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A holistic approach to the composition of ternary relations

Hamza Boughambouz, Lemnaouar Zedam (UGent) and Bernard De Baets (UGent)
(2024) COMPUTATIONAL & APPLIED MATHEMATICS. 43(2).
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Abstract
In this paper, we present a systematic approach to the study of the composition of ternary relations from the point of view of the degrees of freedom available when linking a 3-tuple to two given 3-tuples. We propose a way of enumerating all possible 4-point compositions (one degree of freedom) and 5-point compositions (two degrees of freedom) of ternary relations, and establish a correspondence between them. Furthermore, we identify the associative compositions and explore interesting mixed-associativity cases. Finally, we use the tools of projection and cylindrical extension to relate the 4-point and 5-point compositions of ternary relations to the 3-point compositions of binary relations.
Keywords
Ternary relation, Relational composition, Associativity, Mixed-associativity

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MLA
Boughambouz, Hamza, et al. “A Holistic Approach to the Composition of Ternary Relations.” COMPUTATIONAL & APPLIED MATHEMATICS, vol. 43, no. 2, 2024, doi:10.1007/s40314-023-02562-w.
APA
Boughambouz, H., Zedam, L., & De Baets, B. (2024). A holistic approach to the composition of ternary relations. COMPUTATIONAL & APPLIED MATHEMATICS, 43(2). https://doi.org/10.1007/s40314-023-02562-w
Chicago author-date
Boughambouz, Hamza, Lemnaouar Zedam, and Bernard De Baets. 2024. “A Holistic Approach to the Composition of Ternary Relations.” COMPUTATIONAL & APPLIED MATHEMATICS 43 (2). https://doi.org/10.1007/s40314-023-02562-w.
Chicago author-date (all authors)
Boughambouz, Hamza, Lemnaouar Zedam, and Bernard De Baets. 2024. “A Holistic Approach to the Composition of Ternary Relations.” COMPUTATIONAL & APPLIED MATHEMATICS 43 (2). doi:10.1007/s40314-023-02562-w.
Vancouver
1.
Boughambouz H, Zedam L, De Baets B. A holistic approach to the composition of ternary relations. COMPUTATIONAL & APPLIED MATHEMATICS. 2024;43(2).
IEEE
[1]
H. Boughambouz, L. Zedam, and B. De Baets, “A holistic approach to the composition of ternary relations,” COMPUTATIONAL & APPLIED MATHEMATICS, vol. 43, no. 2, 2024.
@article{01HT56904ZZVP6Q33D15WTBQ8G,
  abstract     = {{In this paper, we present a systematic approach to the study of the composition of ternary relations from the point of view of the degrees of freedom available when linking a 3-tuple to two given 3-tuples. We propose a way of enumerating all possible 4-point compositions (one degree of freedom) and 5-point compositions (two degrees of freedom) of ternary relations, and establish a correspondence between them. Furthermore, we identify the associative compositions and explore interesting mixed-associativity cases. Finally, we use the tools of projection and cylindrical extension to relate the 4-point and 5-point compositions of ternary relations to the 3-point compositions of binary relations.}},
  articleno    = {{94}},
  author       = {{Boughambouz, Hamza and Zedam, Lemnaouar and De Baets, Bernard}},
  issn         = {{2238-3603}},
  journal      = {{COMPUTATIONAL & APPLIED MATHEMATICS}},
  keywords     = {{Ternary relation,Relational composition,Associativity,Mixed-associativity}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{23}},
  title        = {{A holistic approach to the composition of ternary relations}},
  url          = {{http://doi.org/10.1007/s40314-023-02562-w}},
  volume       = {{43}},
  year         = {{2024}},
}
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