Pat, you wrote:
In fact, with a bit of extra work one can embed almost all the
necessary temporal reasoning into a generalized unification algorithm which
extracts temporal constraints during the unification process. I have all the
details somewhere if you (or anyone else) are interested. (01)
Please do send me the "details" about the "generalized unification algorithm
which extracts temporal constraints within the unification process". I am
very interested in such material and references. (02)
Thanks for the offer,
-Rich (03)
Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5 - 5 7 1 2 (04)
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pat Hayes
Sent: Thursday, February 03, 2011 1:38 AM
To: ian@xxxxxxxxxxxxxxxx; [ontolog-forum]
Subject: Re: [ontolog-forum] 3D+1 (was presentism...was blah blah blah) (05)
Ian, here's a non-philosophical way to characterize it. Start with an atomic
sentence of the form R(a, b), with no time involved, and suppose that a and
b here are ordinary uncontroversial physical objects, say. Intuitively, they
are 3D things. Now add time, t. Where do we put the time parameter? Several
answers can be given. (06)
1. Attach it to the sentence, meaning that the sentence R(a,b) is true at
the time t. This gives you a hybrid or context logic where the times are
possible temporal worlds/indices or contexts, to which truth is relativized.
But the sentences being so relativized do not themselves make any reference
to time. Call this 3D. (07)
2. Attach it to the relation as an extra argument, and call the relation a
'fluent': R(a, b, t) This gives you the classical AI/KR approach which used
to be called the situation calculus, where one quantifies over times in the
KR language itself, but the object terms are still thought of as denoting 3D
rather than 4D entities. Call this 3D+1. (08)
3. Attach it to the object terms (using a suitable function, written here as
an infix @): R(a@t, b@t) This requires us to make sense of this @ operation,
and it seems natural to say that it means the t-slice of the thing named,
which now has to be re-thought as a 4D entity. So the a, b things have
morphed form being 3D (but lasting through time) to being genuinely 4D, and
having temporal slices or parts. Call this 4D. (09)
For some folk this last step is apparently mind-boggling, although to me it
is puzzling how one can think of something being 3D and also extended in
time and have it *not* be 4D. For yet other people (think OBO), there are
apparently two kinds of thing in the world, one kind (continuants) which
must be described using the 3D+1 style , the other (occurrents) which should
be described using the 4D style. God alone knows why anyone would believe
that there are two ways to exist in time, but there's nowt as queer as folk,
as someone's grandmother used to say. (010)
What I like about this way of contrasting the options is that it makes it be
simply a matter of syntax - where in the sentence to attach the temporal
parameter - and not one of metaphysics. Syntax is way easier than
metaphysics. It also means that one can see quite clearly how to make the
various formal techniques work together, by allowing the temporal parameter
to 'float'. In fact, with a bit of extra work one can embed almost all the
necessary temporal reasoning into a generalized unification algorithm which
extracts temporal constraints during the unification process. I have all the
details somewhere if you (or anyone else) are interested. (011)
Pat (012)
On Jan 27, 2011, at 11:19 AM, Ian Bailey wrote: (013)
> Thanks John,
>
> So in a 3+1 approach, when they actually "cut some ontology code", if I've
> understood you correctly, I'm guessing they timestamp the properties and
> relationships ? This contrasts with a 4D approach where the Individual is
> sliced up into temporal stages and the properties are associated with the
> stages (apart from those properties that apply to the whole-life
> individual).
>
> If I've got that right, then 3+1 is the approach the oil and gas folks
used
> in late 80s early 90s on EPISTLE and the first drafts of ISO10303-221. Am
I
> in the right ball park there ? Matthew ?
>
> Cheers
> --
> Ian
>
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F. Sowa
> Sent: 27 January 2011 17:05
> To: ontolog-forum@xxxxxxxxxxxxxxxx
> Subject: Re: [ontolog-forum] 3D+1 (was presentism...was blah blah blah)
>
> On 1/27/2011 11:17 AM, Ian Bailey wrote:
>> I get 4D, finally, after years of hanging on Chris and
>> Matthew's coattails, but the 3D+1 thing is a mystery.
>
> The basic issue is the definition of a physical object
> and its relationship to a privileged time called 'now':
>
> 1. In 3+1 D, which is the implicit assumption in ordinary
> language, an object (human, animal, plant, or artifact)
> comes into existence at some time t1 (e.g., birth),
> ceases to exist at some time t2 (e.g., death), and
> for each now between t1 and t2, all parts of it
> exist together now.
>
> 2. In 4D, a physical object extends over a 4D volume, whose
> lower and upper time coordinates are t1 and t2 and whose
> spatial coordinates trace out a volume that spans the
> object's travels.
>
> 3, In 3+1 D, the object undergoes various changes, which
> cause some properties to become true or false at different
> times called now.
>
> 4. In 4D, the object doesn't change, but it has time-dependent
> parts (slices or stages) at which various properties may be
> true or false.
>
> The analogy I prefer (since I studied fluid mechanics at one
> time in my life) is between Lagrangian and Eulerian coordinate
> systems for representing and computing fluid flow:
>
> 1. Lagrangian coordinates are like a 3+1 D system: the
> observer follows a particular parcel of fluid as it moves.
>
> 2. Eulerian coordinates are like a 4D system: the observer
> sits on the side and watches the flow of all the fluid
> as a whole.
>
> In our ordinary language, we talk about our bodies in Lagrangian
> terms. We observe our own motion through space and time, and
> relate everything else to where we are *now*.
>
> An Eulerian system is like a God's eye view of the universe.
> God sees everything spread out in all dimensions of space
> and time. There is no privileged point of time or space.
>
> John
>
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