On Feb 4, 2011, at 4:03 PM, Rich Cooper wrote:  (01)
> 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.
>
> 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) 
The only write-up is in a final report to the Army written in 2004. I've put a 
copy here:  (03)
 http://beta.ihmc.us/users/phayes/Trickledown2004.pdf  (04)
feel free to use it. The Army didn't think enough of it to continue funding the 
project, so its been languishing since then.  (05)
Pat  (06)
> 
> Thanks for the offer,
> -Rich
>
>
> Sincerely,
> Rich Cooper
> EnglishLogicKernel.com
> Rich AT EnglishLogicKernel DOT com
> 9 4 9 \ 5 2 5 - 5 7 1 2
>
> -----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)
>
> 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. 
>
> 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.
>
> 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.
>
> 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.
>
> 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. 
>
> 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. 
>
> Pat
>
>
> On Jan 27, 2011, at 11:19 AM, Ian Bailey wrote:
>
>> 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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