Barry Smith wrote: (01)
> Responding to Nicolas and Denise:
>
>> >I also do not think, though, that the relationships I have seen
>> defined by the
>> >ontology community are sufficiently rigorous to meet the needs of
>> individual
>> >domains.
>> >
>> Do you have an idea about what's missing?
>>
>> Barry distinguishes 3 worlds of things:
>>
>> - concept systems (describing the meaning of terms w.r.t. relations
>> among terms)
>> - real-world entities (instances & types organized in an ontology)
>> - information models about the world (e.g., an allegorical document)
>
>
> Better not to call these three worlds. There is only one world, built
> up out of instances organized (in complex ways) by types. (02)
Ouch... Perhaps I have improperly made a reference to your paper
(http://ontology.buffalo.edu/concepts/ConceptsandOntologies.pdf)
in which you state: (03)
"The following figure illustrates the different worlds of concept
systems, ontologies and
the information models." (04)
and show a figure with captions: (05)
a) "The world of concepts - meaning of terms"
b) "The real world of entities"
c) "The world of information about the real world" (06)
Are you saying you don't like your own terminology?
Ok, I'm being picky here. Seriously though, can you please
suggest a better terminology to refer to (a), (b), (c)
that is succinct enough yet precise enough to avoid
the trap I fell into? (07)
>> When we use 'part-of' at the instance level to be ontologically accurate
>> in the sense of Barry,
>> we are still vague about what is the criteria by which we adjucate on
>> parthood. This goes
>> back to issues of defining criteria of identity and unity.
>
>
> Every descriptive/scientific endeavor will face cases where instances
> clearly stand in a given relation (e.g. my heart part-of me); other
> cases where they clearly do not stand in this relation (e.g. NOT: my
> heart part-of the Arc de Triomphe); and yet other cases where it is
> hard to tell (e.g. ?: my heart part-of ONTAC-WG)
>
> My advice to all is to concentrate initially on the first group of
> cases (low hanging group). Certainly you should not allow the
> existence of the third group to block your efforts from the start. (08)
Indeed, this is a reasonable strategy to follow.
However, it is nonetheless insufficient w.r.t.
how to deal with the 'context' behind the meaning of
relaitonships like 'part-of'. (09)
We can specify the meaning of a relationship on an axiomatic basis like
you describe below.
This amounts to requiring that (b) is an axiomatized ontology. (010)
Your advice implies that an axiomatization of (b) will be done w.r.t.
certain assumptions and criteria
of modeling granularity, dependence, rigidity, etc... That information
is not part of the axiomatization
of an ontology. It is meta-knowledge about the axiomatization of an
ontology that I'm advocating
should be explicitly and declaratively specified relative to something
else (e.g., (a) or (c)).
This metaknowledge is important to make sure that two agents (e.g., you
and I) can reach
a consensus about how we are interepreting the axioms of a given
relationship (e.g., the 'part-of' relationship you describe below). (011)
>> We need identity to make sense of "a123 part-of b456". How do I
>> recognize 'a123' among all possible instances?
>
>
> Typically it will be you who has baptised the relevant instance by
> using this designation. Thus you may have baptised your heart as
> 'a123'. If you do not know what instance 'a123' stands for, then do
> not use this instance designator in your work! (012)
It seems to me you are reading me a bit too litterally. (013)
By 'identity', I'm referring to criteria that *I* have established as
the axiomatic
basis with which I can tell which unique entity in the real world
correspond to 'a123'. (014)
I need to be able to communicate these 'identity' criteria to *you* to
make sure that,
as long as you are reasonable, you are able to recognize which
real-world entity
corresponds to my symbolic designator: 'a123'. (015)
If it is established that we already share the same 'identity' criteria,
then it is clearly unecessary to go through alignment of
frame/context/whatever 'thing'
includes metaknowledge about 'identity' and whatever other meta-property
criteria
we need to share to understand one another's symbols and meanings. (016)
>> I have a feeling that, at a coarse level, we're more or less in
>> agreement.
>> At a practical level, there are wholes that are problematic w.r.t what
>> should we be doing next.
>
>
> Don't let worries about the problematic cases keep you from doing good
> work with the non-problematic cases.
>
The problematic cases are twofold: (017)
- specifying the meaning of axiomatized relationships w.r.t. some
metaknowledge about (b)
- communicating the basis of such specifications across agents (people,
machines, databases, etc...)
where we care to ensure that meaning is preserved across communication. (018)
>
>> In this example, suppose we want to practically account for the meaning
>> of the 'part-of' relationship at the instance level
>> (i.e., the 'part-of' relationship in the ontology of real-world
>> entities)
>>
>> - in 'conventional' ontologies, we'd have things like:
>>
>> owl:Class A
>> owl:Class B
>> part-of: A -> B
>> A a123
>> B b456
>> part-of(a123,b456)
>
>
> The issue is how does the part-of relation between A and B, which we
> might write:
>
> PART-OF(A,B)
>
> relate to the part-of relation between given instances, say:
>
> part-of(a123,b456)
>
> My answer is as follows:
>
> PART-OF(A,B) =def for every instance a of A there is some instance b
> of B which is such that part-of(a,b)
>
> In brief: all As are part-of some Bs
>
> This is simplified somewhat since it does not take account of time.
> However, the detailed (all-some) account is still quite simple (see
> http://genomebiology.com/2005/6/5/R46), and has the advantage that it
> applies in just the same way to all the so-called associative
> relations. Thus for example
>
> LOCATED-IN(A,B) =def for every instance a of A there is some instance
> b of B which is such that located-in(a,b)
>
> In brief: all As are located-in some Bs.
>
> I believe that this all-some approach is consistent, too, with the
> underlying idea of Description Logic, where type-level relations must
> always be defined through the instance level.
>
> But if any members of the list have a better account of how type-level
> relations are to be defined, I would be pleased to hear what it is. (019)
As far as modeling relationships on an axiomatic basis, I'm OK with what
you say.
As far as relating the meaning of relationships modeled according to
different criteria that are
largely compatible but that have some differences, we then get in to
trouble quickly. (020)
In the biology context, suppose we define 'PART-OF(A,B)' where A,B are
sequences (e.g. DNA, RNA, etc...) (021)
The 'PART-OF' relationship then allows us, for example, to talk about
'viral infection scenarios' for example:
i.e., whether a virus has incorporated itself into a host chromosome. (022)
This perspective is relevant to analyze the viral immunity of certain
chromosomes or the effectiveness of
various mechanisms against viral infection. In this context, it is
reasonable to expect the 'PART-OF' relationship
to satisfy the following logical property: PART-OF(v123,c456)=true if
and only if virus v123 has infected chromosome c456. (023)
Yet, there is a closely-related context where we might want to 'trace'
the origin of a particular virus that has managed to clone itself
from a host chromosome and is therefore 'out there' on the prowl for
infecting other chromosomes, perhaps in the same cell, perhaps
in a different cell. It would be conceivable that someone, e.g.,
Nicolas, would use PART-OF(v123,c456) with the same axiomatic basis
as yours to talk about v123 as a copy of the same virus in c456; except
that here, v123 isn't chemically bonded within
the structure of chromosome but instead is the result of cloning a
virus, say, v12, that is chemically bonded within the chromosome c456.
Perhaps Nicolas doesn't really care about v12 after all, only that v123
came from c456. Perhaps Barry would argue that Nicolas' PART-OF
relationship should be called something else. The point here is that in
order for us to recognize that Barry and Nicolas have the same axiomatic
formalization of their respective 'PART-OF(x,y)' relationships defined
over the same domains for x & y, these two relationships clearly
express different properties. (024)
I believe my concern is still unanswered at the practical level which I
venture to summarize as follows: (025)
Given reasonable axiomatizations of relationships, what additional
information about each relationship do we need
to specify the range of contexts where that relationship is meant to be
interepreted? (026)
With doubts,
-- Nicolas. (027)
>
> With greetings
> Barry
>
>
>
> (028)
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