Monadic pseudo-equality algebras

Ghorbani, Shokoofeh

doi:10.1007/s00500-019-04243-5

Cited by 14 publications

(8 citation statements)

References 19 publications

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“…In a future work we will define and study the state monadic quantum B-algebras. Based on the monadic deductive systems, the uniform topology on a monadic pseudo-equality algebra has been introduced and studied in [29]. As another topic of research, one could define a topology on monadic quantum B-algebras.…”

Section: Discussionmentioning

confidence: 99%

“…Recently, the theory of monadic MV-algebras has been developed in [1], [16], [24]. Monadic operators were defined and investigated on various algebras of fuzzy logic: Heyting algebras ( [2]), basic algebras ( [5]), GMV-algebras ( [41]), involutive pseudo BCK-algebras ( [35]), bounded commutative Rℓ-monoids ( [39]), bounded residuated lattices ( [40]), residuated lattices ( [36]), BE-algebras ( [51]), Wajsberg hoops ( [6]), BL-algebras ( [4]), bounded hoops ( [47]), pseudo equality algebras ( [29]), pseudo BCI-algebras ( [50]), NM-algebras ( [48]), pseudo BE-algebras ( [11]). The monadic operators on quantum B-algebras have been recently introduced in [12].…”

Section: Introductionmentioning

confidence: 99%

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Quantum B-algebras with involutions

Ciungu¹

2020

Preprint

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The aim of this paper is to define and study the involutive and weakly involutive quantum B-algebras. We prove that any weakly involutive quantum B-algebra is a quantum B-algebra with pseudo-product. As an application, we introduce and investigate the notions of existential and universal quantifiers on involutive quantum B-algebras. It is proved that there is a one-to-one correspondence between the quantifiers on weakly involutive quantum B-algebras. One of the main results consists of proving that any pair of quantifiers is a monadic operator on weakly involutive quantum B-algebras. We investigate the relationship between quantifiers on bounded sup-commutative pseudo BCK-algebras and quantifiers on other related algebraic structures, such as pseudo MV-algebras and bounded Wajsberg hoops.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum B-algebras with involutions

Ciungu¹

2020

Preprint

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“…Some types of filters of equality algebras are introduced in [3]. Since then many researchers have worked on this area (see [4,6,14,12]).…”

Section: Introductionmentioning

confidence: 99%

“…14 (Local Deduction Theorem). Let Γ be a theory over the propositional equality logic EL and ϕ, ψ be formulas.…”

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confidence: 99%

Equality Logic

Ghorbani

2020

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In this paper, we introduce and study a corresponding logic toequality-algebras and obtain some basic properties of this logic. We provethe soundness and completeness of this logic based on equality-algebrasand local deduction theorem. Then we introduce the concept of (prelinear)equality-algebras and investigate some related properties. Also, westudy -deductive systems of equality-algebras. In particular, we provethat every prelinear equality-algebra is a subdirect product of linearly orderedequality-algebras. Finally, we construct prelinear equality logicand prove the soundness and strong completeness of this logic respect toprelinear equality-algebras.

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“…Recently, the theory of monadic MV-algebras has been developed in [1], [12], [14]. Monadic operators were defined and investigated on various algebras of fuzzy logic: Heyting algebras ( [2]), basic algebras ( [6]), GMV-algebras ( [34]), involutive pseudo BCK-algebras ( [24]), bounded commutative Rℓ-monoids ( [32]), bounded residuated lattices ( [33]), residuated lattices ( [27]), BE-algebras ( [41]), Wajsberg hoops ( [7]), BL-algebras ( [5]), bounded hoops ( [38]), pseudo equality algebras ( [18]), pseudo BCI-algebras ( [40]), NM-algebras ( [39]).…”

Section: Introductionmentioning

confidence: 99%

Monadic pseudo BE-algebras

Ciungu¹

2019

Preprint

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In this paper we define the monadic pseudo BE-algebras and investigate their properties. We prove that the existential and universal quantifiers of a monadic pseudo BE-algebra form a residuated pair. Special properties are studied for the particular case of monadic bounded commutative pseudo BE-algebras. Monadic classes of pseudo BE-algebras are investigated and it is proved that the quantifiers on bounded commutative pseudo BEalgebras are also quantifiers on the corresponding pseudo MV-algebras. The monadic deductive systems and monadic congruences of monadic pseudo BE-algebras are defined and their properties are studied. It is proved that, in the case of a monadic distributive commutative pseudo BE-algebra there is a one-to-one correspondence between monadic congruences and monadic deductive systems, and the monadic quotient pseudo BE-algebra algebra is also defined.

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Monadic pseudo-equality algebras

Cited by 14 publications

References 19 publications

Quantum B-algebras with involutions

Quantum B-algebras with involutions

Equality Logic

Monadic pseudo BE-algebras

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