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Re: [ontolog-forum] Ontology similarity and accurate communication

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Thu, 20 Mar 2008 15:54:10 -0500
Message-id: <p06230902c40877992405@[]>
At 3:35 PM -0400 3/20/08, Patrick Cassidy wrote:
  There is an axiom provide by you during this thread which I would like to

    >> (forall (x (t Time) P)(iff (P x t)(P (x during t)) ))

 I have not seen the two different syntactic expressions:
    (P x t)   and  (P (x during t))
 Used together before.  The first suggests a 3D perspective, and the second
suggests a 4D perspective.

Yes, exactly. Think of this as a 'bridging' axiom, part of a translation specification, if you like.

OK, I'll come clean and tell you what I really think. There are a variety of notational options in combining a simple timeless assertion with a temporal parameter. One is to treat the time as a context, in effect attaching it to the entire sentence (or in IKL, proposition):

(ist t (P x y))
(ist t (that (P x y)))

another is as an extra relational argument, giving the 'fluent' style which goes naturally with continuants:

(P x y t)

and a third is to connect it to the object(s) being related, the relation then being naturally understood as a relation between time-slices:

(P (x at t)(y at t))

But in fact, these are really all just notational variations on a single theme. They amount to choosing where in the parse tree of the simple _expression_ to attach the parameter, is all. If we simply FORGET the philosophy for a second, then we can treat this as an arbitrary conventional choice, and think of them as all meaning exactly the same thing, and therefore equivalent. Then it makes literally no difference if you say "At t, its true that P holds between x and y" or "P is true of x and y and t" or "P holds between the t-slices of x and y" , as these all mean the same. As to what exactly x and y are in this, I don't really care what your favorite philosophical answer is. Choose the philosophy you like best: but then be prepared to have your head exploded by some of the things that you might have to read. Maybe this is what you meant by 'dimension neutral', but I don't like that way of describing it, as I see them myself as inherently 4-D. Attaching the temporal parameter 'higher up' the tree is just a handy shorthand convention useful at times; but there are some things

(Q (x at t)(y at t'))

that just cannot be said any other way. So we have to have the 4D picture as a kind of base case; and once we have that, we really don't need the others (all of which are based on highly questionable philosophical foundations in any case. Trying to make actual physical sense of the notion of 'continuant' is just about impossible.)

This is a 'unified' ontology. But note, the result would not be acceptable to a confirmed 3D modeler; it is for example incompatible with the OBO foundational ontologies or DOLCE.

  How would you describe the type that "x" belongs to?

Type?? Do you mean, what kind of thing is it supposed to denote? Anything with an extension in space and time. This seems to me to be a basic ontological category. I'd say that if you are a 3D man, think of it as the union of continuants and occurrents; if a 4D man, think of it as a 4D 'worm' or history.

  The way it is used in those expressions, it looks a lot like the
"dimension neutral object" that I suggested as a way of providing both 3D
and 4D perspectives in the same ontology.

 In my case, however, I did not
use the (x during t) _expression_, but created a type "TimeSlice" so that
time-slices (any temporal length) of 4D objects could be expressed in an OWL

Oh sure, any 2-argument function is basically trinary, so has to be re-manipulated to get it into a binary language like OWL.
   Is there a documentation somewhere that additionally explains the
intended meaning and use of that type (of which "x" is an instance)?

See above.
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