RE: SUO: Irreducible Triadicity
Dear Lee,
I thought we had gotten beyond this. Indeed I thought we had got to the
point where it was demonstrated (by Pat, but by me previously) that in
representation terms anything can be reduced to dyadic relations.
This caused a change in tack to saying that there are axioms that require
more than 2 arguments (not a particular surprise to me). The question
remaining is then whether there are any axioms that cannot be reduced to
some set of independent axioms that involve only 3 elements.
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
===============================================================
> -----Original Message-----
> From: Josiah Lee Auspitz [mailto:lee@textwise.com]
> Sent: 17 March 2001 13:24
> To: West, Matthew MR SSI-GREA-UK
> Cc: Standard-Upper-Ontology (E-mail); lee@sabre.org
> Subject: Re: SUO: Irreducible Triadicity
>
>
>
> Matthew,
>
> The "triadic" issue in the example you have given is whether we can
> analyze this example into triads which add up to the whole
> picture without
> any loss of logical content. In listing the attributes of
> the measurement
> problem you have already done this, if we can show that each
> element of
> the problem-- time of observation, measurement device,
> measurement scale,
> place of observation, observing subject, observed object etc.-- is
> reducible to the pattern O(for object)-R(for representamen)-I (for
> interpretant), where any R can also be seen as an O for some further
> O-R-I, and any I can be seen as an O or R for some further
> O-R-I, and any
> O may also be an R or an I, and so on, this whole business being the
> continuum of semiosis, infinitely extendable and infinitesimally
> refinable.
>
> Lee
>
> On Sat, 17 Mar 2001, West, Matthew MR SSI-GREA-UK wrote:
>
> >
> > Dear Colleagues,
> >
> > This has been a very interesting discussion, in which I
> have learnt some
> > things, and been surprised at some things that I thought
> were common ground
> > but were not.
> >
> > Firstly the good news. I think I now understand what John
> means when he says
> > "mediating". He means an activity, or the result of an
> activity, in which
> > more than two things are necessarily involved form an
> ontological viewpoint.
> >
> > Pat has explained some theoretical background to graph
> theory from which I
> > draw (actually I already knew this) that there is more than
> one way that the
> > world can be represented as a graph (or some other
> formalism) and that the
> > triadic iirreducibility only applies when you take one particular
> > representation.
> >
> > I have one unanswered question. Part of the claim about irreducible
> > triadicity is that anything that is higher than triadic can
> be reduced to
> > triadic. Pat and Nicola (I think) have suggested that there
> is no reason why
> > the limit should be 3 for ontological dependence. So I have
> presented a test
> > example about measurement. Measurement is just about the
> most complicated
> > thing I have come across in my years of analysis, and I am
> prepared to
> > believe that if the information about a measurement can be
> reduced to triads
> > that are independent, then it is likely that anything else
> can. On the other
> > hand John has not responded to this example, which I repeat below.
> >
> > > MW: OK. In that case please show me how a measurement can be
> > > reduced to triads. A Measurement is an activity that:
> > >
> > > has a subject (the thing measured)
> > > an observer (doing the measuring)
> > > an instrument (e.g. thermometer)
> > > a measure (what about the thing is being measured, e.g.
> temperature)
> > > a result (the value e.g. 20)
> > > a Unit of Measure (e.g. Celsius)
> > > the time when the measurement was taken.
> >
> > I would be interested to see whether and how this can be
> reduced to triadic
> > or less ontologically dependent elements. If it can't, then
> there is at
> > least one case where this does not apply (which is enough)
> or perhaps as Pat
> > has been suggesting there has been confusion between graph
> theory and
> > ontology.
> >
> > Well I guess the next question is "does it really matter?".
> By this I mean,
> > does it really matter that there are different mappings
> from the world onto
> > graph theoretic representations.
> >
> > Unfortunately the answer is "yes", as we discovered in
> Shell some 10-15
> > years ago. At about that time many of the 200 or so
> companies in the Shell
> > Group were getting into relational databases, mostly
> developing much the
> > same systems to do much the same thing in different
> countries. Something
> > that we noticed to our horror was that all these systems
> were generally
> > incompatible, and that generally they were not
> transferrable either. We
> > (then the corporate data management group) were asked to
> look at why this
> > was the case.
> >
> > The databases were generally documented in data models.
> (Data Models can be
> > seen as graphs with entity types as nodes, relationship
> types as edges, and
> > attribute types as leaf nodes.) When we examined the data
> models we found
> > that one of the (many) problems was that people had mapped
> the real world
> > onto these constructs in a variety of ways. Let us take
> activities as an
> > example:
> >
> > 1) as a relationship type, with the participants at either
> end of the
> > relationship.
> > 2) as a "transaction" - an entity type with a number of dependent
> > relationships.
> > 3) as an independent entity type with non-dependent
> relationships to the
> > objects involved.
> > 4) a mixture of 2 & 3.
> >
> > 1)
> >
> > o------------o o----------o
> > | | throws | |
> > | person |>-------------<| ball |
> > | | | |
> > o------------o o----------o
> >
> > 2)
> >
> > o------------o o----------o
> > | | thrower | |
> > | |>--------------| person |
> > | throws | | |
> > | | o----------o
> > | | o----------o
> > | | thrown | |
> > | |>--------------| ball |
> > | | | |
> > o------------o o----------o
> >
> > and even 3)
> >
> > o------------o o----------o o----------o
> > | | | | | |
> > | |--------------<| thrower |>---------| person |
> > | throws | | | | |
> > | | o----------o o----------o
> > | | o----------o o----------o
> > | | | | | |
> > | |--------------<| thrown |>---------| ball |
> > | | | | | |
> > o------------o o----------o o----------o
> >
> > Of course these different structures are not directly compatible
> > and in many cases arbitrary combinations of these different
> approaches
> > were taken.
> >
> > So one of the things we did was to study the differences
> between these
> > (and other) representations. The conclusions to these have been
> > implemented in the EPISTLE Core Model. Incidently, the ECM V4.0
> > has just been published, and can be found at:
> >
> http://www.stepcom.ncl.ac.uk/epistle/data/epistle_core_model_v
ersion_4.htm
>
> 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
> ===============================================================
>