Issue 597: define irreflexivity and asymmetry
Irreflexivity and asymmetry are not defined in the document (under terminology) despite there being properties bearing characterizations "irreflexive" and "asymmetric".
This is a problem, because irreflexivity and nonreflexivity stand for different things (irreflexive: no instance of a property is reflexive vs. nonreflexive: some instances of the property are reflexive and some are not). The same holds for asymmetry and nonsymmetry (asymmetry: no instance of a property is symmetric vs. nonsymmetry: some instances of the property are symmetric and some are not).
The problem was identified by Wolfgang, during the 53rd CIDOC CRM Sig meeting, in the context of issue 561. It was also relevant for issue 517.
In the 53rd CIDOC CRM & 46th FRBRoo SIG meeting, the SIG decided to start a new issue where to discuss the definitions provided for irreflexivity and asymmetry. The definitions should be included in v.7.1.2 and v7.2.1. Their place in the document will be in the "Terminology" section of the introduction.
HW: CEO
May 2022
Post by ChristianEmil Ore (7 September 2022)
The issue is about how to define asymmetric and irreflexive.
Background
Usually the prefix 'non' in a compound negates the main part. So 'nonsymmetric' should have the same meaning as 'not symmetric'.
From Latin the prefix 'in' has a similar function. So irreflexive means 'not reflexive'.
From Greek the prefix 'a/an' has a similar function: asymmetric is a+symmetric (as Ancient Greek ἀσυμμετρία (asummetría), “disproportion, deformity”, wiktionary.org).
This is not very helpful since 'nonsymmetric', 'asymmetric' and 'not symmetric' all have the same general meaning. However, this is not the case for specialized language in a given domain. In set theory the terms 'asymmetric' and 'irreflexive' have a specialized meaning stronger than just 'not ...':
1) A relation R is asymmetric if there are no pair x,y such that x relates to y and at the same time y relates to x. 'less than' (<) is a good example of an irreflexive relation.
2) A relation R is irreflexive if no x is related to itself. 'less than’ (<) is a good example of a asymmetric relation.
In the formal parts of the definition of CRM we use first order logic and follow standard definitions in set theory. In CRM 'P is not reflexive' means that at least one x is not related via P to itself. My suggestion is that we use 'irreflexive' and 'asymmetric' as in common set theory:
A) reflexive: for a property P with domain and range E, P(x,x) for all instances x in E.
B) irreflexive: for a property P with domain and range E, P(x,x) for no instance x in E.
C) nonreflexive/’not reflexive’: For a property P with domain and range E, P(x,x) is not true for one or more instances x in E.
B implies C, so nonreflexive/’not reflexive’ is weaker.
Proposal:
Change from noun to adjective; add two new entries in the term definition list.
asymmetric 
asymmetric is defined in the standard way found in mathematics or logic: A property P is asymmetric if the domain and range are the same class and for all instances x, y of this class the following is the case: If x is related by P to y, then y is not related by P to x. An example of a asymmetric property is E18 Physical Thing. P46 is composed of (forms part of): E18 Physical Thing.

irreflexive 
irreflexive is defined in the standard way found in mathematics or logic: A property P is irreflexive if the domain and range are the same class and for all instances x, of this class the following is the case: x is not related by P to itself. An example of a irreflexive property is E33 Linguistic Object. P73 has translation (is translation of): E33 Linguistic Object.

symmetric

Symmetric A property P is symmetric if the domain and range are the same class and for all instances x, y of this class the following is the case: If x is related by P to y, then y is related by P to x. The intention of a property as described in the scope note will decide whether a property is symmetric or not. An example of a symmetric property is E53 Place. P122 borders with: E53 Place. The names of symmetric properties have no parenthetical form, because reading in the rangetodomain direction is the same as the domaintorange reading. 
reflexive

Reflexive A property P is reflexive if the domain and range are the same class and for all instances x, of this class the following is the case: x is related by P to itself. The intention of a property as described in the scope note will decide whether a property is reflexive or not. An example of a reflexive property is E53 Place. P89 falls within (contains): E53 Place.

Post by Franco Niccolucci (8 September 2022)
Dear ChristianEmile
1) A relation R is asymmetric if there are no pair x,y such that x relates to y and at the same time y relates to x. 'less than' (<) is a good example of an irreflexive relation.
2) A relation R is irreflexive if no x is related to itself. 'less than’ (<) is a good example of a asymmetric relation.
Post by ChristianEmil Ore (13 September 2022)
Dear Franco,
You are quit correct. I swapped irreflexive and asymmetric in the two paragraphs, sorry. It is easy to undo and correct.
P46:
subset and proper subset. It has been discussed several times. The idea is that P46 denotes proper subpart. This is stated implicitly in the scopenote by "This property is asymmetric." However the FOL is wrong.
P46(x,y) ⇒ P46(y,x)
Must be corrected to
P46(x,y) ⇒ ¬P46(y,x)
This is a typo and should be corrected in the current 7.1.2 and 7.2.2 and in the ISO document.
Best,
ChristianEmil
In the 54th CIDOC CRM & 47th FRBR/LRMoo meeting, the SIG decided for the issue to be resolved through an evote. CEO will share the text to be decided on in the following days.
Rome, September 2022
Post by ChristianEmil Ore (14 September 2022)
Dear all,
Yesterday we decided that the issue '597 define irreflexive and asymmetric ' should be reduced to an evote.
The changes is to be inserted in the terminology subchapter of the CIDOC CRM document.
In the text below I have incorporated Franco's concern about proper subsets. The yellow is the new texts and the read should be deleted. In case the colours disappear the word 'symmetry' is replaced by 'symmetric' and 'reflexivity is replaced by 'reflexive', see also
https://docs.google.com/document/d/1yrxtWNn6hfWRg4_IhUdl7lT_nqoxuizTuX_sWLDXGnA
or
https://www.cidoccrm.org/Issue/ID597defineirreflexivityandasymmetry
Please vote YES for accepting these changes, NO for rejection or VOTE if you whish a new discussion in hte next sig meeting
Deadline is 28th September, 2022 (two weeks from now)
Best,
ChristianEmil
There were three positive votes (CEOpersonal communication) for the proposed change (and no objections). It is an editorial issue that minmally influences the CRM as a whole. According to the outcome of the evote, the change has been accepted.
The change will be implemented for CIDOC CRM v7.2.2.
Issue closed