Databases

Jaoua, Ali; Belkhiter, Nadir; Ounalli, Habib; Moukam, Théodore

doi:10.1007/978-3-7091-6510-2_13

Cited by 5 publications

(5 citation statements)

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“…(iv) Since H-classes are the cells in the egg-box picture of the J -classes Jr and there are S(n + 1,r + 1) rows and S(n + 1,r + 1) columns. Thus it follows that there are S(n + 1,r + 1) 2…”

Section: Theorem 25: ([5]mentioning

confidence: 94%

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On cardinalities of Green’s equivalence classes in the semigroup of difunctional binary relations

Ibrahim¹

2022

SLUJST

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In this paper, we considered the set DX, consisting of all binary relations α ⊆ X × X satisfying (∀x,y,u,v ∈ X) (x,u),(x,v),(y,u)∈α ⇒(y,v) ∈ α. This set is an inverse semigroup under a binary operation defined by xα = yβ−1 ≠ ∅, where xα denotes the set of images of x under α, and yβ−1 denotes the set of pre-images of y under β. Combinatorial results relating to Green’s relations in semigroup are obtained. In particular, we obtained cardinalities of Green’s equivalence classes in the semigroup for the case where X is finite. Also, we obtained the number of idempotent elements in to be equal to , where n = |X| and B(k) is the Bell number defined as the number of partitions of a set of k elements.

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Section: Theorem 25: ([5]mentioning

confidence: 94%

“…Difunctional binary relations, which were introduced in [4], appear in different areas of Discrete Mathematics, for example in [2] difunctional relations were used in databases. In this paper, we examine some combinatorial properties of the inverse semigroup of all difunctional binary relations.…”

Section: Introductionmentioning

confidence: 99%

On cardinalities of Green’s equivalence classes in the semigroup of difunctional binary relations

Ibrahim¹

2022

SLUJST

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“…Relation algebra can hence be viewed both as an assembly language for knowledge representation and as a common ancestor of the many systems of algebraic logic available today. It has also been used for decomposing relations in a database according to functional dependencies in [13], but these methods have not yet be utilized for a systematic investigation of the dynamic behavior of a data base.…”

Section: Motivationmentioning

confidence: 99%

“…Relational algebra has been used for decomposing relations in a database according to functional dependencies in [13]; these methods, however, have not yet be utilized for a systematic investigation of the dynamic behavior of a data base.…”

Section: Related Workmentioning

confidence: 99%

ER modelling from first relational principles

Doberkat

Omodeo

2004

Theoretical Computer Science

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Entity-Relationship (ER) modelling is a popular technique for data modelling. Despite its popularity and widespread use, it lacks a firm semantic foundation. We propose a translation of an ER-model into relation algebra, suggesting that this kind of algebra does provide suitable mechanisms for establishing a formal semantics of ER modelling. The work reported on here deals first with the techniques necessary for the translation, thus constructing a static view of an ER-model in an abstract setting of what might be called logic without variables. We then undertake a detailed analysis of the insertion and deletion operations for an ER-model represented in terms of the relation calculus

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“…), a branch of Logic brought to ourish through the work of Ernst Schr oder (see the historical introduction in [1]). Relational algebra has been used for decomposing relations in a database according to functional dependencies in [9], these methods have not yet be utilized for a systematic investigation of the dynamic behavior of a data base. We separate the static structure (the topology) of the ER model from its dynamic counterpart, and we have shown already how to model the static view using relational algebra in a companion paper [11].…”

Section: Introductionmentioning

confidence: 99%