# Edu:Relation

From IAOA Wiki

## 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*.