Re: [Crm-sig] Issue 407: Ordinal Property for E55 Type

[Martin Doerr]

On 6/11/2019 7:15 PM, Simon Spero wrote:
On Tue, Jun 11, 2019, 11:21 AM Martin Doerr > wrote:


Detail: from a maths point of view, partial ordering may be
allowed for: I.e.: not all value pairs can  be compared with
respect to the order relation. This happens in spaces with more
than one dimension, but does not affect transitivity. Any math
freak here to confirm?;-)


A partial order defined by < is transitive, irreflexive, and 
asymmetric (≤ is transitive, reflexive, and antisymmetric).


Also, there can be total orders on multi-dimensional spaces - e.g. 
museums ordered by distance from Bloomsbury, and partial orders on a 
single dimension - e.g. (proper) part-of on physical objects.


Simon


Some questions:

What about "If a ≤ b {\displaystyle a\leq b} a\leq b and b ≤ a 
{\displaystyle b\leq a} {\displaystyle b\leq a} then a = b 
{\displaystyle a=b} a=b;" if there are two museums at the same distance 
from Bloomsbury?


Why should "part-of" be one-dimensional? Do you have details?

Best,

Martin


--

 Dr. Martin Doerr

 Honorary Head of the
 Center for Cultural Informatics

 Information Systems Laboratory
 Institute of Computer Science
 Foundation for Research and Technology - Hellas (FORTH)

 N.Plastira 100, Vassilika Vouton,
 GR70013 Heraklion,Crete,Greece

 Vox:+30(2810)391625
 Email: mar...@ics.forth.gr
 Web-site: http://www.ics.forth.gr/isl

Re: [Crm-sig] Issue 407: Ordinal Property for E55 Type

[Simon Spero]

On Tue, Jun 11, 2019, 11:21 AM Martin Doerr  wrote:

Detail: from a maths point of view, partial ordering may be allowed for:
> I.e.: not all value pairs can  be compared with respect to the order
> relation. This happens in spaces with more than one dimension, but does not
> affect transitivity. Any math freak here to confirm?;-)
>

A partial order defined by < is transitive, irreflexive, and asymmetric (≤
is transitive, reflexive, and antisymmetric).

Also, there can be total orders on  multi-dimensional spaces - e.g. museums
ordered by distance from Bloomsbury, and partial orders on a single
dimension - e.g. (proper) part-of on physical objects.

Simon

>

Re: [Crm-sig] Issue 407: Ordinal Property for E55 Type

[Martin Doerr]

I agree.

Detail: from a maths point of view, partial ordering may be allowed for: 
I.e.: not all value pairs can  be compared with respect to the order 
relation. This happens in spaces with more than one dimension, but does 
not affect transitivity. Any math freak here to confirm?;-)


Martin

On 6/11/2019 12:43 PM, Robert Sanderson wrote:


Homework assigned to me to add a notion of concept schemes / context 
to the scope note.  Agreement at Paris SIG that this could go into 
CRMsci and thus “Oxx is conceptually greater than”


Proposed modification to the scope note:

This property allows an instance of E55 Type from a particular concept 
scheme or vocabulary to be declared as having an order relative to 
other instances of E55 Type in the same or other concept schemes, 
without necessarily having a specific value associated with either 
instance.  This allows, for example, for an E55 Type instance 
representing the concept of "good" in a conservation report vocabulary 
to be greater than the E55 Type instance representing the concept of 
"average" in the same vocabulary. This property is transitive, and 
thus if "average" is greater than "poor", then "good" is also greater 
than "poor". In the domain of statistics, types that participate in 
this kind of relationship are called "Ordinal Variables"; as opposed 
to those without order which are called "Nominal Variables". This 
property allows for queries that select based on the relative position 
of participating E55 Types.


Let me know if that does not fulfil the HW assignment ☺

Rob

*From: *Crm-sig  on behalf of Stephen 
Stead 

*Organization: *Paveprime Ltd
*Reply-To: *"ste...@paveprime.com" 
*Date: *Thursday, January 3, 2019 at 6:49 AM
*To: *'crm-sig' 
*Subject: *[Crm-sig] **NEW ISSUE** Ordinal Property for E55 Type

During the discussions at the CRM-SIG meeting during November 2018 in 
Berlin the problem of dealing with instances E55 Type that have 
ordinal relationships with other instances of E55 Type came up. There 
were a number of use cases explored including:-


  * Condition report status values like Excellent, Good, Average,
Poor, Critical where being able to query for all items that were
below “Average” or “Good” and above would be useful.
  * Map scales expressed as types
  * Fire Hazard Ratings

This lead Robert and I to suggest that a new property be created that 
allowed this kind of ordinal relationship to be expressed. The 
quantification allows for parallel hierarchies, e.g. if someone has a 
type that is “slightly better than average but not quite good”, then 
they could align that with an existing hierarchy of Good > Average by 
saying that it is greater than “Average” and that “Good” is greater 
than both it and Average.



  Pxx is conceptually greater than (is conceptually less than)

Domain: E55 Type

Range: E55 Type

Quantification: many to many (0,n:0,n)

This property allows instances of E55 Type to be declared as having an 
order relative to other instances of E55 Type, without necessarily 
having a specific value associated with either instance.  This allows, 
for example, for an E55 Type instance representing the concept of 
"good" to be greater than the E55 Type instance representing the 
concept of "average". This property is transitive, and thus if 
"average" is greater than "poor", then "good" is also greater than 
"poor". In the domain of statistics, types that participate in this 
kind of relationship are called "Ordinal Variables"; as opposed to 
those without order which are called "Nominal Variables". This 
property allows for queries that select based on the relative position 
of participating E55 Types.


Examples:

  * Good (E55)/is conceptually greater than/ Average (E55)

  * Map Scale 1:1 (E55) /is conceptually greater than/ Map Scale 
1:2 (E55)


  * Fire Hazard Rating 4 (E55)/is conceptually greater than/ Fire 
Hazard Rating 3 (E55)


Comments Welcome

SdS & Robert S


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--

 Dr. Martin Doerr

 Honorary Head of the
 Center for Cultural Informatics

 Information Systems Laboratory
 Institute of Computer Science
 Foundation for Research and Technology - Hellas (FORTH)

 N.Plastira 100, Vassilika Vouton,
 GR70013 Heraklion,Crete,Greece

 Vox:+30(2810)391625
 Email: mar...@ics.forth.gr
 Web-site: http://www.ics.forth.gr/isl

[Crm-sig] Issue 407: Ordinal Property for E55 Type

[Robert Sanderson]

Homework assigned to me to add a notion of concept schemes / context to the 
scope note.  Agreement at Paris SIG that this could go into CRMsci and thus 
“Oxx is conceptually greater than”

Proposed modification to the scope note:

This property allows an instance of E55 Type from a particular concept scheme 
or vocabulary to be declared as having an order relative to other instances of 
E55 Type in the same or other concept schemes, without necessarily having a 
specific value associated with either instance.  This allows, for example, for 
an E55 Type instance representing the concept of "good" in a conservation 
report vocabulary to be greater than the E55 Type instance representing the 
concept of "average" in the same vocabulary. This property is transitive, and 
thus if "average" is greater than "poor", then "good" is also greater than 
"poor". In the domain of statistics, types that participate in this kind of 
relationship are called "Ordinal Variables"; as opposed to those without order 
which are called "Nominal Variables". This property allows for queries that 
select based on the relative position of participating E55 Types.


Let me know if that does not fulfil the HW assignment ☺

Rob


From: Crm-sig  on behalf of Stephen Stead 

Organization: Paveprime Ltd
Reply-To: "ste...@paveprime.com" 
Date: Thursday, January 3, 2019 at 6:49 AM
To: 'crm-sig' 
Subject: [Crm-sig] **NEW ISSUE** Ordinal Property for E55 Type

During the discussions at the CRM-SIG meeting during November 2018 in Berlin 
the problem of dealing with instances E55 Type that have ordinal relationships 
with other instances of E55 Type came up. There were a number of use cases 
explored including:-

  *   Condition report status values like Excellent, Good, Average, Poor, 
Critical where being able to query for all items that were below “Average” or 
“Good” and above would be useful.
  *   Map scales expressed as types
  *   Fire Hazard Ratings
This lead Robert and I to suggest that a new property be created that allowed 
this kind of ordinal relationship to be expressed. The quantification allows 
for parallel hierarchies, e.g. if someone has a type that is “slightly better 
than average but not quite good”, then they could align that with an existing 
hierarchy of Good > Average by saying that it is greater than “Average” and 
that “Good” is greater than both it and Average.

Pxx is conceptually greater than (is conceptually less than)
Domain: E55 Type
Range: E55 Type
Quantification: many to many (0,n:0,n)

This property allows instances of E55 Type to be declared as having an order 
relative to other instances of E55 Type, without necessarily having a specific 
value associated with either instance.  This allows, for example, for an E55 
Type instance representing the concept of "good" to be greater than the E55 
Type instance representing the concept of "average". This property is 
transitive, and thus if "average" is greater than "poor", then "good" is also 
greater than "poor". In the domain of statistics, types that participate in 
this kind of relationship are called "Ordinal Variables"; as opposed to those 
without order which are called "Nominal Variables". This property allows for 
queries that select based on the relative position of participating E55 Types.

Examples:
  * Good (E55) is conceptually greater than Average (E55)
  * Map Scale 1:1 (E55) is conceptually greater than Map Scale 1:2 (E55)
  * Fire Hazard Rating 4 (E55) is conceptually greater than Fire Hazard Rating 
3 (E55)

Comments Welcome
SdS & Robert S