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

Martin Doerr martin at ics.forth.gr
Tue Jun 11 21:33:15 EEST 2019


On 6/11/2019 7:15 PM, Simon Spero wrote:
> On Tue, Jun 11, 2019, 11:21 AM Martin Doerr <martin at ics.forth.gr 
> <mailto:martin at ics.forth.gr>> 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


-- 
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  Dr. Martin Doerr
               
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