On Sep 12, 2008, at 1:11 AM, John F. Sowa wrote: (01)
> Dear Matthew and Pat,
>
> MW> The real difference is that 3D sees that what exists now is all
>> that exists, whilst 4D sees the past and the future as part of
>> what exists as well as the present. This is what it means to stand
>> outside time.
>
> I agree with that description, but you seemed to suggest that the
> notion of change does not exist in a 4d view, but I think that
> we were using different definitions of 'change'. (02)
Indeed. And of course, change occurs in the real world and is
described by both 3d and 4d ontologies, but in different ways. This
is so obvious that nobody felt any need to say it. (03)
>
>
> MW>> all spatiotemporal extents exist (at all times, but
>>> strictly independent of time).
>
> PH> Agreed, and a nice analysis. Putting the same point in logical
>> terms, the universe of discourse shouldn't be in a state of flux,
>
> I have no quarrel with that, but it has nothing to do with the
> definition of the concept of change. (04)
BUt that, unlike the 'concept of change' , is what the thread was
about until you introduced this irrelevant aside. I think you can take
it that most of us don't need elementary calculus explained to us
again, John. (05)
> According to the most common
> definition, if time slices at t=0 and t=1 are identical, there is
> no change.
>
> Another way to say it: if the partial derivative with respect
> to the time coordinate is 0, there is no change; otherwise, there
> is change in that region of spacetime. The existence of change
> does not imply that the global 4d universe is in flux. It just
> means that there is some region in the universe where the derivative
> with respect to time is not zero. (06)
Quite. (07)
>
>
> MW>> And interestingly, I again use possible worlds as an alternative
>>> to modal logic. Not that I object to others using modal logic, but
>>> I do not see that I am obliged inevitably to do so.
>
> PH> Again, I agree that this is the best approach. I think this is
>> widely accepted, by the way: John McCarthy made the same point many
>> years ago :
>> http://wwwformal.stanford.edu/jmc/modality/modality.html
>
> I believe that what John McC, Matthew, and Pat are recommending is
> very close to Dunn's semantics for modal logic. (08)
Not McCarthy or me, I am quite sure; and given his stance on 4d
extensionality, I doubt if Matthew is either. (09)
>
>
> Most AI work with "possible worlds" is actually based on metalevel
> reasoning about sets of propositions that describe those worlds,
> not with the worlds themselves. (010)
Wrong. It is based on  it actually uses  inferences made in a theory
which refers directly to the worlds. Any planner which has an explicit
notion of timeinterval or timepoint or 'situation' (as in sit.
calc., not situation theory) or worldstate or context, is reasoning
in a theory whose semantics is more Kripkean than Dunnian. (For an
early exposition of the relationship of situation calculus to Krikpe,
see section 4 of McCarthy & Hayes 1969.) None of this is based on
METAlevel reasoning about sets of propositions. Of course, like all
reasoning, it is PERFORMED by sets of sentences, but it is not ABOUT
them. (011)
> Starting with any Kripke model
> K=(W,R,Phi), where W is the set of words, R is the accessibility
> relation among worlds, and Phi is the evaluation function, those
> sets can be derived:
>
> 1. For each word w in W, define the facts of w as the set of all
> propositions p that are true in w: {p  Phi(w,p) = True}.
>
> 2. Define the laws of w as the set of all propositions p that are
> necessarily true; i.e., p is true in all worlds accessible from w.
>
> 3. Define the accessibility relation R(w, w') as True iff every
> proposition p that is necessarily true in w is also true in w'.
>
> This construction replaces every world in a Kripke model with a set
> of laws and facts in a Dunnstyle model. Any theorem that can be
> proved about a Kripke model is also true of the corresponding Dunn
> model. But Dunn's version is more *usable* because it makes the
> laws and facts available for further analysis and manipulation. (012)
Nonsense. Not only is Dunn's version not more usable, it is not in
fact used. The laws and facts are stated explicitly as sentences in
theories using Kripkestyle semantics. Check out any of the hundreds
of papers on planning using a situationcalculus style of
representation. (013)
> PH> John's way follows Dunn's theory and is based on intensional
>> descriptions. The far more commonly used view uses Kripke's
>> possibleworlds account of modalities. Kripke's is widely accepted
>> as the standard, and certainly gives a more usable semantics...
>
> Not true. Nobody actually implements "possible worlds" (014)
I never said they did. They implement systems which reason, using
formalisms which refer to possible worlds. Remember, we are talking
here about SEMANTICS, not implementation. (015)
> . What they
> implement and reason with and about are sets of statements of the
> laws and facts of those worlds. (016)
Yes, exactly. And the question is, what is the appropriate SEMANTICS
for those statements? Answer: they REFER TO possible worlds. They do
not refer to sets of sentences; they are not in a METAtheory. (017)
> Since the above construction can
> map any Kripke model into such sets, most people who implement such
> systems pay lip service to Kripke's version, but they actually use
> something that is much closer to Dunn's version. (018)
They  and here I speak as one of them  use Kripkestyle semantics
when doing semantic analysis. They do not, as a broad rule, use Dunn
style semantics. In fact, I do not know of any significant body of
work in AI planning based on Dunnstyle semantics. I believe you are
the only writer who argues for Dunn's model in this context. (019)
Pat (020)
>
>
> For further discussion of these and related issues, see
>
> http://www.jfsowa.com/pubs/laws.htm
> Laws, Facts, and Contexts
>
> http://www.jfsowa.com/pubs/worlds.pdf
> Worlds, Models, and Descriptions
>
> John
>
>
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