Difference between revisions of "Edu:Relation"

From IAOA Wiki
(Created page with " == Relation== ''Disambiguation'': the term as used in the literature can refer to either one of the following, depending on the context: * Instance-level Edu:entity|entit...")
 
(Moved first three entries from 'Discussion' page to main 'Relation' page.)
 
(One intermediate revision by the same user not shown)
Line 2: Line 2:
 
== Relation==
 
== Relation==
  
 
+
''Disambiguation'': The term 'Relation' as used in the literature may refer to one of the following, depending on the context:
''Disambiguation'': the term as used in the literature can refer to either one of the following, depending on the context:
 
 
* Instance-level [[Edu:entity|entity]]
 
* Instance-level [[Edu:entity|entity]]
 
* Type-level [[Edu:entity|entity]], used interchangeably with, mainly, relationship (e.g., in Entity-Relationship diagrams), association (UML class diagrams), and object property (in OWL)
 
* Type-level [[Edu:entity|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 [[Edu:Logic | logic]]  
 
* Its definitions in mathematics, notably [[Edu:Logic | logic]]  
 
 
=== Definitions===
 
  
  
Line 19: Line 15:
  
  
==== Definition Variants====
+
=== 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. ( [[Edu:TermlistReferences#MacBride2016 | MacBride, 2016]] ])
 +
 
 +
:3. [BFO2.0] The manner in which two or more [[Edu:entity | entities]] are associated or connected together. [[Edu:Basic Formal Ontology - BFO | BFO]] recognizes three basic types of relation: connecting [[Edu:universal|universal]] to [[Edu:universal|universal]], [[Edu:universal|universal]] to [[Edu:particular|particular]], and [[Edu:particular|particular]] to [[Edu:particular|particular]]. ([ [[Edu:TermlistReferences#arpetal2015|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''. ([ [[Edu:TermlistReferences#Chen1976 | Chen, 1976]] ])
  
  
'''V1''' [ [[Edu:TermlistReferences#MacBride2016 | MacBride, 2016]] ]
+
''' Commentary '''
* 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.
+
* 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)
 +
* [[Edu:Predicate|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.
  
'''V2''' [ [[Edu:TermlistReferences#Chen1976 | Chen, 1976]] ]
 
*  A relationship set, ''R'', is a mathematical relation among ''n'' entities, each taken from an entity set: {(e1, e2, ..., en) | e1 &isin; E1, e2 &isin; E2, ..., en &isin; En}, and each tuple of entities, (e1, e2, ..., en), is a ''relationship''.
 
  
'''V3''' [ [[Edu:TermlistReferences#arpetal2015|Arp et al., 2015]] ]
 
*  The manner in which two or more [[Edu:entity | entities]] are associated or connected together. [[Edu:Basic Formal Ontology - BFO | BFO]] recognizes three basic types of relation: connecting [[Edu:universal|universal]] to [[Edu:universal|universal]], [[Edu:universal|universal]] to [[Edu:particular|particular]], and [[Edu:particular|particular]] to [[Edu:particular|particular]].
 
  
==== Closely related terms====
+
''' Closely Related Terms '''
  
 
* Domain and range/codomain, also called, more generally, relata
 
* Domain and range/codomain, also called, more generally, relata

Latest revision as of 18:41, 20 January 2020

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)

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


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.