Christopher Menzel wrote: (01)
> On May 25, 2005, at 9:50 PM, Nicolas F Rouquette wrote:
>
>> The formal ontology approach is very appealing to me for several
>> reasons.
>>
>> 1) it is a "relative" formalization of 'context', 'description', ....
>
>
> Ontologies do indeed often provide clusters of related information
> that capture several important aspects of context, but I think it is
> good to qualify that with the observation that a lot of folks working
> in formal ontology also think there is a place for a single, "upper
> level", non-contextual ontology that captures the logic of the most
> general categories that are (allegedly) applicable across most if not
> all ontologies. Examples are:
>
> * DOLCE (http://wonderweb.semanticweb.org/deliverables/documents/
> D18.pdf)
> * SUMO upper ontology fragment (http://ontology.teknowledge.com/)
> * GOL (http://www.ontology.uni-leipzig.de/Publications/Paper-FOIS-
> Herre-2001.pdf)
> * CYC upper ontology (click on the pyramid for a nice javascript pop-up
> http://www.cyc.com/cyc/technology/whatiscyc_dir/whatdoescycknow)
> * John Sowa's Top Level Ontology (http://www.jfsowa.com/ontology/
> toplevel.htm)
>
> The fact that there are some significant differences across even
> these supposedly conceptually basic and general ontologies, of course
> is, and has been, a matter for vigrous discussion. Notably, this
> divergence might suggest that even top level ontologies are context-
> senstive!
>
Yes, I agree. However, I believe that this context-sensitivity owes a
great deal
to the way we compare top-level ontologies, particularly, w.r.t. how do we
express differences among them. (02)
One important difference is scope (coincidently, we started to talk
about context!) (03)
For example, one cannot directly compare PSL's core ontology (process,
activities, activity occurences and timepoints)
to DOLCE's ontology of "descriptions and situations" (DnS). The former
has 4 concepts, the latter has many more,
some concepts of PSL core are not in DOLCE' DnS. Clearly, this
comparison doesn't make sense without additional
criteria. (04)
Another important difference is in the signature of ontological commitments
made in the definition of the concepts & relations in the ontologies we
compare. (05)
For example, Mike Grunninger told me once that comparing PSL and DOLCE
is not straigthforward:
In PSL, all timepoints in the domain of discourse must have an infinite
linear ordering.
There is just one time axis for everybody in the universe of discourse.
PSL doesn't talk
about multiple universes, the one universe in which we interpret "?t" in
"(timepoint ?t)"
So far so good.. but DOLCE's notion of time is something else ... He
said time in DOLCE is modal
but didn't elaborate much. (06)
Well, I have struggled with this for a while. It's clear to me now that
DOLCE allows a very expressive way to talk about *multiple* concepts of
time;
not just one univeral time axis but multiple axes and "segments" of axes. (07)
For example, there is one notion of time used as an abstract concept
when it refers to the particular time characteristics of a situation we
are describing
(e.g., the time when the sun rose this morning) There is a different
notion of time
that provides the time "data" corresponding to a specific situation
(e.g., the sun rose at 7am this morning). (08)
It is easy to make the mistake of comparing ontologies in terms of their
respective
vocabularies and axioms. This is what is implicitly happening in a lot
of "mapping" tools
where a user attempts to match ontologies in terms of their concepts,
relations and axioms.
WIthout Matt's keen observation, I might have made that mistake when I
started comparing DOLCE & PSL. (09)
Now, I believe that before we even attempt to compare 2 ontologies with
tool support
and fancy guis for aligning ontological taxonomies, we need to to do an
aligment of
ontological commitments first! (010)
In fact, I have found one illustrative example of this idea in the draft
CL standard: (011)
http://cl.tamu.edu/docs/cl/32N1238-WD24707-CommonLogic.pdf (012)
The example in 5.2.2 discusses how CL allows a logical "name" to
have multiple and fundamentally different semantic intepretations: (013)
(married Jack Jill)
(exists (x) (and (married x) (= Jack (husband x)) (= Jill (wife x)) ))
(= (when (married Jack Jill)) (hour 3 (pm (thursday (week 12 (year
1997))))) )
(= (wife (married 32456)) Jill)
(ConjugalStatus married Jack)
((ConjugalStatus Jack) Jill) (014)
As a superset of OWL-DL, it seems perfectly reasonable to
use CL as a neutral, abstract syntax for writing each meaning
of "married" and CL's semantics make it possible for us
to compare these meanings without mixing the axioms of one meaning
(binary relation between people) with the axioms of
another meaning (function from numbers to individuals) in a way
where we can add bridging axioms to relate related
terms (e.g., people vs. individuals) when it is important
to explain expressiveness differences (e.g., the former can talk about
being married to the people of mob but the latter cannot because
mob individuals are, by definition, incognito and even if we had
a separate group of numbers for the mob, we would then need a
multi-valued function since an individual could be at the same
time a member of the mod with a public pesonality). (015)
My point here is that I believe the notion of "top-level ontology"
should not be the kind of concept taxonomies
we currently have but instead a set of disjoint, parsimonous
independent and compositional commitment ontologies that allow
us to precisely define what we "mean" by a specific concept or relation
in terms of 4 things: (016)
- the ontological commitments we attribute to that concept or relation. (017)
In distributed AI, we often talk about "shared commitments" as the basis
of negotiation in distributed problem solving and coordination. This is the
"ontological" equivalent, in my view, of the critical importance these ideas
represent to reach a consensus about what allows us to say when two things
are comparable in which case we might debate whether they are identical
or different
vs. when two things are just not comparible and it is therefore
pointless to even
talk about their differences. (018)
- how each concept or relation has an axiomatic grounding in terms of
other concepts/relations (019)
So far, this is very "static" and "dry" picture of things.
We have 2 axiomatic theories about what "married" means in CL
and we have reached a consensus about whether we're talking about
pollyanna's world where the mob doesn't exist or some other kind of world.
That's progress but you might ask: so what? (020)
- the kind of ontological judgements we can reason about this concept or
relation (021)
This is where we put the cards on the table. What game are we playing?
poker? ... If we know the rules of the game and we know what a 4 of spade
is and we agree on practices that we will call "fair play", then we can
sit down
and have fun at the table. (022)
- the kind of expectations we have about what answers must be decidable
and computable (023)
How long do we play? how long does it take to find out if someone is
cheating?
w.r.t. ontologies, similar issues arise w.r.t. the practical aspects of
reasoning over
an ontology. If a particular kind of inference is theoretically
decidable but computationally
very expensive, then the ontology will not be practically useful. OWL-DL
is attractive
because we have reasoning engines that are just amazingly given the
theoretical
complexity of the problems they solve relatively quickly in most cases. (024)
>> 2) there is already a lot of solid work that has been done to
>> "formalize" these notions ...
>>
>> - NIST's Process Specification Language is another example, albeit
>> more limited in
>> scope
>
>
> Although the notion of an activity occurrence in PSL does capture one
> aspect of context, according to its designers the theory is intended
> to be a general, foundational theory of discrete processes. PSL is
> in my view perhaps the most mathematically rigorous ontology in
> existence, thanks mostly to the work of its chief author, Michael
> Grüninger (who is moving from NIST to the University of Toronto this
> fall) (025)
PSL is indeed awesome! Of course, one still has to define an inpretation
of PSL for a particular universe
and I believe this is where we have to make a number of ontological
commitments that ultimately
result in an axiomatic defintion of ?p in the universe is a PSL process
-- (process ?p) holds true. (026)
It's troublesome that in order to say that ?p has the properties
representative of what we consider is a "process",
we need, somehow, to have an idea of what a "proces" is before we can
recognize it. This is in part why
I think that to avoid the endless philosophical debates, we need a set
of pragmatic "boundaries" that will
keep the debate within a reasonable range of contention: (027)
- commitments (e.g., 3D, 4D, modalities, ...)
- grounding
- judgements
- performance (028)
>> - There's another "Bob Smith" ;-) who has a lot of interesting
>> things to say on the matter as well: http://ontology.buffalo.edu/
>> smith/
>
>
> This B. Smith is "Barry". :-)
>
>> 3) At the end of the day, what matters is to have an explicit
>> definition of what "context" is that is independently verifiable by
>> a third-party. To verify context claims, we need a simple way to
>> reach an agreement on the semantic meaning of a context definition.
>> This is sometimes more difficult to achieve with commercial systems
>> that might rely on proprietary systems & whose semantics might
>> change. Commercial enterprises have a role to play but I don't
>> believe we have yet established a synergetic symbiosis of academic
>> research, open-source practices critical for standarization /
>> reference implementations and proprietary systems that add a non-
>> functional value-added to the whole picture (if there's functional
>> distortion, then we're back to square one w.r..t. having to validate
>> proprietary systems or having our IP locked in a proprietary tool)
>
>
> A very cogent observation.
>
>> 4) Although formal ontology offers the intellectual "high-road"
>> approach to 'context' , 'situation', 'process', etc...there is, in
>> practice, a significant gap between how much of this can actually be
>> achieved with the current state of the affairs w.r.t. tools,
>> standards, validation suites, etc.. We don't even "apply" the
>> notions of context, description, etc... to talk about our own
>> semantic web technology, processes, etc...
>
>
> There is on-going work in the Common Logic project to fold in a
> semantic web oriented notion of context. The current CL ISO draft is
> available at (http://cl.tamu.edu/docs/cl/32N1238-WD24707-
> CommonLogic.pdf) but there are only vague allusions to context
> there. I will send out links to drafts of the current work as they
> become available in search of comments and in the hope that the work
> might prove useful.
>
Thank you very much for the info!
It is indeed very useful (at least to me).
I believe there is a significant potential
for practical solutions to the issues of
negotiating, defining and describing
context information w/ CL as a kind
of "lingua franca" for the neutral
exchange of information (e.g., my context vs. your context)
the semantics of that information,
and the reasoning and other problem solving
activities we need to do with this information. (029)
-- Nicolas. (030)
> Chris Menzel
>
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