[protege-discussion] modal logics

[Thomas Schneider]

Hi Emmanuelle,

I'll try to give an answer from a logician's point of view. You might  
need to translate my OWL-Manchester syntax into  
Protégé-Frames syntax---or maybe  
someone else here can do this please?!?

On 29 May 2008, at 13:37, Emmanuelle Pellegrino wrote:

> Dear Colleagues,
>
> We are developing an ontology of architecture. The architect  
> conceives a project and thus not only existing real objects, but  
> virtual objects.
>
> Consequently, one puts the question to know how to treat modal  
> logics with Protégé.

Well, modal logics (ML) aren't so much different from description  
logics (DL), and I don't see why modal logics are necessary here:  
can't you say things about objects that aren't explicitly named in  
your ontology using DLs, too?

> In Protégé, one can put existential  
> or universal restrictions on classes ; these restrictions are of a  
> kind obligatory. To be member of a class, one must [necessarily]  
> have at least this or that (existential restriction) or only this or  
> that (universal restriction).
>
> For the moment, therefore, one can say :
> “Must have at least”; “must only have”
> “Must be at least”; “must be only”
> → character of necessity

Yes, for instance:

Human implies hasPart some Leg
Human implies hasAncestor only Human

> We would like to pass from the necessary field to the possible field.
>
> In other words, how to bring restrictions on classes which  
> don’t have all an obligatory character?
>
> And in complement, to express the opposite of the necessity,  
> contingency :
> “Not to have to be”
> “Not to have to have”
> → character of what is contingent (not-necessary)

 From your explanation, it seems to me that, by "opposite", you refer  
to the negation of necessity? So you don't seem to need any new  
modality, just some sort of negation. Suppose you want to express the  
"opposite" of

Animal implies hasPart some Leg ,

because not all animals *need* to have a leg. This means that there  
are animals that have no legs, hence the classes "Animal" and "not  
(hasPart some Leg)" are not disjoint. This requires quite some  
expressivity, for instance individuals in the terminological part of  
your ontology:

dummyIndividual implies Animal and not (hasPart some Leg)

What exactly do you want to express in your ontology?

> To express the possibility :
> “To be able to be”; “must not not to be”
> “To be able to have”; “must not not to have”
> → character of possibility

What's the difference between possibility and contingency in your  
scenario? From my abstract point of view, they look the same. An  
animal does not need to have a leg if (and only if) it is able to have  
no legs, which can be expressed by the previous axiom.

> And in complement, the opposite of the possibility, impossibility :
> “Not to be able not to be”, “Must not be”
> “Not to be able not to have”, “Must not have”
> → character of impossibility

Through the abstract glasses again, impossibility looks the same as  
necessity: If it's impossible that humans have no legs, it's necessary  
that they have a leg---and vice versa.

> In architecture, to put the question of the description of the  
> necessary or possible character of a restriction reverts at the  
> bottom raising the question of a combinatory of the possible. The  
> combinatory is the even fact of opening on possibilities. To combine  
> supposes to select in various paradigms each time a paradigmatic  
> element (one chooses this one or that one). Then the various  
> paradigmatic elements selected are connected. One places this  
> element in this place and this other at that one[1].

I'm sorry, I can't quite follow this explanation. What are you trying  
to say? I'd like to see concrete examples of what you want to express  
in your ontology.

Hope this has helped a bit.

Cheers

Thomas

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|  Dr Thomas Schneider                             
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