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Re: [ontolog-forum] Accommodating legacy software

To: doug@xxxxxxxxxx, "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: William Frank <williamf.frank@xxxxxxxxx>
Date: Thu, 6 Sep 2012 09:28:37 -0400
Message-id: <CALuUwtAoKO=8Ex6DWuOUgmXeYRm=nGt+WpOswzBkKOopmkuWLA@xxxxxxxxxxxxxx>


On Thu, Sep 6, 2012 at 1:08 AM, doug foxvog <doug@xxxxxxxxxx> wrote:
On Wed, September 5, 2012 09:29, William Frank wrote:

> would the following be a gloss applied to the between example:

> 1. there is a betweeness relation B with respect to the less than relation
> among integers,

This is valid for the example using integers because there exists an
absolute ordering relation on integers that applies to the examples i gave.

Yes, and the key thing is, that there is a binary relationship in the assertion, restating 1 so that it bones show:

exists relation B
withRespectTo relation LT. 

where the withRespectTo binary relation means "can be defined in terms of".

> in which integers play three roles:
 
the between integer;
the below
> integer,
> and the above integer.

This assumes that the second argument must be the below integer
and the third argument the above integer.  

it does not "assume it", it will be directly asserted  as the parse of your examples, when we get to the final unpacking of this.

If i gave the example:
  (and
    (between 10 5 11)
    (between 10 11 9) )
this mapping would not apply.

Yes, Of course not.   One of Andris van Ressenn's many points is that positional notations have an undesireable implicit semantics, in which position plays a hidden role as indicator of the role in the relation.  Thus, when you make the roles explicit, and make separate assertions about each role played, you get a set of assertions, as all sets should be, that are order independent.
 

> 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,

> ?

Yes, this gloss is a valid way for expressing in 4 triples what i
expressed in one quad.

Actually, none of these are triples. They are all binary relations.

For example, 

5 isTheBelowIntegerIn b

Where the first relation I chose to use is

isTheBelowIntegerIn b

 I have used in fact only binary relations, but rather quite many of them.

First of all, the binary relation

withRespectTo

then, for each of the three roles R, there is the use of the binary relation

R isAroleIn B

where B, again, was the betweeness relation.

This sets of the definition of type B, through the use of 4 relations,

Then, with all of this set up, we assert the existence of b, an instance of the type B.

and we need the addition of the three independent assertions of what roles what integers play in b.


all quantificationally bound to be, so that we have:

for the relation instance b,

{

(5 isTheBelowIntegerIn b)

and

etc.

}

:

If i gave an example without a pre-existing default ordering
relation, e.g. with spatial betweeness, i'm not sure how you
would identify two different roles for arguments 2 and 3:

Well, first of all,

if you don't SAY what kind of betweeness you are talking about, there is simply MORE that the reader must discern with his mind, what kind of betweeness you had in mind. 

Second,
all betweenenss relations are based on SOME partial order or spacing,   The example I gave used an ordering on integers. 

(between GoldenGateBridge SanFranciscoBay PacificOcean)


but you can now construct your own examples following the standard pattern for reducing n-nary relations to a set of binary relations among roles in a higher order logic.

For example, there is a geographical  betweeness relation GB, with respect to locations on the globe, with three roles yada yada 

but here, we might want to define what everyone intuits,

that the defintion of SB is that

a plays the bottom role in SB
b plays the middle role in SB
c plays he top role in SB

if and only if

the great circle distance between a and c is greater that the distance between a and b and the distance betwen b and c, and the great circle displacement of b from the great circle between a and c is less that the the distance between a and c.



Betweenness could be non-spatial as well:

Absolutely, betweeness depends on a partial order relationship of any kind.  For example, is the child of.  between in a line for musical chairs, between in class rankiing at harvard law. you name it.

(between ModeratePoliticalPhilosophy ConservativePoliticalPhilosophy
              ProgressivePoliticalPhilosophy)

Again, assigning two different roles to arguments 2 and 3
is problematic.


I do not see why.  Needs a slow, careful, thinking cap.   That cap has to help one discern what the underling partial order is, and the further underlying metric on which that order is based, and Bob's your uncle. 


Here, we have a degree of difference between views.  Fits the bridge example quite well.


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.


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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