William,
Nicely formulated.
The _expression_ of higher arity relations by a collection of binary involvement relations (between the N-ary relation and the various ‘involved things’) has other advantages above its modeling as one higher arity relation.
Its main advantage is that it enables to describe that each role player can change, while it still remains the same relation.
For example, assume that the thing T that is between A and B on path P is moving.
That movement can be described as one (dynamic) higher arity relation.
Modeling this as a higher order relation that has binary relations with involved things, means that there is one (dynamic) higher arity relation that has a number of non-changing binary ‘involvement relations’ with ‘involved things’ and one binary relation that is described by a sequence of relations to describe the movement (e.g. as located in P1 at T1, in P2 at T2, in P3 at T3, etc.).
All occurrences (activities, processes and events) are basically higher arity relations (interactions between things).
The same holds for property value measurements over time.
Regards,
Andries
Van: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] Namens William Frank
Verzonden: woensdag 5 september 2012 15:29
Aan: [ontolog-forum]
Onderwerp: Re: [ontolog-forum] Accommodating legacy software
beautifully said,
would the following be a gloss applied to the between example:
there is a betweeness relation B with respect to the less than relation among integers,
in which integers play three roles: the between integer; the below integer, and the above integer.
and there is an instance of this relation, b, such that in that instance
5 is the below integer in b
11 is the above integer in b.
10 is the between integer in b,
?
On Wed, Sep 5, 2012 at 8:47 AM, Andries van Renssen <andries.vanrenssen@xxxxxxxxxxx> wrote:
Doug and Kingsley,
In any relation (of any arity) the related things play roles of different
kinds that are specific for the kind of relation.
The semantics of the kind of relation depends on the roles that the related
things play in the relation.
An explicit specification of roles is required to define the semantics. This
is independent of the sequence of arguments in an _expression_.
If you don't make those roles explicit, then you have find an alternative,
such as the sequence of the arguments (as in <is between on path>). Their
sequence becomes a pseudo specification of the kinds of roles in the
definition of the meaning of the relation.
Furthermore, the inverse _expression_ has a different sequence of arguments,
and is also a valid _expression_ of the same fact.
Therefore, semantically it is purer to explicitly specify the kinds of
roles.
Therefore, a basic semantic structure for the expressions of facts could be:
* kind of relation - kind of role - related thing
For an n-ary relation you need n such expressions.
The form
* related thing - kind of relation - related thing
is just a short cut for a pair of such expressions, in which the kinds of
roles are assumed to be known from the definition of the kinds of relation.
This short cut is only suitable for binary relations and needs a mechanism
to determine which role is played by the left hand thing and right hand
thing respectively.
A semantic model of the definition of a kind of relation requires even more
detailed relations.
Such a model requires the specification of which kinds of roles are required
by which kind of relation and which kinds of things may play such a role.
This implies expressions such as:
* kind of relation - required played - kind of role
* kind of role - required player - kind of thing
Note that the individual relations and roles are not yet explicit in these
expressions. The basic semantic structures that I developed includes also
the individual roles and relations and allows for the short cut expressions
(see http://www.gellish.net/topics/semantic-modelling.html).
Each of these triples requires the _expression_ of auxiliary facts, such as
their intention (illocutionary force), author, dates, context, etc.
In my view it is therefore not a question whether facts can be expressed in
triples, but whether triples are a suitable structure when we in practice
always model in collections of triples.
The Gellish Data Table is a universal structure for all these kinds of
expressions, including the _expression_ of auxiliary facts. That table is an
alternative to RDF (with some creativity it can be converted into
collections of triples if you like). It is described in the document
"Definition of Universal Semantic Databases and Data Exchange Messages" on
http://www.gellish.net/downloads/category/2-english.html.
Andries
-----Oorspronkelijk bericht-----
Van: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] Namens doug foxvog
Verzonden: woensdag 5 september 2012 6:02
Aan: [ontolog-forum]
Onderwerp: Re: [ontolog-forum] Accommodating legacy software
On Tue, September 4, 2012 17:02, Kingsley Idehen wrote:
> On 9/4/12 3:41 PM, doug foxvog wrote:
>> On Tue, September 4, 2012 12:34, Kingsley Idehen wrote:
...
>>> I believe Data denotes Subject Observation.
>>> I believe all observations are comprised of:
>>> 1. a subject
>>> 2. subject attributes
>>> 3. subject attribute values.
...
>> One common type of observation is that A is between B and C.
>> How would you express this with a single triple? 8)#
> I would state that A is between B. A is Between C. Then I would define
> the semantics of the 'Between' predicate .
!??
Let's explore this:
(and
(between 10 5 11)
(between 10 4 11)
(between 10 6 11)
(between 10 7 11))
Using the KI translator this becomes:
AND
10 is between 5
10 is between 11
10 is between 4
10 is between 11
10 is between 6
10 is between 11
10 is between 7
10 is between 11.
What semantics does the between predicate have?
How about the quaternary predicate, isBetweenOnPath?
Can you express the following with triples:
(and
(isBetweenOnPath WashingtonDC Maryland Virginia I95)
(not (isBetweenOnPath WashingtonDC Maryland Virginia I495)))
-- doug foxvog
...
>
> Kingsley
>>
>> -- doug foxvog
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