Gian, The (my) purpose is to come to a universal data structure that can be used for (nearly) all databases and enables unambiguous interpretation. In my opinion higher order expressions have the disadvantage that, if you express them in tabular form, then you arrive at an endless number of different kinds of tables, each with its own definition. That will be difficult to generalize and interpret. Thus you have to keep them in parameterized form, with auxiliary facts (or meta data if you like) for every relation and allowing for variable numbers of parameters and parameter values for different instances. I understand that that is rather difficult to implement. Binary expressions allow for one uniform table, and auxiliary facts (or meta data if you like) for every binary relation, arranged in multiple tables of identical structure. I think that the latter has more advantages. Andries Van: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] Namens Gian Piero Zarri
Verzonden: donderdag 6 september 2012 16:31
Aan: [ontolog-forum]
CC: Gian Piero Zarri
Onderwerp: Re: [ontolog-forum] Accommodating legacy software On 06/09/2012 15:28, William Frank wrote: But more generally, an n-ary relation instance is always expressable as n independent role assertions.
For example:
George gave the book to Mary.
There is an instance g of the giving action G. and
In g, George played the role of giver, the book played the role of given, and Mary played the role of reciever.
Yes, and this is simply expressed in NKRL - an n-ary representation language, see http://www.springer.com/computer/ai/book/978-1-84800-077-3 - as a "predicative occurrence" (instance of a standard NKRL template) like:
MOVE
SUBJ GEORGE_
OBJ BOOK_1
BENF MARY_
date-1: 2012-09-06-16:30
date-2:
BENF = BEN(e)F(iciary) role. Why always reinvent the wheel?
Regards,
Gian Piero ZARRI
Now, just because one CAN reduce n-aries to binaries, this does not mean it is a good thing to do, except to acheive a specific purpose. The lack of attention to purposes seems to me to be the biggest problem with "modern" logical education. Leads to unsaid ssumptions.
-- doug foxvog
> 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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