Re: SUO: Questions-comments about SUMO116.pprj: Concepts and Types
Adam,
> Do you have a formal definition in first order logic that you recommend for
> type and subclass that shows how these differ?
I'm afraid I haven't a formal definition. But the difference is pretty
clear to me (which is a start...):
1. A class (or a concept, e.g. Entity) is a set of slots (or
attributions, in Guarino's terminology, e.g. :location). A subclass of a
class is the given class plus one slot.
Example: Entity={}; Physical-Entity={:location}; Object={:location,
:mass}; ...
2. A type is an instantiated class. As most classes are defined by more
than one slot, depending on the order in which you instantiate them, you
generate different types, i.e. different typologies
Example: Say you want to define a typology of the class
Object={:location, :mass}. Do the following:
a. Fix the values of your slots (i.e., the attributes in Guarino's terminology):
:location = Location{Sky, Earth}
:mass = Mass(0, 1, 2}
b. Fix the (cognitive) order (what I call Priority) in which you want
your attribution to appear in your typology.
For Object={:location, :mass} there are two possible priorities:
Priority 1: :location < :mass
Priority 2: :mass < :location
c. Define your typologies:
Typ1, according to Priority 1: :location < :mass you have the
following hierarchy:
T1 (UniversalObject) where :location = Sky or Earth
T1.1 (Concentrated) where :mass > 0
T1.2 (Distributed) where :mass = 0
Typ2, According to Priority 2: :location > :mass you have the
following hierarchy:
T1 (UniversalObject) where :mass = 0, 1, 2
T1.1 (Celestial) where :location = Sky
T1.2 (Terrestrial) where :location = Earth
> I wasn't aware there was an ambiguity in the subclass relation, but I'd be
> happy to be made aware.
Well, I think that Object={:location, :mass} is not the same as T1
(either in Typ1 or Typ2). The former is a concept, just a bunch of
slots, the latter is an ordered and instantiated bunch of slots.
>
> Thanks go to Pat Cassidy for producing the SUMO in Protege version.
Thanks.
>
> Could you explain further the semantics of the ordering you propose? What
> does it mean to have "an order between the attributions"
> What does the priority signify? What inferences does it allow you to draw?
Well I would call it something like "combinatorial ontology". In
ordering your attributions (which, by the way, should be defined by
means of ordered categories, but this is another story...):
1. You implicitly state which dimensions of your World, at your level of
granularity, ontologically come first.
Example: Priority 1 encapsulates a Galilean view on the world, which
states that the location of an object gives you no clue on the type of
object you're considering (i.e. :location comes first), while the mass
does. On the contrary, Priority 2 encapsulates a Aristotelian view on
the world, which states that the mass of an object gives you no clue on
the type of object you're considering (i.e. :mass comes first), while
its location does.
2. You guess what attributions you loose first when using the set of
your attributions for jumping from your level of granularity to a lower
one.
I still have to spell out 1 and 2. I'm working on them right now.
Anyway, I'm convincing meself that priority is of primary importance in
(my reconstruction) of causal reasoning, because it bridges the gap
between the ontology and the epistemology of a phenomenological
representation (or descriptive metaphysical representation, in Guarino's view).
> That sounds very interesting. Have you already developed the 40 natural
> language definitions? If so, could you post them? We'd be happy to help
> formalize them.
ASAP: Let me get to a decent version of them...
It would be nice to have more feed-back.
But I'm off for today.
It's Friday!
Jos.