On Thu, September 6, 2012 15:44, Andries van Renssen wrote:
> Doug,
> Your statement that occurrences cannot be higher arity relations, because
> they are first class objects implies that you see an opposition between
> 'first class' objects and occurrences.
> I don't know what 'first class objects' are, and I don't see why higher
> arity relations cannot be first class objects. (01)
I guess we have different understanding of what is meant by "relation".
I was taking you to be using two definitions (as many in this forum do):
* A predicate or function, which when applied to a set of values returns
a truth value.
* A logical statement made using such a predicate/truth function.
To make the distinction, i'll call the second meaning a relation instance. (02)
I agree that an ontology can treat anything it desires as a "first class
object" -- something that it can make statements about by including
it as an argument to a predicate or function. (03)
My objection to equating occurrences to relation instances is that
i take the meaning of a relation instance to be fully implied by the
relation itself plus its arguments. I take any statement about an
actual occurrence to, in the vast majority of cases, only partially
describe the occurrence. Many additional statements may be made
about the same occurrence -- statements that are not implied by
the first statement. (04)
> Nijssen introduced the
> concept 'objectified relations' for such a thing. They are relations and
> they are 'objects in their own right'. Relations with relations should not
> be forbidden. (05)
Agreed. (06)
> Indeed, other relations can express facts about occurrences (that is what
> e.g. binary involvement relations do). (07)
> You also ask:
>> why not just define classes of occurrences, and reify any individual
> occurrence that is to be referenced? (08)
> I agree, that should be done. Subtypes of 'occurrence' are all kinds of
> activities, processes and events.... Any individual occurrence should be
> classified
> by a such a kind of occurrence, when it is used in a formal language.
> Then its involvement relations of various kinds (such as <has as input>,
> <has as performer>, etc.) specify the various roles of the involved things
> in the occurrence. (09)
Agreed. (010)
> I am not aware of examples of problematic examples of extremely
> high arity relations that are objects in their own right. (011)
My meaning is that they can not fully describe an occurrence. (012)
> By the way, also most correlations and states are higher order relations
> (that are objects in their own right).
> Do you also disagree with that? (013)
I understand these to have facets that are expressible by higher order
relations. I would not consider them to be either predicates or
statements made using predicates. (014)
Again, i think calling them "relations" is a language issue. Perhaps there
is a word in Dutch that has one meaning that covers statements (and
predicates?) and the state of affairs referred to in the statement. (015)
-- doug foxvog (016)
> Thanks for the fruitful discussions up to now,
> After today I will be on holidays for two weeks.
> Thus, during that 'occurrence' I will not reply.
>
> With kind regards,
> Andries
>
>> -----Oorspronkelijk bericht-----
>> Van: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
>> bounces@xxxxxxxxxxxxxxxx] Namens doug foxvog
>> Verzonden: donderdag 6 september 2012 18:35
>> Aan: [ontolog-forum]
>> Onderwerp: Re: [ontolog-forum] Binary versus N-ary relations
>>
>> On Thu, September 6, 2012 06:40, Andries van Renssen wrote:
>> > ...
>> > 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.
>>
>> Can it? You have described features of the object M (a movement);
>> (isa M Movement-TranslationEvent)
>> (primaryObjectMoving M T)
>> (movementConstrainedTo M P)
>> (holdsDuring M (betweenOnPath T A B P))
>> ; ... if you mean that A & B are on the path.
>> ; If A and B are on alternate sides of the path, e.g., P is
>> ; a north-south alley with building A to its west and building B
>> ; to its east:
>> (holdsDuring M (between P A B))
>> M would have many other features.
>>
>> > 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.).
>>
>> If the instantiated (dynamic) higher arity relation (DHAR) has
>> a number of relations to other things (be they binary or
>> higher-arity themselves), it suggests to me) that it is an object
>> in its own right. Instead of making it an extremely high arity
>> relation (with thousands of arguments for any possible relation
>> that the event could have with other things) why not just define
>> classes of occurrences, and reify any individual occurrence that
>> is to be referenced?
>>
>> > All occurrences (activities, processes and events) are basically
>> higher
>> > arity relations (interactions between things).
>>
>> I would disagree. Occurrences are first class objects. Higher (or
>> not)
>> arity relations can describe aspects of such occurrences.
>>
>> -- doug
>>
>> > 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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>> >
>> > --
>> > William Frank
>> >
>> > 413/376-8167
>> >
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