Thank you for your insightful response. I will respond
holistically.
One of the purposes of this email is to show(? or explore the idea)
that there is not a fundamental incompatibility between the perdurantist and
endurantist points of view - at least at the pragmatic level.
I should clarify some terms right now. I lifted
"ontological equivalence" from Gibson's phd thesis. I imagine it to
mean exactly what it says, an equivalence on the level of things that exist.
IMO this is too strong for the 3D-4D debate, since they each offer a
fundamentally different perspective on how things exist.
[MW] I agree with you. The two theories assert that different
sorts of things exist – spatio-temporally extended, or just spatially
extended.
I used the term logical
equivalence only in response to the preceding phrase.
[MW] heuristically I would expect logically equivalent to mean
that everything that could be said using one theory could be said using the
other. I don’t think this is true, so I think this is still too strong.
Admittedly it is a broad term, so let me delimit it by
instead using Definably Interpretable.
We can say that ontology A is definably
interpretable in ontology B, if the concepts of A may be
defined using B's lexicon.
[MW] Much the same as I have suggested, with an implicit “all”
before concepts. If it were just “some” concepts then you would be
with me.
For a more thorough exposition of this type of
"equivalence" people might want to refer to:
Brandon Bennet - Relative
Definability in Formal Ontologies - FOIS2004
I think a lot of the
apparent incompatibilities arise from choices that are orthogonal to whether
one is using a 3D or 4D point of view. For example, a 3Dist might have objects
that endure but have no notion of time, instead populating their ontology with
events which account for the change that an object undergoes. Though even such
a position can be mapped into an ontology which does admit time.
[MW] Actually a 4Dist might do the same, since one view of time
is one **** thing after another.
Ultimately, I suppose, my goal
is to show that this problem, while certainly real in the philosophical realm,
does not pose unsurmountable problems in ontological engineering.
[MW] I agree.
Particularly, if we focus on
what the axioms of a given ontology are positing, we may establish logical
equivalences which enable the interoperability we seek. At times, we may find
that we don't have full logical equivalence, but even partial semantic mappings
enable a lot of reuse and interoperability.
[MW] Exactly. Where
there is no mapping, the lost knowledge is, more or less by definition,
irrelevant in the other ontology. By the way I think interoperability is a good
word to use for what we are looking for.
Consequently, I would hope we
might shift focus more on how people are using the 3D or 4D views to answer
specific questions about their domains, and what things they might expect in
the reuse.
Imagine there are two
biological ontologies, one in 3D and the other in 4D. If the 4Dist wants to
reuse concepts defined in the 3D view, how might they extract the relevant
information? What types of contextual information are needed to reconstruct an
adequate picture? If i am developing a 4D ontology or 3D one, and if I want to
be sure I can interoperate with others, is there metadata that i need to keep
track of? I think these types of questions are pretty useful.
[MW] I’m not sure about meta-data, although that certainly
comes into play when you are translating between different formalisms (how was
that OWL statement rendered in CL). However, I expect that there is a high
level mapping between 3D and 4D that can be defined for those things that both
theories can say.
Now on some specific points:
[MW]you need to remember that this is written from a 3D
perspective. Strictly, 4D can say things that 3D cannot (no concern to a 3Dist
since they would not want to say them). So strictly this is a full mapping in
one direction and a partial mapping in the other. The other thing I notice
here is that the equivalence seems to be presented in terms of stage theory for
4D rather than perdurance theory (Hawley’s terminology). The stage theory
version of 4D has an infinite number of temporal slices linked by some sort of
“followed by” relation. Perdurance theory allows for objects that a
truly extended in time as well as space. The account above does not seem to
account for temporal parts that are not temporal stages, but aggregates of
them. [/MW]
Could you posit some things that appear to be untranslatable
into the other formulation?
[MW] I will try to remember some. Perhaps Pat H or Chris P could
help me out here.
I haven't had time to go through Hawley's book (you would think in this day
and age, access to information wouldn't be the limiter...) in
detail yet, except through excerpts on google books. Without actual axioms,
it's difficult to show that perdurance theories are definably interpretable in
endurance theories, but I am fairly confident it is doable. I haven't come
across anything that would suggest that it isn't. We would do well to
recall that most 3Dists also admit events, which are 4D entities with temporal
parts.
[MW] Of course, and some of them even use events for the lives
of objects, so they can really then do anything 4D can do (but of course then
why retain the 3D bit?)
[AH]some cl axioms
[MW] I don’t really follow that I’m afraid.
Can you give a clue as to what the variables/constants mean, and which is
which.[/MW]
What I was trying to do in the above is to place a restriction
on the types of relations a 4Dist would want to enforce.
The first snippet was stating that a particular relation was
a relation ranging over 4D objects. The second was to enforce that such a
relation requires a time argument.
[MW] Ah. But it doesn’t. That is what the 3D relation
needs to have (when did it apply). In 4D the relation would simply between the
states of the objects for which it was true, and the time element is derived
from the start and end time of the state. You would also need to know which
objects the states were temporal parts of of course.
I also neglected to include axioms for what
"temporal_part" might mean in such a perspective, which is absolutely
essential.
[MW] A temporal part is probably best seen as the intersection
of a period (or point) in time and an object (for the whole of its life).
For the record, i'm neither a 3Dist nor a 4Dist, i think
each perspective has advantages depending on the types of questions and
problems we're trying to answer.
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?
[MW]
Probably not at present, because most people developing an ontology pick one or
the other at the outset (or both as in BUFO for different sorts of things). The
interest comes when you want to interrelate existing ontologies and/or
use them together.[/MW]
Hehe. I was hoping to see how the 3D-4D debate has practical
implications for ontology interoperability. I have difficulty pinning down
these problems. Maybe it's still too early to be asking these questions...
[MW] Well as long as we are talking about interoperability, I
see no reason why this is not achievable. It would make a good research project
for someone.
Regards
Matthew West
Information Junction
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