On Thu, Sep 6, 2012 at 6:40 AM, Andries van Renssen <andries.vanrenssen@xxxxxxxxxxx> wrote:
William,
Nicely formulated.
The _expression_ of higher arity relations by a collection of binary involvement relations (between the Nary 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 nonchanging 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).
This is quite cool. As to me a simpler example, I imagine a soccer
game. There is a soccer game, with these players playing these roles.
Later on, the same game, different players.
The same holds for property value measurements over time.
Would be interested to understand this.
Regards,
Andries
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 nary 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/semanticmodelling.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/2english.html.
Andries
Oorspronkelijk bericht Van: ontologforumbounces@xxxxxxxxxxxxxxxx [mailto:ontologforumbounces@xxxxxxxxxxxxxxxx] Namens doug foxvog
Verzonden: woensdag 5 september 2012 6:02 Aan: [ontologforum] Onderwerp: Re: [ontologforum] Accommodating legacy software
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