On Mar 16, 2009, at 4:16 PM, Michael Gruninger wrote: (01)
> Hi Pat,
>
> Pat Hayes wrote:
>
>>
>> Ali Hashemi wrote:
>>
>>> I guess, if there are no serious errors in this email and the last,
>>> are there any practical considerations which might hinder such
>>> interoperability (aside from the non-existence of axioms thus far)?
>>> Is the 3D-4D debate really an issue for people developing actual
>>> ontology applications?
>>
>>
>> It is, because there really are some tricky problems in making the
>> various formal ontologies cooperate, and because both views have been
>> used in actual deployed ontology standards. So we really do have an
>> interoperability issue here. I don't say the situation is impossible,
>> but it is of more than purely theoretical or philosophical interest.
>
>
> What are the actual deployed ontology standards and where are their
> axiomatizations?
>
> I realize that ISO 15926 is always promoted as a 4D ontology, but it
> is
> not axiomatized. (02)
It is fairly tightly formalized, and one can map it into axioms. (03)
> One point of Ali's posting is that until we get a concrete fixed set
> of
> axioms for a 3D ontology
> and a concrete fixed set of axioms for a 4D ontology, we cannot say
> anything about whether
> or a semantic mapping exists or what such a mapping requires.
> (04)
Sure we can. (05)
OBO and its cognates, including DOLCE, follow the continuant/occurrent
division quite rigorously, so can stand for the "3-D" case. Though
this 3/4-D terminology is misleading, as the 4-D of course includes 3-
D entities. The key dividing line is between those who insist that
continuants are distinct from occurrents, and the rest of us. (06)
I am working with Barry and others right now to rigorously axiomatize
a mereology of continuants, and hopefully this will result in a
rigorous mapping between (axiomatizations of) the two frameworks. But
the basic picture of how to map between them is pretty clear, in
outline. The endurantists refuse to write terms of the form (at C t)
when C is a continuant. Rather than write (P (at C t)), they want to
write (P C t). OK, the perdurantist can take (P C t) to be simply a
shorthand for (P (at C t)): (07)
(forall ((Continuant C)(time t) P) (iff (P C t)(P (at C t)) )) (08)
Note, this axiom (or translation rule if you prefer) is obvious to a
perdurantist but anathema to an endurantist. Looked at the other way,
the endurantist takes this to mean that the perdurantist is really
talking about the lifetime of C, not C itself: (09)
(forall ((Continuant C)(time t) )(= (at C t) (at (lifetime C) t) )) (010)
and again, this is a translation axiom for the endurantist, who can
treat the apparently meaningless term as a shorthand for the longer
term; and for the perdurantist, this is harmless because for them,
(lifetime C) = C in any case: the occurrent/continuant split that this
function bridges is meaningless to the perdurantist. So if both sides
are willing to not gag when they see something apparently meaningless,
treating it as ugly sugar for something meaningful, then both can get
along. (011)
The hard part is social, getting each side to not gag when they see
apparent nonsense in their ontology. (012)
Pat (013)
PS. Obviously this needs to be extended to handle relations between
continuants and temporal assertions about non-continuant entities, so
the details can get a bit messy, but the outline is clear. (014)
> - michael
>
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