02@xxxxxxxxxxx> <4b7af923.0707d00a.3507.4772@xxxxxxxxxxxxx>
X-Mailer: Apple Mail (2.936) (01)
On Feb 16, 2010, at 1:59 PM, Matthew West wrote: (02)
> ....
> MW: The other thing that occurs to me is that there will also be a
> value for
> what I would call abstract theories that are not attached to any upper
> ontology, but are crafted so that they take on the characteristics of
> different upper ontologies when included. For example, you could
> have a
> Linean structure of living things that did not know about 3D or 4D,
> but
> could take on either flavour when incorporated into those theories. (03)
Yes indeed. I now think this is quite straightforward, at least if one
is willing to use ISO Common Logic. Here's a sketch. (04)
There is a high-level category which I will call 'STT' (spatiotemporal
thing). This is the class of all entities which occupy, or can be
located within, physical space, and last for a time. [1] The time can
be very short, a mere moment. We do not go into the question of what
'dimensionality' they have. Call the elements of STT, *stets*. Stets,
like everything else, can have all kinds of non-temporal properties,
relationships and so on. But they can also have time-sensitive
properties, and we have two ways to express those in CLIF. (05)
Consider an atomic sentence which expresses such a time-sensitive
relation; there has to be some way to include a temporal parameter
into the atomic expression. One way is to include it as a relational
parameter, increasing the arity of the relation by one. The relation
is then called a *fluent*, a term introduced many years ago by John
McCarthy: by convention, the last argument is always the temporal
parameter. Another is to associate the temporal parameter with the
term referring to the stet itself. We could introduce a special
function called 'at' to do this, so that (in CLIF syntax) (at S t) can
be read "S at t", but CLIF gives us an even neater option, which is
just to treat the stet name itself (more generally, the term referring
to the stet) as a function that takes a temporal parameter. Then for
example if A and B are stets, and R is a time-sensitive relation
between them, the two ways to say that it hold at time t are
(R A B t)
where R has become a a fluent, and
(R (A t)(B t))
where the stet names have become functions. Call the first the
*fluent* style, and the second, the *timeslice* style. (06)
Now, so far, this is just a notational variation. One could axiomatize
their equivalence in CLIF, with a bit of work. In CL, it is fine to
have the same relation with different numbers of arguments, or to
treat the name of a thing as a function. But the 3D versus 4D
doctrines come by imposing various constraints on this unified
picture, in two different ways. (07)
3D. This partitions STT into two disjoint subclasses, CONT and OCC,
and imposes a rigid constraint upon how the language is used: it
requires that elements of CONT are described using only the fluent
style and those of OCC using only the timeslice style. The
philosophical justification for this is often explained by the idea
that elements of CONT ("continuants"), are "inherently 3-D" in nature,
so to use the timeslice construction on them would be incoherent.
("Continuants cannot have temporal parts.") [2] (08)
4D. This takes the timeslice style to be the primary 'factual'
description for all stets; it does not recognize any partitioning that
indicates any distinction relevant for how temporal relations are
described. Depending on the particular ontology, it might treat fluent
style assertions as simply syntactic sugar for the corresponding
timeslice style assertion. On this view, all stets can be described as
4-dimensional, or at least embedded within a 4-dimensional space, with
three spatial and one temporal dimensions. (09)
Obviously, this simple picture needs some work to flesh out the
details, but I think it is essentially correct, and can be the basis
of a quite workable unified picture for this particular awkwardness.
One gets back to the unified top level from a "3D" ontology by
creating the class (CONT union OCC) and adding the axioms which define
the equivalence mappings between the two notational styles. To map in
the other direction, introduce a new class CONT, with appropriate
syntactic restrictions on how they are to be described, and a mapping
which we could call *blur* from a subset of ATT onto CONT, and its
inverse mapping *life*, which is already used in 3D ontologies as the
function from a continuant to the occurrent called the 'lifetime' or
'lifespan' of the continuant. (010)
Pat Hayes (011)
[1] As an aside, I find it *very* hard to understand how something can
be said exist in physical space without also existing in time. As the
proponents of the 3D view often claim that 4D is unintuitive,
unnatural, etc.., I sometimes wonder if they inhabit the same universe
that I do. Of course, if they do not, that would explain quite a lot. (012)
[2] It is easy to see how the partitioning may have been created by
the syntactic limitations of traditional FO notations, where relations
must have fixed arities. The two R's have different numbers of
arguments, so would have to be thought of as distinct. Where does one
use R1 and where R2? The question must be answered; so the syntactic
limitation forces one to impose a semantic distinction between kinds
of argument to the two relationships. (013)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (014)
|