Issue 597: define irreflexivity and asymmetry

ID: 
597
Starting Date: 
2022-05-18
Working Group: 
3
Status: 
Done
Background: 

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 non-reflexivity stand for different things (irreflexive: no instance of a property is reflexive vs. non-reflexive: some instances of the property are reflexive and some are not). The same holds for asymmetry and non-symmetry (asymmetry: no instance of a property is symmetric vs. non-symmetry: 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. 

Current Proposal: 

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 Christian-Emil Ore (7 September 2022)

 

Dear all, 
Please find my hw below and in the attachment. 
 
Best,
Christian-Emil

 

 
 

The issue is about how to define asymmetric and irreflexive.

 

Background

Usually the prefix 'non-' in a compound negates the main part. So 'non-symmetric' 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 'non-symmetric', '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) non-reflexive/’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 non-reflexive/’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

symmetry

Symmetric Symmetry is defined in the standard way found in mathematics or logic:

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 range-to-domain direction is the same as the domain-to-range reading.

reflexive

reflexivity

 

ReflexiveReflexivity is defined in the standard way found in mathematics or logic:

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 Christian-Emile

 
two quick comments.
 
1) In the discursive parts, probably you swapped the examples:
 
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.
 
While both good examples are correct, they are - in my opinion - quoted in the wrong place. I would expect that when defining asymmetric you would mention an asymmetric relation as example;  same for irreflexive.
 
---------------------------------------------------------------------------------------------
 
2) I am not so comfortable with the example in the Definition of Asymmetric, for which you quote P46. I checked the scope note of P46 and it does not clarify if the part is a “proper” part: 
 
"This property associates an instance of E18 Physical Thing with another instance of Physical Thing that forms part of it. The spatial extent of the composing part is included in the spatial extent of the whole.” (from the P46 scope note)
Inclusion (part-ness), in set theory, does not exclude that A is included in A, or in other terms that A is a subset of A (part of A, in common speech),  To quote an authoritative source  wikipedia states the following:
 
In mathematics, set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment). 
 
So either the scope note of P46 should clarify that the part is a “proper” part; or self-inclusion (“self part-ness") is allowed, but then your example of P46 does not work.I would rather go for this second case, but perhaps common sense is for the other one and I am biased by an ancient and long-lasting mathematical infection.
 
Best,
 
Franco
 

Post by Christian-Emil 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,

Christian-Emil

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 Christian-Emil Ore (14 September 2022)

Dear all,

Yesterday we decided that the issue '597 define irreflexive and asymmetric ' should be reduced to an e-vote. 

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.cidoc-crm.org/Issue/ID-597-define-irreflexivity-and-asymmetry

 

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,

Christian-Emil

Outcome: 

There were three positive votes (CEO-personal 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 e-vote, the change has been accepted.

The change will be implemented for CIDOC CRM v7.2.2. 

Issue closed