SUO: RE: Re: Expostulation
Dear Jon,
> ¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
>
> Matthew,
>
> It has begun to occur to me over the last few days that
> the difference between our prespectives -- "prespective"?
> hmm, that was a genuine typo, but prehaps it will turn out
> to have a meaning that is telling in the present application --
> arises more than anything else from divergent ways of seeing
> the use of "formal or logical or mathematical" (FOLOM) models.
> I am going to think about this a little more and maybe try to
> write out a separate comment about it, but it takes us back to
> a couple of pictures that we have seen here before, to a whole
> array of issues that I myself have been thinking about for quite
> some time, and over all to a problematic that is rather ancient --
> Immanuel Kant's use of what he called "schemata" as intermediate
> representations between realities and the mind is the first thing
> that comes to mind, but I am sure that the topic goes back further
> than that -- anyway, here are links to a few of the occasions that
> I can find on which we broached this subject locally and recently:
>
> http://suo.ieee.org/email/msg00657.html
> http://suo.ieee.org/email/msg00671.html
> http://suo.ieee.org/email/msg00676.html
> http://suo.ieee.org/email/msg01251.html
> http://suo.ieee.org/email/msg01293.html
> http://suo.ieee.org/email/msg01350.html
> http://suo.ieee.org/email/msg01772.html
> http://suo.ieee.org/email/msg01969.html
> http://suo.ieee.org/email/msg01973.html
> http://suo.ieee.org/email/msg02005.html
> http://suo.ieee.org/email/msg02123.html
>
> http://www.bestweb.net/~sowa/ontology/
> http://www.bestweb.net/~sowa/ontology/gloss.htm
> http://www.bestweb.net/~sowa/ontology/causal.htm
> http://www.bestweb.net/~sowa/ontology/mthworld.gif
>
> As I tried to follow this thread, it turned out to be
> a lot more tangled than I thought, going in, it would be.
> Since the fine old philosophical concept of "reification"
> seems to be yet another one of those ideas that will soon
> be rendered meaningless by the cargo cultists of the world,
MW: I don't understand this remark.
> if not by the flushed enthusiasts of the WW-WC,
MW: WW-WC is??
> if you catch
> my drift, I have tossed in a number of classical references
> to the vast and now distant ocean of good sense, of which
> our own humankind was long ago the master on this score,
> to wit, the associated ideas of abstraction and analogy
> that go into our once-evolved crafts of hypostasis and
> modeling, in other words, reification and simulation,
> as I knew them, once, to be in their glory days --
> alas! those days are now gone and quite forgotten.
> But I nostalgicize ...
>
> More specific remarks interspersed below,
>
> Jon Awbrey
>
> ¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
>
> Matthew West wrote:
> >
> > Dear Jon,
> >
> > I've read ahead a number of messages,
> > and this is a summary of where I am
> > at present.
> >
> > In what you say below it seems that you are using
> > a different definition of what a relation and tuple
> > is to me (at least).
>
> I have been suspecting this for quite some time now, but
> you have insisted on repeating the standard definition of
> a relation as a set of tuples, even though you rarely ever
> use this defintion when it comes down to cases.
MW: This is not what I meant. I may make mistakes sometimes
(sloppiness) but I really do mean a relation is set of tuples.
>
> > To you it seems that any construct ...
>
> I think that we may have to pause at this point and discuss
> what is meant by "construct", no doubt as used within various
> dialects, and if we fail to find a common meaning then we may
> need to look for a way to disptch the word without portfolio.
MW: (data) Construct, an assemblage used to represent something,
e.g. a relation, a tuple, a constant, a variable, a set,
a predicate.
>
> > To you it seems that any construct
> > that has to involve at least three
> > things to be valid is necessarily
> > a 3-adic relation.
>
> I try to take you at your word, but I honestly never know for sure
> when you are using the word "relation" to mean "relation" and when
> you are using the word "relation" to mean "relation instance", as
> seems to be required to make sense of what you go on to predicate.
>
> If I try to read this straightforwardly,
> I must amend it to read a bit like this:
>
> | To you it seems that any construct
> | that has to involve at least three
> | things to be valid is necessarily
> | [a (>= 3)-adic relation instance].
>
> Can you clarify for me what you mean in this instance?
I was thinking at the set level, like Chris M's signature, e.g.
gives involves a giver, a receiver, and a given.
>
> In order to continue without going totally bats,
> I will have to substitute in your text below,
> in square brackets, the changes that I need
> to make sense of what you say. Please let
> me know if these are not agreeable to you.
>
> > The problem with this is that a 3-adic relation [instance]
> > requires EXACTLY 3 components, not at least 3 components,
> > and that these three components are necessary for identity.
>
> I do not know what the last clause, about identity, means here.
MW: That without all 3 elements, in this representation form,
you cannot identify the object uniquely.
>
> > Relatively few things [relation instances?] in real life meet
> > the criterion of exactly 3 components, and though I agree that
> > the example you have used of logical operators is one of them,
> > activities [activity instances?]
MW: My sloppiness, I should have said activity classes.
> generally are not.
>
> You must try to remember whose team you are on --
> it is not my fault that you keep throwing me all
> of these interceptions! My team is the one that
> keeps on saying that there are things in reality,
> the activities of communicating, giving, learning,
> and thinking, just to name a few, whose inherent
> complexities -- the full measure of which no doubt
> goes beyond our meagre mortal abilities to render
> effable, effectively describabel, f-able, or even
> formalizable at all -- are such that they require
> relational models whose arity is at least three
> in order to represent them with anything like
> the requisite adequacy.
MW: Actually I am arguing that many 3-adic relations (or
higher) are inadequate for modelling these situations
adequately. This is because 3+adic relations imply
constraints that are just no true of the wolrd in many
cases, particularly in the cases of the examples given
above. I am also arguing that even for those where a
3-adic relation is valid, as in your logic example, it
is possible to replace it with a set of binary relations
that convey the same information.
> Your team is the one
> that keeps on saying that it just ain't so,
> that anything that can be talked to death
> can be talked to death, without loss of
> adequate descriptive power, solely in
> the reduced medium of 2-adic relations.
> Every now and then, you appear to want
> to switch sides, and yet without having
> your move be counted a foul of the game
> in play, as if to say that references to
> realities more complex than 3-adic should
> count on the side of 2-adic reductionists.
> I do not understand this sort of thinking.
MW: Perhaps because I (my team) is trying to discover
the truth rather than argue a point. Further, I assume
that there is something in what you say, and I would
prefer to understand what it is, rather than just dismiss
it because I don't understand.
>
> > However, even with logical operators it is possible
> > to represent these without using 3-adic relations, ...
>
> No, it is not.
MW: T'is so :-o) (sticks tongue out)
>
> > although I agree that this does not remove
> > the three-ness of what is represented.
>
> ???
MW: I am quite happy that in a "giving" that ontologically
there are necessarily at least 3 things involved, at least
one giver, at least one given and at least one receiver.
However, I do not agree that there is at most one giver,
at most one receiver and at most one given, and this is what
is implied by a 3-adic relation.
>
> > I have demonstrated this.
>
> No, you have not.
MW: Then you have to explain what is wrong (and don't give
me stuff about (and a b c d) since this can easily be
replaced, and is strictly not necessary anyway, since the
simple set of relations - since they are enumerated -
is all that is required.
>
> > You claim (elsewhere) that I have only presented tuples,
> > but in fact I have presented fully enumerated relations.
>
> And by this "enumerated" to say that you changed the subject from
> a 3-adic relation to a 4-adic relation. "Changing the subject"
> appears to be the solecism of choice in regard to this matter.
MW: What do you mean here by "changed the subject"?
MW: My interpretation is "changed the identifier". In your
3-adic relation, all 3 elements are needed in order to identify
any particular row. I have started by adding a "row id" which
alone is capable of representing the same object. This is quite
a legitimate move, even when it isn't necessary.
>
> > Finally, there is still the issue of your claim that things
> > can be reduced to triads. You have however singularly failed
> > to provide the solution to this for the measurement example I
> > presented for those who think this can always be done without
> > violating the constraints that you wish to impose on others as
> > to what adacity is.
MW: I note the continued failure to respond to this.
> >
> > I'm going to write two brief papers:
> >
> > 1. The transformation of a ternary relation into
> > some set of binary relations (and vice versa)
> >
> > 2. The use of relations to represent the world about us,
> > practice and limitations.
> >
> > These should at least put in one place where I stand currently.
> >
> > Regards
> > Matthew
> >
> > > -----Original Message-----
> > > From: Jon Awbrey [mailto:jawbrey@oakland.edu]
> > > Sent: 25 April 2001 07:30
> > > To: West, Matthew MR SSI-GREA-UK
> > > Cc: Frederick N. Chase; Chris Menzel;
> > > IEEE Standard Upper Ontology List
> > > Subj: SUO: Re: Expostulation
> > >
> > > Matthew West wrote:
> > > >
> > > > Dear Fred,
> > > >
> > > > > Chris Menzel wrote:
> > > > > >
> > > > > > <snip>
> > > > > > ..............................
> > > > > >
> > > > > > Of course, I think what you *really* want is
> > > > > > the purely generalized form of this axiom,
> > > > > > of which the above is just an instance:
> > > > > >
> > > > > > (forall (?x ?y ?z)
> > > > > > (<=> (gives ?x ?y ?z)
> > > > > > (exists (?e)
> > > > > > (and (giving ?e)
> > > > > > (giver ?e ?x)
> > > > > > (receiver ?e ?y)
> > > > > > (given ?e ?z)
> > > > > > (forall (?e')
> > > > > > (=> (and (giving ?e')
> > > > > > (giver ?e' ?x)
> > > > > > (receiver ?e' ?y)
> > > > > > (given ?e' ?z))
> > > > > > (= ?e ?e')))))))
> > > > >
> > > > > Now I think we're getting there.
> > > > > But even more is needed after the "<=>" to assure that:
> > > > > 1) The same giving does not have more than one giver.
> > > > > 2) The same giving does not have more than one given
> > > > > 3) The same giving does not have more than one receiver.
> > > >
> > > > MW: This actually gets to the heart of the issue quite nicely,
> > > > and provides one of the reasons I am unhappy with more
> > > > than binary relations.
> > > >
> > > > MW: You are right that the ternary relation does not
> > > > only say that a giving relation involves at least
> > > > a giver a receiver and a gift, but that it involves
> > > > exactly one giver, receiver, and gift. I think others
> > > > have pointed out that this is not necessarily the case
> > > > for all givings. There may be many givers, many receivers
> > > > or many gifts.
> > > >
> > > > MW: This is what has driven us away from triadic or higher
> > > > relations, rather than anything else.
> > > >
> > > > MW: So I will now argue that the form that we have
> > > > ended up with for giving is actually a more
> > > > acurate reflection of reality.
> > > > >
> > > > > (I'm not quite up to writing what I want in KIF,
> > > > > with certainty. Perhaps someone will step in
> > > > > and add the gory detail.)
> > > > >
> > > > > So,
> > > > >
> > > > > 1) The <=> axiom above is invalid and probably
> > > > > could be used to prove a contradiction.
> > > > >
> > > > > 2) An augmented <=> axiom like the one above but
> > > > > disallowing two receivers, etc., might not lead
> > > > > to contradictions and a generalization of it
> > > > > might be OK in the SUO.
> > > > >
> > > > > 3) I certainly would not personally want to call
> > > > > the change from what precedes the <=> to what
> > > > > follows the <=> a "reduction".
> > > >
> > > > MW: Indeed, the only thing that is reduced is the arity
> > > of the relations used. On the other hand we do have
> > > a more accurate model.
> > >
> > > ^^^
> > > False statement. |||
> > >
> > > Because I still believe that you really want to know.
> > >
> > > Exercise for the reader:
> > >
> > > What is the arity of the first "and" relation
> > > that is invoked in the above bit of kiffage?
> > >
> > > ...
> > >
> > > > > > (and (giving ?e)
> > > > > > (giver ?e ?x)
> > > > > > (receiver ?e ?y)
> > > > > > (given ?e ?z)
> > > > > > (forall (?e')
> > >
> > > ...
> > >
> > > Hint: It has 5 arguments, and therefore represents
> > > a map 'And<5>' such that 'And<5>' : B^5 -> B.
> > >
> > > The use of a single symbol, in the way that "and" is used above,
> > > to denote a series of operations 'And<j>', for j = 1, 2, 3, ...,
> > > tantamount to an indefinite degree of equivocation, constitutes
> > > what is commonly known as a "multigrade operator". They can be
> > > very convenient bits of syntactic sugar, but they do not alter
> > > the underlying logical complexity of the operations invoked.
> > >
> > > This is, of course, aside from the fact that the relation "giving"
> > > is at least as complex as a 3-adic relation, since its argument is
> > > at least a 3-tuple -- and you can tell that it's at least
> a 3-tuple
> > > from the fact that it has at least 3 components. That's all that
> > > a 3-tuple is.
> > >
> > > The basic principle here is:
> > >
> > > | If it looks like a k-tuple,
> > > | if it talks like a k-tuple,
> > > | if it walks like a k-tuple,
> > > | then abduce it's a k-tuple.
> > >
> > > Jon Awbrey
> > >
> > > ¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
> ¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
>
Regards
Matthew
===============================================================
Matthew West http://www.matthew-west.org.uk/
Principal Consultant Shell Visiting Professor
Operations & Asset Management The Keyworth Institute
Shell Services International The University of Leeds
http://www.shellservices.com/ http://www.keyworth.leeds.ac.uk/
H3229, Shell Centre, London, SE1 7NA, UK.
Tel: +44 207 934 4490 Fax: 7929 Mobile: +44 7796 336538
===============================================================