On Jul 13, 2009, at 12:15 PM, Ed Barkmeyer wrote: (01)
> I wrote:
>
>>> (3) Matt doesn't mention the CDIF notation for "subtype"/
>>> subsumption.
>>> This is a foundational concept in OWL, and it is very important to
>>> modeling measurement concepts. In particular, every 'measurement
>>> unit'
>>> is_a 'quantity'. I would be wary of a notation like:
>>> measurement-unit -- is a --> quantity
>
> Matthew West wrote:
>> [MW] I do not recall that CDIF has a specific notation, so you can
>> either do
>> what you have done here, or quite often I use the EXPRESS notation
>> as an
>> extension.
>
> My point is that we need notation for subsumption, at least, and I
> think
> it useful to have a notation for unions and intersections and
> exclusions
> (all of which the ODM added to UML, for OWL). I also believe in
> ternary
> and occasionally quaternary relations, and I prefer to see some
> distinguishing notation for them. (The VIM has at least one ternary
> relationship in it: system-of-units appoints base-measurement-unit for
> quantity-kind.)
>
>>> because it makes the notation ambiguous. 'is_a' is a class-to-class
>>> relationship, rather than an instance-to-instance relationship (like
>>> 'part of'). It models an axiom, not just a relation. That is:
>>> A -- is part of --> B
>>> models a relation "is part of" whose domain is things that satisfy
>>> relation (class) A, and whose range is things that satisfy
>>> relation B -
>>> -
>>> a vocabulary item. It has two free variables. Whereas,
>>> A -- is a --> B
>>> models a proposition, a statement: Every A is a B. Formally,
>>> (forall x) (if (A x) (B x))
>>> It has no free variables. And the model asserts that proposition,
>>> making it an axiom.
>>> So I would object to overuse of the arrow notation, if it leads to
>>> such
>>> an ambiguity.
>>
>> [MW] I'd just like to push back on this a bit. I agree that you
>> need to be
>> careful to distinguish between relationships between classes and
>> relationships that hold between members of classes. However, I had
>> understood subtype/supertype as being able to be seen in either
>> way. So that
>> one way of seeing subtype/supertype is as an identity relationship
>> between
>> members of the subtype and members of the supertype.
>>
>> Comments?
>
> This might be better discussed on the Forum exploder.
>
> In languages like CDIF and UML, specifying A and B to be "classes" or
> "entities", defines a relation with one free variable (A x) or (B x),
> where x is an arbitrary thing from the universe of discourse -- a
> discovered entity instance or object -- and the "result" of (A x) is
> either true or false -- the new x either is an A or it isn't. (It is
> possible that we don't know which, but there is an underlying
> epistemological assumption that exactly one of those statements is
> true,
> axiomatized as the "law of the excluded middle": (forall x)(OR (A x)
> (NOT (A x)).)
>
> And in those same languages: "A is-part-of B" introduces a relation
> (is-part-of a b)
> which maps an ordered pair of arbitrary things (a, b) to either true
> or
> false. There are some semantic scoping rules that have various
> interpretations, but let us assume that "is-part-of" is a unique
> relation that is specified to be meaningful only for class A. (The
> alternative is that it specifies a relationship "A:is-part-of",
> which is
> different from an "X:is-part-of" relationship for any other domain X.)
> That means that the specification implies an axiom:
> (forall a b)(if (is-part-of a b) (A a))
> in any such actual relationship, the first thing must be an A.
> And similarly, the second thing must be a B.
>
> Notably, this specification, of itself, does NOT say that every A is
> part of some B. In UML, I can add a notation, which we could
> represent as:
> A -- is part of --> 1..1 B
> and that adds two more axioms:
> (forall a)(if (A a) (exists b)(is-part-of a b))
> If a thing is an A then there is a b that it is part of. Each A
> is-part-of at least 1 B. And:
> (forall x b c)(if (and (is-part-of x b) (is-part-of x c))
> (= b c))
> If a thing x is a part of two things b and c, b and c must be the same
> thing. Each A is part of at most one B.
>
> So, following the above semantic interpretation patterns:
> A -- is-a --> B
> means (forall x y)(if (is-a x y) (A x))
> If for any two things x and y "x is-a y" is true, then x must be an A.
> The alternative interpretation, noted above, is that:
> A -->is-a --> B
> specifies a relationship "A:is-a", which is different from any other
> "is-a" relationship. I doubt that either of these is the
> interpretation
> we want for "is-a", which means that the notation doesn't have
> consistent semantics.
>
> And this goes further. If one chooses Matthew's SQL-like
> instance-to-instance identity relationship as the meaning, we have the
> further problem that
> A -- is-a --> B
> does not by itself say that every A is-a some B. We would need
> something like:
> A -- is-a --> 1..1 B.
> That is, we want to assert that the instance-to-instance relationship
> must exist. "pediatrician is-a doctor" is different from
> "pediatrician is-a-member-of preferred-provider-organization".
>
> This is why I am uncomfortable with such ad hoc conventions. It's not
> that one cannot agree to use: A -- is-a --> B to represent
> subsumption;
> it is that one must be clear that:
> -- is-a -->
> has importantly different semantics from
> -- <term> -->
> where the <term> is anything other than "is-a". (02)
While I agree with most of what you say above, I don't accept this
strong a statement. A --is-a--> B asserts a relationship between
classes, is the point, not between members of the classes. But there
isn't anything particularly unique about is-a in this regard: there
are other useful relationships between classes, such as
isDisjointFrom, and relationships between classes and properties, such
as Domain and Range (in the OWL sense). All of this is very
transparently stated in CLIF logic, by the way, for example (03)
(forall (A B)(iff
(is-a A B)
(forall (x)(if (A x)(B x)))
)) (04)
> And this violates what
> Bernd Wenzel calls the Law of Least Astonishment: it encourages false
> analogies and erroneous interpretations. (05)
Only if there is a presumption that we are speaking only of
individuals, not classes, at the nodes. That is the error of
interpretation that we should guard against. (06)
Pat (07)
>
> -Ed
>
> --
> Edward J. Barkmeyer Email: edbark@xxxxxxxx
> National Institute of Standards & Technology
> Manufacturing Systems Integration Division
> 100 Bureau Drive, Stop 8263 Tel: +1 301-975-3528
> Gaithersburg, MD 20899-8263 FAX: +1 301-975-4694
>
> "The opinions expressed above do not reflect consensus of NIST,
> and have not been reviewed by any Government authority."
>
> _________________________________________________________________
> Message Archives: http://ontolog.cim3.net/forum/uom-ontology-std/
> Subscribe: mailto:uom-ontology-std-join@xxxxxxxxxxxxxxxx
> Config/Unsubscribe: http://ontolog.cim3.net/mailman/listinfo/uom-ontology-std/
> Shared Files: http://ontolog.cim3.net/file/work/UoM/
> Wiki: http://ontolog.cim3.net/cgi-bin/wiki.pl?UoM_Ontology_Standard
>
>
> _________________________________________________________________
> Msg Archives: http://ontolog.cim3.net/forum/ontology-summit/
> Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontology-summit/
> Unsubscribe: mailto:ontology-summit-leave@xxxxxxxxxxxxxxxx
> Community Files: http://ontolog.cim3.net/file/work/OntologySummit2009/
> Community Wiki: http://ontolog.cim3.net/cgi-bin/wiki.pl?OntologySummit2009
> Community Portal: http://ontolog.cim3.net/
>
> (08)
------------------------------------------------------------
IHMC (850)434 8903 or (650)494 3973
40 South Alcaniz St. (850)202 4416 office
Pensacola (850)202 4440 fax
FL 32502 (850)291 0667 mobile
phayesAT-SIGNihmc.us http://www.ihmc.us/users/phayes (09)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/uom-ontology-std/
Subscribe: mailto:uom-ontology-std-join@xxxxxxxxxxxxxxxx
Config/Unsubscribe: http://ontolog.cim3.net/mailman/listinfo/uom-ontology-std/
Shared Files: http://ontolog.cim3.net/file/work/UoM/
Wiki: http://ontolog.cim3.net/cgi-bin/wiki.pl?UoM_Ontology_Standard (010)
|