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Re: [ontolog-forum] Foundation ontology, CYC, and Mapping

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Thu, 18 Feb 2010 21:33:44 -0600
Message-id: <D2400A85-E10F-4DB9-90C0-6C97B9D84851@xxxxxxx>
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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)

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