Edu:Relation

Relation

Disambiguation: The term 'Relation' as used in the literature may refer to one of the following, depending on the context:

• Instance-level entity
• Type-level entity, used interchangeably with, mainly, relationship (e.g., in Entity-Relationship diagrams), association (UML class diagrams), and object property (in OWL)
• Its definitions in mathematics, notably logic

D1 (as instance-level entity)

• A relation is an entity that asserts a (meaningful) connection between two or more other entities, where the entities are individuals, such as objects, processes, or qualities.

D2 (as type-level entity)

• A relation is an entity that asserts a (meaningful) connection between two or more other entities, where the entities are generally denoted with class/ concept/ universal.

Definitions

1. [Natural Language] The way in which two or more people or things are connected. (https://www.lexico.com/definition/relation)

2. Relations hold between things, or, alternatively, relations are borne by one thing to other things, or, another alternative paraphrase, relations have a subject of inherence whose relations they are and termini to which they relate the subject. ( MacBride, 2016 ])

3. [BFO2.0] The manner in which two or more entities are associated or connected together. BFO recognizes three basic types of relation: connecting universal to universal, universal to particular, and particular to particular. ([ Arp et al., 2015 ])

3. A relationship set, R, is a mathematical relation among n entities, each taken from an entity set: {(e1, e2, ..., en) | e1 ∈ E1, e2 ∈ E2, ..., en ∈ En}, and each tuple of entities, (e1, e2, ..., en), is a relationship. ([ Chen, 1976 ])

Commentary

• Guarino and Guizzardi have presented a view that a 'relationship' and 'relation' are different, " ... a relation holds in virtue of a relationship's existence. Relationships are therefore truthmakers of relations." (https://www.academia.edu/28108703/Relationships_and_Events_Towards_a_General_Theory_of_Reification_and_Truthmaking and https://www.academia.edu/11814659/_We_need_to_discuss_the_Relationship_Revisiting_Relationships_as_Modeling_Constructs)
• Predicate is also used in relation to relation, but that covers either sense as well, and it can be unary (which a relation cannot be).
• Relation has a specific meaning in relational database theory, it being a set of tuples (d1, d2, ..., dn) where each dj (with 1 <= j <= n) is a member of data domain Dj. (reference: any database text book)
• If one takes the mathematics definition of relation, then also functions and attributes are relations.

Closely Related Terms

• Domain and range/codomain, also called, more generally, relata
• Relational properties / property characteristics
• The entities mentioned in the definitions above may be one and the same; if that is the case, then that relation is called a recursive relation.