Re: SUO: Re: Registers
Adam,
The definition of equilateral triangle depends upon the definition of
triangle which depends upon the definition of polygon which depends upon
the definition of plane figure which are defined in terms of the notions
of line and of point which are primitive notions of geometry, i.e.
there is no sufficient conditions for being a point or a line.
The definition of 'three-legged dog' in a theory that possesses 'dog' as
a primitive term is not different from that of 'equilateral triangle' in
elementary geometry.
I'm just trying to make a case that there can be non mathematical
notions axiomatized via necessary and sufficient conditions. That such
terms stem from non mathematical terms lacking sufficient conditions of
identification just illustrate the relevance / use / necessity of a
notion of 'primitive terms'.
yours,
Pierre
Adam Pease wrote:
>
> Pierre,
> I'm getting a little lost as to where this is going I'm afraid. If you
> define the concept of "three-legged dog" as a dog that has three legs, you
> still have only a necessary definition, not a necessary and sufficient one,
> since the definition of "three-legged dog" depends upon the concept "dog"
> which does not have a necessary and sufficient definition.
>
> Adam
>
> At 01:40 PM 10/25/2001 -0500, Pierre Grenon wrote:
> >Adam,
> >
> >Where is the flaw in the following? We include Dog as a primitive
> >concept, since we're unbable to define Dog in a theory that doesn't
> >includes this notion. (Is that what was meant?) The theory you seem to
> >refer to allows one to count one dog's legs. I can now define the class
> >of dogs with exactly three legs. Here are two necessary conditions:
> >being a dog, having three and only three legs. Here's a sufficient
> >condition for being a member of this class: being a dog and having three
> >and only three legs.
> >
> >yours,
> >Pierre
> >
> >Adam Pease wrote:
> > >
> > > Pierre,
> > > Sorry I wasn't clear. I'll also try to give a definition of these
> > > notions. My apologies if this is already familiar to you. I'll also
> > > apologize in advance if there are some errors that other, more
> > > mathematically and logically sophisticated list members need to correct.
> > >
> > > Necessary conditions are those that are true and essential to the semantics
> > > of a particular term.
> > >
> > > The set of sufficient conditions are those that completely define a term -
> > > i.e. no other statements are needed to say completely what that term means.
> > >
> > > For example, the concept of "equilateral triangle" is a two dimensional
> > > geometric figure with three sides, all of which are the same length. This
> > > is both a necessary and sufficient definition. While other statements
> > > about equilateral triangles are true (for example that all the angles must
> > > be 60 degrees), nothing else need be said to define exactly what an
> > > equilateral triangle is.
> > >
> > > In contrast, classes such as biological species do not have necessary and
> > > sufficient definitions. The class "Dog" has many necessary conditions such
> > > that healthy members of the class have four legs, bear live young
> > > etc. However there is no complete set of defining characteristics for a
> > > Dog. It's more of an "extensional" set for which humans have abstracted a
> > > set of common intentional conditions.
> > >
> > > I hope this helps.
> > >
> > > Adam
> > >
> > > At 12:42 PM 10/25/2001 -0500, Pierre Grenon wrote:
> > > >Adam, pardon my confusion but I'm not sure I'm following you here.
> > > >
> > > >Pierre
> > > >
> > > >Adam Pease wrote:
> > > > >
> > > > > oops, I meant "thank goodness it isn't since concepts other than
> > > > > mathematical notions **don't** have both necessary and sufficient
> > > > definitions"
> > > > >
> > > > > At 09:55 AM 10/25/2001 -0700, Adam Pease wrote:
> > > > >
> > > > > >Pierre,
> > > > > >
> > > > > >At 11:10 AM 10/25/2001 -0500, Pierre Grenon wrote:
> > > > > >>Adam,
> > > > > >>
> > > > > >>Adam Pease wrote:
> > > > > >> >
> > > > > >> > Pierre,
> > > > > >> > This process sounds fine to me. In fact, it's consistent
> > with what
> > > > > >> were
> > > > > >> > already doing. I have only two caveats
> > > > > >> >
> > > > > >> > 1. We haven't yet found a compelling case for alternate
> > axiomatizions
> > > > > >> (not
> > > > > >> > that alternate axiomatizations aren't possible, just that they
> > haven't
> > > > > >> been
> > > > > >> > necessary to support any other component of the ontology).
> > > > > >>
> > > > > >>Well, I don't know what to reply that wouldn't be foolish,
> > undocumented
> > > > > >>and/or irrelevant, anyway. It seems that I'm inconsequent in my
> > use of
> > > > > >>the term 'alternative axiomatization' (based on C. Menzel & M. West's
> > > > > >>exchange). In particular, it seems that alternatives axiomatization
> > > > > >>would be equivalent axiomatizations of a same concept / domain.
> > That's
> > > > > >>not what I meant, maybe 'rival axiomatizations' would be better. Two
> > > > > >>theories would be similar (actually would share a common part) and
> > > > > >>differ in a finite number of axioms, maybe only one. For
> > instance, you
> > > > > >>can have two theories of geographical location. One requiring every
> > > > > >>geographical location to have one and only one object located at it,
> > > > > >>another would allow colocation of different objects. I meant
> > > > > >>'alternative axiomatization' in this sense: arguably the same concept
> > > > > >>receives different axiomatizations.
> > > > > >>That kind of issue doesn't seems to make a case for having two
> > notions
> > > > > >>of geographical location, rather two independent (inconsistent?)
> > > > > >>axiomatizations of that notion.
> > > > > >>What kind of sense does that make?
> > > > > >
> > > > > >In the abstract it makes perfect sense. The issue is whether
> > alternate
> > > > > >theories are required in practice. Pat Hayes has made a strong
> > case about
> > > > > >the need for alternate (contradictory) temporal
> > theories. However, Cyc
> > > > > >doesn't have contradictory temporal theories, nor does SUMO and it
> > seems
> > > > > >possible to me to represent anything you'd want to say at a more
> > domain
> > > > > >specific level by just adopting one theory of time. I guess the
> > jury is
> > > > > >still out on this issue since both camps feel strongly about their
> > side of
> > > > > >this issue.
> > > > > >
> > > > > >> > 2. We should clarify the use of the word 'primitive'. My
> > > > > >> understanding is
> > > > > >> > that since few terms in SUO have necessary and sufficient
> > definitions,
> > > > > >> > that, formally, they are primitive. On the other hand, all terms
> > > > in the
> > > > > >> > SUMO other than Entity make use of other SUMO terms in their
> > > > 'definitions'
> > > > > >> > (again with the clarification that those definitions are
> > > > necessary, not
> > > > > >> > necessary and sufficient).
> > > > > >>
> > > > > >>Indeed, I was using those terms loosely. What I actually meant by
> > > > > >>'primitive' is precisely 'undefinable'. Could a primitive term be one
> > > > > >>definable within a theory only by mean of circular definition?
> > (Is that
> > > > > >>again a loose talk?)
> > > > > >>
> > > > > >>Now you seem to suggest that there are interdefinable terms. Well
> > maybe
> > > > > >>that suggest that primitivity is just arbitrary and relative to your
> > > > > >>means, in other words, interdefinable terms are equally
> > primitive. And
> > > > > >>maybe that suggests that primitivity is irrelevant, I don't
> > know. I'd
> > > > > >>be happy to receive a 'lesson' on this issue, or maybe just
> > pointers to
> > > > > >>document that discuss this in any way.
> > > > > >
> > > > > >I'd say that primitivity isn't irrelevant, just that it's not
> > required,
> > > > > >and thank goodness it isn't since concepts other than mathematical
> > notions
> > > > > >have both necessary and sufficient definitions. These definitions
> > need
> > > > > >not be circular however.
> > > > > >
> > > > > >I probably need a "lesson" this this stuff just as much as you
> > :-). If
> > > > > >Fritz were still at Cycorp I'd say he'd be the person to talk to,
> > or folks
> > > > > >like Chris Menzel or Pat Hayes might be able to give us some
> > references.
> > > > > >
> > > > > >>Anyway, roughly a primitive term is not definable in terms of other
> > > > > >>terms of a given theory. Indeed you might be able to state necessary
> > > > > >>conditions within the theory, however to state sufficient ones,
> > > > > >>presumably you'd need introducing more primitive terms (or introduce
> > > > > >>circular definitions), etc.
> > > > > >
> > > > > >yes, that sounds right
> > > > > >
> > > > > >>yours,
> > > > > >>Pierre
> > > > > >>
> > > > > >> >
> > > > > >> > Adam
> > > > > >> >
> > > > > >> > At 06:49 PM 10/24/2001 -0500, Pierre Grenon wrote:
> > > > > >> > >Adam,
> > > > > >> > >I could not help giving it a shot, for all it's worth see in
> > line.
> > > > > >> > >Pierre
> > > > > >> > >
> > > > > >> > >Adam Pease wrote:
> > > > > >> > > >
> > > > > >> > > > Matthew,
> > > > > >> > > > Thanks for clarifying. However, if we have trouble
> > agreeing on
> > > > > >> this
> > > > > >> > > > list when a particular term or definition belongs in the
> > > > standard, why
> > > > > >> > > > would you think that we could devise a precise methodology for
> > > > doing
> > > > > >> > > > so? More to the point, for you or anyone who believes
> > that such a
> > > > > >> > > > methodology is possible, can you propose one that
> > addresses the
> > > > > >> scope and
> > > > > >> > > > purpose of the SUO?
> > > > > >> > > >
> > > > > >> > > > Adam
> > > > > >> > >
> > > > > >> > >What about this?
> > > > > >> > >
> > > > > >> > >Start from whatever you have (SUMO, IFF). That becomes your
> > > > 'reference
> > > > > >> > >data librairy', right?
> > > > > >> > >
> > > > > >> > >Bring in some term candidate to addition / system candidate to
> > > > > >> > >merge/extension and apply some combination of the criteria
> > discussed
> > > > > >> > >earlier.
> > > > > >> > >
> > > > > >> > >-For addition of a term: Is the candidate term an SUO term?
> > (or more
> > > > > >> > >interestingly: is the candidate term a redo of an SUO term?) Is
> > > > the term
> > > > > >> > >defined solely in terms of SUO terms? Does the introduction
> > > > generate a
> > > > > >> > >contradiction?
> > > > > >> > >
> > > > > >> > >-For merging into / extending the SUO:
> > > > > >> > >Check wether the candidate uses SUO terms, derived SUO terms.
> > Would
> > > > > >> > >fusion / merging generate inconsistencies? redundancy? [So far,
> > > > any new
> > > > > >> > >material may be said to carve out further the meaning of SUO
> > terms.]
> > > > > >> > >
> > > > > >> > >If addition / fusion appeared to lead to inconsistency, consider
> > > > > >> > >enriching the SUO with an alternative axiomatization (module).
> > > > > >> > >
> > > > > >> > >If there are parts of the system not fitting into this first
> > picture,
> > > > > >> > >then consider extending the SUO by adding new primitive terms to
> > > > the SUO
> > > > > >> > >basis.
> > > > > >> > >
> > > > > >> > >I don't see how the criteria for addition will differ from that
> > > > used in
> > > > > >> > >agreeing on the 'reference data librairy', that is, a consensus
> > > > among a
> > > > > >> > >community that a term is useful, handy, correspond to a
> > fundamental
> > > > > >> > >intuition active in a given community of users and that the
> > proposed
> > > > > >> > >axiomatization of the term is adequat. Could there be aesthetic
> > > > > >> > >criteria? Should there be a principal of economy (against
> > redundancy,
> > > > > >> > >against introduction as primitive terms of some that could be
> > > > defined in
> > > > > >> > >terms of primitive SUO terms, etc.)? For a standard ontology,
> > that
> > > > > >> > >presume awarness of potential candidates needs and interest,
> > > > doesn't it?
> > > > > >> > >
> > > > > >> > >Is that too naive or maybe too general?
> > > > > >> > >
> > > > > >> > >
> > > > > >> > > >
> > > > > >> > > > At 11:11 PM 10/24/2001 +0200, West, Matthew R SITI-ITPSIE
> > wrote:
> > > > > >> > > > >Dear Adam,
> > > > > >> > > > >
> > > > > >> > > > >The content of a register is standardised by having a
> > standard
> > > > > >> > > > >method used for how content is added to the register.
> > There is
> > > > > >> > > > >also an initial content (say the SUO).
> > > > > >> > > > >
> > > > > >> > > > >ISO15926 has the following parts:
> > > > > >> > > > > Part 1 - Overview
> > > > > >> > > > > Part 2 - Data Model (part of the ontology and the data
> > > > > >> > > > > structure for the register)
> > > > > >> > > > > Part 4 - Initial content of the register (we call it a
> > > > Reference
> > > > > >> > > > > Data Library)
> > > > > >> > > > > Part 5 - Administrative Standard for the Register
> > > > > >> > > > > Part 6 - Technical Standard for the Register Content
> > > > > >> > > > >See: http://www.iso15926.freeserve.co.uk/register/index.html
> > > > > >> > > > >
> > > > > >> > > > >The TEchnical Standard provides the methodology for
> > adding new
> > > > > >> > > > >content to the register. By following this process, the
> > content
> > > > > >> > > > >is deemed to be standardised.
> > > > > >> > > > >
> > > > > >> > > > >You may recall that I have been suggesting that a defined
> > > > methodology
> > > > > >> > > > >for how we develop the SUO would have value.
> >4-0500 x571
>
> Adam Pease
> Teknowledge
> (650) 424-0500 x571