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

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "doug foxvog" <doug@xxxxxxxxxx>
Date: Mon, 15 Mar 2010 18:13:28 -0000 (GMT)
Message-id: <23190.>
Pat Hayes wrote:
> On Mar 11, 2010, at 11:23 PM, John F. Sowa wrote:
>> Chris M wrote:
>> CM> As you note, a 3D ontology is in fact fully 4D -- "3+1 D" as
>>> you put it -- in the sense that time is not ignored (the way the
>>> "z-axis" of R3 is ignored in R2, say).  Rather, the difference
>>> between the two ontologies concerns how they conceive the relation
>>> between individuals and time.
>> Yes.  The difference between a 3D and a 4D ontology is not in the
>> geometry, because every point in a 3+1 D ontology can be mapped
>> to and from every point in a 4D ontology by an isomorphism.
>> The critical issues for ontology arise with the nature of individuals,
>> the question of temporal "parts" of individuals, and the nature of
>> changes to individuals.  Those go beyond the geometry of space-time
>> to the issues of how to represent physical things that reside, move
>> around, and change in that geometry
>> CM> ... the endurantist ontology doesn't "embed" isomorphically in any
>>> obvious way into the perdurantist ontology (unless, perhaps, you also
>>> introduce temporal parts into the endurantist ontology, which seems
>>> sort of self-defeating).    (01)

>> I agree.    (02)

>> CM? So what, exactly, are you proposing?
>> I am definitely *not* proposing any kind of embedding of a 3+1 D
>> theory into a 4D theory or vice-versa.
>> As many people who use a 4D approach have observed, it is possible
>> to exchange data among different computer systems based on different
>> ontologies.  But then we have to ask:  "How can they exchange names
>> of people and their addresses, dates of birth, etc., and use that
>> data successfully in systems that have different and inconsistent
>> theories about the nature of the individuals?"
>> What I am proposing, as I have said many times, is a lattice of
>> theories -- or at least a finite subset (hierarchy) of theories
>> that have actually been defined and stored in a repository).
>> To illustrate the issues, let me consider a particular individual
>> named Kermit.  Somebody who talks in ordinary English with a
>> 3+1 D ontology might make the following observations:
>>  1. At time t1, Kermit was an egg.
>>  2. Later, at time t2, Kermit was a tadpole.
>>  3. Later, at time t3, Kermit was a frog.
>> Another person who uses a 4D ontology might say that the individual
>> named Kermit has temporal parts.  His egg part has a range of times
>> that includes t1, his tadpole part includes t2, and his frog part
>> includes t3.
>> This example shows that the problem arises with talk about parts.
>> There is a simple way to avoid that problem:  don't talk about
>> parts.  Just talk in simple observation terms:
>>    at t1, Kermit egg.
>>    at t2, Kermit tadpole.
>>    at t3, Kermit frog.    (03)

The issue is how to phrase "at t0".  In broader terms, a basic issue
is how to state the context for various statements using an FO.  The
temporal specification can be interpreted as a context wrapper.    (04)

A 4D theory can interpret a temporal context in one way, while a 3+1 D
theory can interpret it differently.    (05)

For expressing statements using an FO, there seems to be a need for
specifying contexts -- not everything asserted in every knowledge base
using any ontology is consistent with everything else asserted in every
other knowlege base.  Contexts could be defined as distinct models; in
Cyc terms, they would be "data microtheories".    (06)

>> A theory that can express just these observations would be
>> very underspecified.  It couldn't express or reason about
>> the many things one might want to say about frogs and their
>> spatial and/or temporal parts.  But any data that can be
>> expressed in simple, observational terms can be shared among
>> more detailed theories that do detailed reasoning about
>> those observations.    (07)

>> But somebody might ask,...    (08)

> But the question I would ask is, how can you write that in FOL in such
> a way that you don't fall into one or the other of the 4D/(3+1)D
> frameworks? Put another way, how can one formalize this 'minimalist/
> neutral' way of talking? This isn't at all obvious.    (09)

> One way would seem
> be to have a temporally indexed hybrid logic, where entire sentences
> (tenseless and timeless) are associated with times, with the meaning
> 'this is true then'.    (010)

They need only be associated with contexts.  The interpretation of
what it means to be associated with a temporal context would be
different in 4D & 3+1 D theories.    (011)

> But then the sentences themselves have to be
> understood as written in 'presentist' language, so they quantify over
> entities which exist **at a time**, and there is no way to quantify
> over entities which, um, endure over several times, such as Kermit in
> the example. In fact, this whole "sequence-of-presentist-views" idea
> is, I strongly suspect, what gives rise to the whole warped idea of a
> 'continuant' in the first place. OR, you can give the same formalism a
> rather different semantics,    (012)

No single semantics can be given to such a context syntax (imho).  The
semantics would depend on the theory (3D or 4D) used.  Different semantics
would apply for different dimentionality.  Without assigning a syntax at
the FO level, the following issues should not come up.  In order to reason
about statements, instead of merely translating them, a dimentionality
would have to be selected.    (013)

> in which the successive sentences are
> considered to be about 3-d slices of a 4-d world, but then... you see
> where this is going. It really is extremely hard to come up with a
> single semantic picture or account which is neutral towards these two
> views of time. They are profoundly irreconcileable. (Your reassuring
> talk of 'frogs' begs the question, because the 4d view of what 'frog'
> means is fundamentally different from the continuant view of what
> 'frog' means. The two world-views are not talking about the same kind
> of frogs. Continuants are *logically impossible* in a 4-D world. )    (014)

> What we can do is give a single formal account which can be
> interpreted in either way, and I think this is the best we can do.    (015)

I agree.  Does someone dispute this?    (016)

-- doug f    (017)

> Pat    (018)

doug foxvog    doug@xxxxxxxxxx    (019)

"I speak as an American to the leaders of my own nation. The great
initiative in this war is ours. The initiative to stop it must be ours."
    - Dr. Martin Luther King Jr.
=============================================================    (020)

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