On 2/3/11 3:37 AM, Pat Hayes wrote:
> 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.
By way of a naive, as usual, question, I wonder if the above could not
be syntactically summarized as (02)
3. R(a@t,b@t) (03)
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