Monday, December 12, 2005
The issues related to having a common, widely
used, and available ontology
Footnotes 3 and 4 need further explanation see (in the future) à [ x ]
Some responses and notes:
From Geoff, developer of Intellidimension’s RDF repository
> can you explain what "completeness means" actually?
Since our (Intellidimension’s) reasoning is not complete, there may inferences that are licensed by the semantics of owl that we fail to make [1]. This also means that we can not claim that something is consistent based upon the absence of inconsistencies [2]. All of the inferences that we do make are of course sound. Description logics are carefully crafted to enable a decidable decision procedure, and as such they have to live with a number of restrictions. Some folks think that's a worthwhile trade off, while others don't.
We don't make a closed world assumption (and neither does RDF or OWL). Our core language does have non-monotonic features (e.g. negation as failure [3], aggregation [4]), but those features are not used in the rdfs or owl rulebases [5].
[...]
> so again do you have the SUMO ontology encoded in your repository...if so
> please tell me how many concepts there are in the SUMO. I really need
> this
> exact number so as to talk about the set of concepts.
>
I get 630 classes [6]with the following query:
import "/std/ns.rql";
var ds = new datasource("inet?parsetype=rdf&url=" +
server.urlencode("http://reliant.teknowledge.com/DAML/SUMO.owl"));
select ?c using #ds where {[rdf:type] ?c [rdfs:Class]}
And I get 277 properties with the following query:
import "/std/ns.rql";
import "/std/owl.rql";
var ds = new datasource("inet?parsetype=rdf&url=" +
server.urlencode("http://reliant.teknowledge.com/DAML/SUMO.owl"));
select ?c using #ds rulebase owl where {[rdf:type] ?c [rdf:Property]}
-Geoff
******
Note from Paul ..
Excellent, so there are 630 classes and 277 properties in SUMO. These classes are organized under one subsumption tree.
(Which query language does RDF Gateway use? < answer to be posted here>)
Are there more than one type of property? How many types of properties are there?
Is there any other kind of ontology element, other than properties and classes?
What I am looking for is a statement like:
There are n of things of type a, m of things of type b, and the things of type b can be partitioned into q categories. . . . etc
where at the end of this short description we can all agree that what is stated is in fact perfectly true about SUMO.
Then we can list the things that are mentioned into sets:
the set of all classes (without any properties or subsumption relationships)..
the set of all properties (these are properties that might be used in more than one instance, the property of subsumption "s" might occur in < a, s, b > and in < d, s, r >. But a query would allow one to ask for all "classes" that was in the range of the property "s", ie existed as a third element in the RDF triple.
The query's return would include { r, b }.
But there is a category formation that truncates the "meaning" of the two triples < a, s, b > and < d, s, r > by returning only the information { r, b } in response to this query.
Is everyone following this "aspect of category theory?"
[1] Geoff’s language here is nice. An ontology’s “logical constructions” “licenses a set of inferences. This would be the same as saying that the axioms of geometry license the theorems that one derives from these axioms (using a specific set of inference rules. ) “Licensed by the semantics of OWL, refers to a specific instance of a completed OWL ontology.
[2] That one can compute the fact that there are no inconsistencies in a specific OWL ontology allows one to prove that the software will not fail to deliver an answer. In many specific cases, such as where the system modeled can be properly modeled as a closed world (ie all entailment has been captured in a logically consistent fashion), then this type of theorem proving may provide an assurance that “truth” will be found by the computational processes initiated by a query or reasoner.
[3] I think this means that an query that cannot return will be considered a failure of the query.
[4] I am not sure what this means to Geoff… we will get an explanation and post here
[5] I do not follow what is being said here. It would be good to develop a better, more full, explanation. I used the phrase “closed world assumption” to suggest that the reasoning was “complete”. I am not sure that Godel’s results on the formalization of arithmetic in terms of classical (first order predicate) logic implies (correctly) that Full OWL uses the closed world assumption. But that is what the language closed world assumption means to me. I am open to correction here – as it does seem that the language is not understood the same by myself and by others.
[6] Note, that Adam Pease send a communication to us [297] and identified that the SUMO ontology that Intellidimension uses is one of the first versions, and that there are now over 1,000 concepts. The current number of concepts, properties, assertions and axioms will be reported in 297 when we get that information.