MATHEMATICS, ISSN 2227-7390, 12/2019, Volume 7, Issue 12, p. 1243

In any logical algebraic structures, by using of different kinds of filters, one can construct various kinds of other logical algebraic structures. With this...

Wajsberg hoop | MATHEMATICS | Heyting algebra | BL-algebra | co-filter | Hilbert algebra | hoop | Brouwerian semilattice

Wajsberg hoop | MATHEMATICS | Heyting algebra | BL-algebra | co-filter | Hilbert algebra | hoop | Brouwerian semilattice

Journal Article

Soft Computing, ISSN 1432-7643, 12/2019, Volume 23, Issue 23, pp. 12209 - 12219

In this paper, we introduce some stabilizers and study related properties of them in residuated lattices. Then, we investigate the image and inverse image of a...

Implicative stabilizer | Engineering | Heyting algebra | Computational Intelligence | Control, Robotics, Mechatronics | Artificial Intelligence | Residuated lattice | Multiplicative stabilizer | Mathematical Logic and Foundations

Implicative stabilizer | Engineering | Heyting algebra | Computational Intelligence | Control, Robotics, Mechatronics | Artificial Intelligence | Residuated lattice | Multiplicative stabilizer | Mathematical Logic and Foundations

Journal Article

Algebra universalis, ISSN 0002-5240, 12/2019, Volume 80, Issue 4, pp. 1 - 18

By Priestley duality, each bounded distributive lattice is represented as the lattice of clopen upsets of a Priestley space, and by Esakia duality, each...

06D20 | Distributive lattice | Heyting algebra | Algebra | p-algebra | Priestley duality | Mathematics | 06D05 | 06E15 | Esakia duality | 06D15 | MATHEMATICS

06D20 | Distributive lattice | Heyting algebra | Algebra | p-algebra | Priestley duality | Mathematics | 06D05 | 06E15 | Esakia duality | 06D15 | MATHEMATICS

Journal Article

JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, ISSN 1064-1246, 2019, Volume 37, Issue 4, pp. 5471 - 5485

In this paper, we introduce the notion of co-annihilator in hoops and investigate some related properties of them. Then we prove that the set of filters F(A)...

filter | Heyting algebra | co-annihilator | Hoop | Boolean algebra | pseudo-complement | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Hoops | Algebra | Lattices

filter | Heyting algebra | co-annihilator | Hoop | Boolean algebra | pseudo-complement | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Hoops | Algebra | Lattices

Journal Article

FUNDAMENTA INFORMATICAE, ISSN 0169-2968, 2019, Volume 170, Issue 1-3, pp. 223 - 240

We study a version of the Stone duality between the Alexandrov spaces and the completely distributive algebraic lattices. This enables us to present...

COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | complete Heyting algebra | completeness theorem | second-order intuitionistic propositional logic | Logic | Semantics | Lattices (mathematics)

COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | complete Heyting algebra | completeness theorem | second-order intuitionistic propositional logic | Logic | Semantics | Lattices (mathematics)

Journal Article

Fuzzy Sets and Systems, ISSN 0165-0114, 10/2019, Volume 373, pp. 37 - 61

In this paper, notions of left- and right-state operators on residuated lattices are introduced and some related properties of such operators are investigated....

State filter | Heyting algebra | Galois connection | Residuated lattice | State coannihilator | State congruence | State residuated lattice | MATHEMATICS, APPLIED | ALGEBRAS | FILTERS | STATISTICS & PROBABILITY | COMPUTER SCIENCE, THEORY & METHODS | Algebra

State filter | Heyting algebra | Galois connection | Residuated lattice | State coannihilator | State congruence | State residuated lattice | MATHEMATICS, APPLIED | ALGEBRAS | FILTERS | STATISTICS & PROBABILITY | COMPUTER SCIENCE, THEORY & METHODS | Algebra

Journal Article

Journal of Philosophical Logic, ISSN 0022-3611, 2018, Volume 48, Issue 3, pp. 447 - 469

Conditional logics have traditionally been intended to formalize various intuitively correct modes of reasoning involving (counterfactual) conditional...

Conditional logic | Heyting algebra | Intuitionistic logic | Chellas semantics | Kripke semantics | PHILOSOPHY | Philosophy | Algebra

Conditional logic | Heyting algebra | Intuitionistic logic | Chellas semantics | Kripke semantics | PHILOSOPHY | Philosophy | Algebra

Journal Article

Journal of Algebra and its Applications, ISSN 0219-4988, 06/2018

J. Algebra Appl. 18, no. 6 (2019) 1950107 In 1702.04949 noncommutative frames were introduced, generalizing the usual notion of frames of open sets of a...

Heyting algebra | skew lattice | Noncommutative topos | noncommutative frame | Lawvere–Tierney topology

Heyting algebra | skew lattice | Noncommutative topos | noncommutative frame | Lawvere–Tierney topology

Journal Article

Algebra and Logic, ISSN 0002-5232, 5/2019, Volume 58, Issue 2, pp. 144 - 157

The interpolation problem over Johansson’s minimal logic J is considered. We introduce a series of Johansson algebras, which will be used to prove a number of...

Mathematics | Algebra | Johansson algebra | finite-layered pre-Heyting logic | Mathematical Logic and Foundations | Craig’s interpolation property | DECIDABILITY | MATHEMATICS | MINIMAL LOGIC | PROPERTY | Craig's interpolation property | LOGIC

Mathematics | Algebra | Johansson algebra | finite-layered pre-Heyting logic | Mathematical Logic and Foundations | Craig’s interpolation property | DECIDABILITY | MATHEMATICS | MINIMAL LOGIC | PROPERTY | Craig's interpolation property | LOGIC

Journal Article

Soft Computing, ISSN 1432-7643, 5/2019, Volume 23, Issue 10, pp. 3207 - 3216

The main goal of this paper is to introduce and research co-annihilators and $$\alpha $$ α -filters in residuated lattices. We characterize $$\alpha $$ α...

Engineering | Heyting algebra | Computational Intelligence | Control, Robotics, Mechatronics | Artificial Intelligence | Residuated lattice | Prime $$\alpha $$ α -filter space | Co-annihilator | alpha $$ α -filter | Mathematical Logic and Foundations

Engineering | Heyting algebra | Computational Intelligence | Control, Robotics, Mechatronics | Artificial Intelligence | Residuated lattice | Prime $$\alpha $$ α -filter space | Co-annihilator | alpha $$ α -filter | Mathematical Logic and Foundations

Journal Article

Indagationes Mathematicae, ISSN 0019-3577, 05/2019, Volume 30, Issue 3, pp. 403 - 469

Brouwer’s views on the foundations of mathematics have inspired the study of intuitionistic logic, including the study of the intuitionistic propositional...

Locale | Nucleus | Intermediate logics | Algebraic semantics | Heyting algebra | Intuitionistic logic | Topological semantics | Kripke semantics | Beth semantics | SEPARABLE AXIOMATIZATION | MATHEMATICS | PROPOSITIONAL SYSTEMS SN | Philosophy | Algebra | Lattice theory | Topology | Logic | Semantics

Locale | Nucleus | Intermediate logics | Algebraic semantics | Heyting algebra | Intuitionistic logic | Topological semantics | Kripke semantics | Beth semantics | SEPARABLE AXIOMATIZATION | MATHEMATICS | PROPOSITIONAL SYSTEMS SN | Philosophy | Algebra | Lattice theory | Topology | Logic | Semantics

Journal Article

2019 XXII International Conference on Soft Computing and Measurements (SCM), 05/2019, pp. 15 - 16

Given a crisp tolerance relation, the structure of the fuzzy tolerance classes with the membership values in a complete Heyting algebra is described. It is...

Heyting algebra | tolerance class | tolerance relation

Heyting algebra | tolerance class | tolerance relation

Conference Proceeding

Soft Computing, ISSN 1432-7643, 04/2018, Volume 23, Issue 10, pp. 1 - 10

The main goal of this paper is to introduce and research co-annihilators and alpha-filters in residuated lattices. We characterize alpha-filters in terms of...

Prime $$\alpha $$α-filter space | Heyting algebra | Co-annihilator | alpha $$α-filter | Residuated lattice | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Prime alpha-filter space | alpha-filter | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Prime $$\alpha $$α-filter space | Heyting algebra | Co-annihilator | alpha $$α-filter | Residuated lattice | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Prime alpha-filter space | alpha-filter | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Journal Article

Studia Logica, ISSN 0039-3215, 4/2019, Volume 107, Issue 2, pp. 247 - 282

We characterise the intermediate logics which admit a cut-free hypersequent calculus of the form $$\mathbf {HLJ} + \mathscr {R}$$ HLJ + R , where $$\mathbf...

Intermediate logics | Computational Linguistics | Hypersequent calculi | Algebraic proof theory | Heyting algebras | Logic | Philosophy | Mathematical Logic and Foundations | MATHEMATICS | COMPLETIONS | PHILOSOPHY | ELIMINATION | CANONICAL FORMULAS | RULES | LOGIC | Algebra

Intermediate logics | Computational Linguistics | Hypersequent calculi | Algebraic proof theory | Heyting algebras | Logic | Philosophy | Mathematical Logic and Foundations | MATHEMATICS | COMPLETIONS | PHILOSOPHY | ELIMINATION | CANONICAL FORMULAS | RULES | LOGIC | Algebra

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 03/2019, Volume 371, Issue 3, pp. 2133 - 2158

It is well known that the \ell -spectrum of an Abelian \ell -group, defined as the set of all its prime \ell -ideals with the hull-kernel topology, is a...

Countable | Group | Heyting algebra | Prime | Ideal | Consonance | Distributive | Hyperplane | Lattice | Half-space | Open | Spectrum | Representable | Spectral space | Lattice-ordered | Sober | Difference operation | Closed map | Completely normal | Join-irreducible | Abelian | IDEALS | CONVEX L-SUBGROUPS | MATHEMATICS | SEMILATTICES | join-irreducible | closed map | spectral space | distributive | hyperplane | group | prime | ideal | difference operation | representable | spectrum | completely normal | lattice | abelian | consonance | sober | half-space | countable | open | Mathematics | General Mathematics

Countable | Group | Heyting algebra | Prime | Ideal | Consonance | Distributive | Hyperplane | Lattice | Half-space | Open | Spectrum | Representable | Spectral space | Lattice-ordered | Sober | Difference operation | Closed map | Completely normal | Join-irreducible | Abelian | IDEALS | CONVEX L-SUBGROUPS | MATHEMATICS | SEMILATTICES | join-irreducible | closed map | spectral space | distributive | hyperplane | group | prime | ideal | difference operation | representable | spectrum | completely normal | lattice | abelian | consonance | sober | half-space | countable | open | Mathematics | General Mathematics

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 02/2019, Volume 69, Issue 1, pp. 15 - 34

In this paper, we investigate the variety of regular double -algebras and its subvarieties , ≥ 1, of range . First, we present an explicit description of the...

08B15 | equational basis | 06D50 | Priestley duality | discriminator variety | algebra | simple algebra | subdirectly irreducible algebra | regular double | lattice of subvarieties | double Heyting algebra | Secondary 08B26 | Primary 06D15 | 03G25 | 03G10 | regular double p-algebra | MATHEMATICS | SPACES | HEYTING ALGEBRAS | EQUATIONAL CLASSES | Algebra

08B15 | equational basis | 06D50 | Priestley duality | discriminator variety | algebra | simple algebra | subdirectly irreducible algebra | regular double | lattice of subvarieties | double Heyting algebra | Secondary 08B26 | Primary 06D15 | 03G25 | 03G10 | regular double p-algebra | MATHEMATICS | SPACES | HEYTING ALGEBRAS | EQUATIONAL CLASSES | Algebra

Journal Article

Logical Methods in Computer Science, ISSN 1860-5974, 01/2019, Volume 15, Issue 1, pp. 15:1 - 15:35

In recent years, unified correspondence has been developed as a generalized Sahlqvist theory which applies uniformly to all signatures of normal and regular...

canonicity | Computer Science(all) | bi-Heyting algebras | normal distributive lattice expansions | Theoretical Computer Science | co-Heyting algebras | Sahlqvist theory | Gödel-McKinsey-Tarski translation | Heyting algebras | algorithmic correspondence

canonicity | Computer Science(all) | bi-Heyting algebras | normal distributive lattice expansions | Theoretical Computer Science | co-Heyting algebras | Sahlqvist theory | Gödel-McKinsey-Tarski translation | Heyting algebras | algorithmic correspondence

Journal Article

Logical Methods in Computer Science, ISSN 1860-5974, 2019, Volume 15, Issue 1

In recent years, unified correspondence has been developed as a generalized Sahlqvist theory which applies uniformly to all signatures of normal and regular...

canonicity | bi-Heyting algebras | normal distributive lattice expansions | co-Heyting algebras | Sahlqvist theory | Gödel-McKinsey-Tarski translation | Heyting algebras | algorithmic correspondence | EXTENSIONS | Godel-McKinsey-Tarski translation | COMPLETENESS | COMPUTER SCIENCE, THEORY & METHODS | LOGIC | Mathematics - Logic

canonicity | bi-Heyting algebras | normal distributive lattice expansions | co-Heyting algebras | Sahlqvist theory | Gödel-McKinsey-Tarski translation | Heyting algebras | algorithmic correspondence | EXTENSIONS | Godel-McKinsey-Tarski translation | COMPLETENESS | COMPUTER SCIENCE, THEORY & METHODS | LOGIC | Mathematics - Logic

Journal Article

Journal of Algebra and its Applications, ISSN 0219-4988, 01/2019, Volume 18, Issue 1

We explore algebraic properties of noncommutative frames. The concept of noncommutative frame is due to Le Bruyn, who introduced it in connection with...

Frames | Heyting algebra | noncommutative structure | skew lattice | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Rings and Algebras

Frames | Heyting algebra | noncommutative structure | skew lattice | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Rings and Algebras

Journal Article

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