RE: SUO: questions about SUMO
Hi Michal,
Thanks for your message. See my comments below.
-Ian
<snip>
> Perhaps I did not express myself correctly. I understand that
> TimePoint is more than a RealNumber. I wanted to say this:
> 1) TimePoint is similar to RealNumber. In fact I think that
> everything what holds for instances of RealNumber holds for instances
> of TimePoint too. I do not claim that TimePoint should be a subclass
> of RealNumber (perhaps its not possible to crossover Abstract and
> Physical thing), but maybe TimePoint could inherit RealNumber's
> properties some other way.
To my mind, the relationship between 'RealNumber' and 'TimePoint' is the
same as the relationship between 'RealNumber' and any other unit of measure,
and this relationship is, I think, already captured in the ontology.
However, if you can specify some other relation that allows us to infer
additional, true content, we'll consider adding it to the SUMO.
> 2) Some axioms that say something about TimePoints holds for
> RealNumbers too, and are therefore missing in axiomatization of
> RealNumbers. For example, every TimePoint is greater or equal than
> negative infinity, between two distinct TimePoints there exists other
> distinct TimePoint, etc.
It may be that the axiom that every 'TimePoint' being greater than negative
infinity follows solely from number theory. Unfortunately, I don't know
enough about number theory to say one way or the other. If you can
construct a proof that derives the axiom from principles about the real
numbers, I'll try to make the axiomatization in the SUMO reflect your proof.
As for the claim that 'TimePoints' are dense, I don't think this follows
from what we have in the SUMO. Please let me know, though, if you think any
axiom or combination of axioms implies this.
>
> And finally, I would have another specific comment about SUMO
> content. I thing that the documentation of overlapsTemporally
> relation is somehow misleading:
>
> > (overlapsTemporally ?interval1 ?interval2) means that the two
> > TimeIntervals ?interval1 and ?interval2 have a TimeInterval
> in common.
> > Note that this is consistent with ?interval1 and ?interval2
> being the
> > same TimeInterval.
>
> It suggests that if we think the intervals as sets of TimePoints,
> they have nonempty intersection. However, the axiomatization of this
> relation:
>
> > (<=>
> > (overlapsTemporally ?INTERVAL1 ?INTERVAL2)
> > (or
> > (equal ?INTERVAL1 ?INTERVAL2)
> > (during ?INTERVAL1 ?INTERVAL2)
> > (starts ?INTERVAL1 ?INTERVAL2)
> > (finishes ?INTERVAL1 ?INTERVAL2)))
>
> says that ?INTERVAL1 is a subset of ?INTERVAL2 (in the set analogy),
> which is indeed something different. Am I right?
As I understand you, you're worried about the case of "empty time
intervals", i.e. intervals that have no points in time. If this is indeed
the worry, then I think we should just add the following axiom to the SUMO:
(=>
(instance ?INTERVAL TimeInterval)
(exists (?POINT)
(and
(instance ?POINT TimePoint)
(temporalPart ?POINT ?INTERVAL))))
>
> With best regards,
> Michal Sevcenko
>
> ----------------------------------------
> Ing. Michal Sevcenko
> Department of Computer Science
> Faculty of Electrical Engineering
> Czech Technical University in Prague
> Tel +420 2 2435 3661
> http://webis.felk.cvut.cz/en/people/sevcenm.html
>
>