISSN 0039-3215, 2/2014, Volume 102, Issue 1, pp. 29 - 39

In this note we shall show that if L is a balanced pseudocomplemented Ockham algebra then the set ℐk(L...

Algebra | Mathematical theorems | Lattice theory | Logical theorems | Boolean data | Mathematical lattices | Mathematical congruence | Heyting algebras | Conceptual lattices | Ockham algebra | Heyting algebra | Congruence | Computational Linguistics | 06D30 | Kernel ideal | Logic | Pseudocomplemented algebra | Philosophy | Mathematical Logic and Foundations | 06D15 | Physical Sciences | Science & Technology - Other Topics | Mathematics | Arts & Humanities | Science & Technology

Algebra | Mathematical theorems | Lattice theory | Logical theorems | Boolean data | Mathematical lattices | Mathematical congruence | Heyting algebras | Conceptual lattices | Ockham algebra | Heyting algebra | Congruence | Computational Linguistics | 06D30 | Kernel ideal | Logic | Pseudocomplemented algebra | Philosophy | Mathematical Logic and Foundations | 06D15 | Physical Sciences | Science & Technology - Other Topics | Mathematics | Arts & Humanities | Science & Technology

Journal Article

Algebra universalis, ISSN 1420-8911, 04/2018, Volume 79, Issue 2, pp. 1 - 31

For L a complete lattice L and $$\mathfrak {X}=(X,(R_i)_I)$$
X=(X,(Ri)I)
a relational structure, we introduce the convolution algebra $$L^{\mathfrak {X}}$$
LX...

Relation algebra | 06D20 | Complex algebra | Heyting algebra | Algebra | Boolean algebra with operators | Convolution | Kripke frame | Type-2 truth value algebra | Mathematics | 03B45 | 03G10 | Physical Sciences | Science & Technology | Construction | Boolean algebra

Relation algebra | 06D20 | Complex algebra | Heyting algebra | Algebra | Boolean algebra with operators | Convolution | Kripke frame | Type-2 truth value algebra | Mathematics | 03B45 | 03G10 | Physical Sciences | Science & Technology | Construction | Boolean algebra

Journal Article

Fuzzy sets and systems, ISSN 0165-0114, 03/2017, Volume 311, pp. 86 - 98

In this paper, the notion of a prefilter generated by a nonempty subset of an EQ-algebra is introduced and a characterization of it is...

EQ-algebra | Heyting algebra | Boolean algebra | Statistics & Probability | Physical Sciences | Technology | Computer Science | Computer Science, Theory & Methods | Mathematics | Mathematics, Applied | Science & Technology | Algebra

EQ-algebra | Heyting algebra | Boolean algebra | Statistics & Probability | Physical Sciences | Technology | Computer Science | Computer Science, Theory & Methods | Mathematics | Mathematics, Applied | Science & Technology | Algebra

Journal Article

Soft computing (Berlin, Germany), ISSN 1432-7643, 3/2011, Volume 15, Issue 3, pp. 613 - 618

... Martín, Castiglioni, Menni and Sagastume in Heyting algebras. Since basic algebras form an algebraic tool for simultaneous treaty of many-valued logics and logics...

Engineering | Successor | Heyting algebra | Computational Intelligence | Hedge | Basic algebra | Control , Robotics, Mechatronics | Artificial Intelligence (incl. Robotics) | Mathematical Logic and Foundations | Computer Science, Artificial Intelligence | Computer Science, Interdisciplinary Applications | Technology | Computer Science | Science & Technology

Engineering | Successor | Heyting algebra | Computational Intelligence | Hedge | Basic algebra | Control , Robotics, Mechatronics | Artificial Intelligence (incl. Robotics) | Mathematical Logic and Foundations | Computer Science, Artificial Intelligence | Computer Science, Interdisciplinary Applications | Technology | Computer Science | Science & Technology

Journal Article

Mathematical structures in computer science, ISSN 1469-8072, 01/2020, Volume 30, Issue 6, pp. 1 - 25

Ruitenburg’s Theorem says that every endomorphism of a finitely generated free Heyting algebra is ultimately periodic if fixes all the generators but one...

Theorems | Generators | Algebra

Theorems | Generators | Algebra

Journal Article

Studia logica, ISSN 0039-3215, 10/2012, Volume 101, Issue 5, pp. 1073 - 1092

In this paper, we give an algebraic completeness theorem for constructive logic with strong negation in terms of finite rough set-based Nelson algebras determined by quasiorders...

Equivalence relation | Universal algebra | Rough set theory | Algebra | Approximation | Mathematical theorems | Intuitionistic logic | Boolean data | Heyting algebras | Indiscernibility | Computational Linguistics | Glivenko congruence | Rough sets | Nelson algebras | Logics with strong negation | Knowledge representation | Boolean congruence | Quasiorders (preorders) | Logic | Philosophy | Mathematical Logic and Foundations | Physical Sciences | Science & Technology - Other Topics | Mathematics | Arts & Humanities | Science & Technology | Analysis

Equivalence relation | Universal algebra | Rough set theory | Algebra | Approximation | Mathematical theorems | Intuitionistic logic | Boolean data | Heyting algebras | Indiscernibility | Computational Linguistics | Glivenko congruence | Rough sets | Nelson algebras | Logics with strong negation | Knowledge representation | Boolean congruence | Quasiorders (preorders) | Logic | Philosophy | Mathematical Logic and Foundations | Physical Sciences | Science & Technology - Other Topics | Mathematics | Arts & Humanities | Science & Technology | Analysis

Journal Article