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Re: [ontolog-forum] Scheduling a Discussion [was: CL, CG, IKL and the re

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Sun, 13 Jan 2008 15:28:17 -0600
Message-id: <C6CBA351-A19B-417D-A151-570881B011E9@xxxxxxxx>
On Jan 13, 2008, at 1:15 PM, Pat Hayes wrote:
> ...
> McCarthy claims that and-distribution applies to both:
> (ist c  (p & q)) iff ( (ist c p) & (ist c q) )
> but there are certainly some cases of
> time-context where this fails, eg there was one
> day last year when I was (at various times) in
> five states, but I have never been in five states
> all at once. So apparently
> (ist thatDay (Pat in Mississippi)) & (ist thatDay (Pat in Kentucky))
> but not
> (ist thatDay ((Pat in Mississippi) & (Pat in Kentucky)))    (01)

Not so clear to me that this is a counterexample to and-distribution.   
Seems to me that one _could_ do the semantics of ist vis-a-vis  
temporal contexts so that something that is true with respect to a  
given interval t has to be true with respect to all subintervals of  
t.  On such a semantics    (02)

   (ist thatDay (Pat in Mississippi)) & (ist thatDay (Pat in Kentucky))    (03)

would be false.  Granted, in ordinary language, if you travelled from  
Mississippi to Kentucky on, say, January 5, one can say both that Pat  
was in Mississippi on Jan 5 and that Pat was in Kentucky on Jan 5.   
But one could capture this ordinary usage -- and preserve your  
intuitive data above -- by _defining_ a related notion ist* such that  
(ist* t P) just in case (ist t' P) for _some_ subinterval t' of t  
(which seems to be the semantics you are assigning to ist directly  
above).  and-distribution then rightly fails for ist*: it is  
unproblematically true that    (04)

   (ist* thatDay (Pat in Mississippi)) & (ist* thatDay (Pat in  
Kentucky))    (05)

and just as clearly false that    (06)

   (ist* thatDay ((Pat in Mississippi) & (Pat in Kentucky))),    (07)

Moreover, the reason for the failure would be analyzable in simple  
first-order terms as an instance of the general failure of    (08)

   (exists (x) (P x) & (exists (x) (Q x))    (09)

to imply    (010)

   (exists (x) ((P x) & (Q x))).    (011)

-chris    (012)

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