On Jun 17, 2014, at 6:51 AM, Tara Athan <taraathan@xxxxxxxxx> wrote: (01)
> On 6/17/14 1:03 AM, Pat Hayes wrote:
>>> Using the IKL “that” operator and a “during” relationship and the concept
>“July” (a ‘calendar month’):
>> Whoa. No, this is NOT the right way to do it. In fact, this is meaningless.
>According to the IKL semantics, (that (employs C P)) denotes a fixed
>proposition which is true or false. There is no room for any time-dependent
>variability in its truth value, or for making it depend on some other
>parameter.
>>
> It may not be the *best* way to do it, but I don't agree that it's wrong
> or meaningless. (02)
Yes, you are right, and I withdraw my strong statement. It is indeed one way to
do it. (It is exactly how we coded so-called "context" logic in IKL, in fact,
using 'ist' rather than 'during' and contexts rather than times.) (03)
What I will claim is that it is wrong to claim that one *needs* the 'that'
operator in order to handle time-variation properly, however. The conventional
ways need only conventional reasoning and have a better logical foundation, as
well as being widely used already. (04)
> Using the proposition (that (employs C P)) as an
> argument in a relation is not obstructed by its denotation of a fixed
> proposition which is true or false (in any given interpretation).
>
> Starting off without quantifiers:
>
> (cl:comment 'C employs P'
> (employs C P) )
>
> (cl:comment 'It holds during time interval T that C employs P'
> (during (that (employs C P)) T )
>
> Nothing wrong with that - the truth values of these sentences are
> independent of each other.
>
> Now bring on the quantifiers to relate the two
>
> (forall C P
> (if
> (cl:comment 'C employs P'
> (employs C P) )
> (exists T
> (cl:comment 'It holds during some time interval T that C employs P'
> (during (that (employs C P)) T )
> ) ) )
>
> Some users may find this clearer than the polymorphic representation.
> Why not let them use it? (05)
Well I am hardly in a position to prevent anyone doing anything :-) . But I
will resist the idea that this kind of construction is *necessary* in order to
handle time-relative assertions. (06)
> It is still possible to have the polymorphic representation behind the
> scenes for reasoning purposes.
> (forall C P T
> (iff
> (cl:comment 'It holds during time interval T that C employs P''
> (during (that (employs C P)) T )
> (cl:comment 'C employs P during time interval T'
> (employs C P T)
> ) )
>
> Also, using the "that" operator for temporal context (07)
"temporal context" ? Blech. call them what they are, time-intervals. That
"context" word does nothing but add confusion and muddle. (08)
> is a gateway to
> using it for other contexts/modalities.
> I find the symmetry appealing:
> (cl:comment 'It holds before time interval T that C employs P'
> (before (that (employs C P)) T)
> (cl:comment 'It holds after time interval T that C employs P'
> (after (that (employs C P)) T ) (09)
> (cl:comment 'It is possible that C employs P'
> (possible (that (employs C P)) )
> (cl:comment 'It is forbidden that C employs P'
> (forbidden (that (employs C P)) )
> (cl:comment 'Jane believes that C employs P'
> (believes Jane (that (employs C P)) )
> (cl:comment 'Omar knows that C employs P'
> (knows Omar (that (employs C P)) )
> (cl:comment 'Maria asserts that C employs P'
> (asserts Maria (that (employs C P)) ) (010)
These look cute but all they do is put the entire burden of representing their
meanings on the relation names (possible, forbidden, knows, etc.), and
implicitly make a claim that the relevant concepts (possibility, prohibition,
knowledge,..) are indeed properly representable as relations between
propositions and something else. In some cases, I think this is at best
doubtful: possibility for example is usually thought of as a modality rather
than a relation. (011)
And in any case, none of this has any actual content until one gives axioms for
these intended meanings. One needs to mirror all the conventional inferences in
explicit axioms. For example, from P being true at T and Q being true at T, it
should follow that (and P Q) is true at T. In the conventional ways of writing
time-dependent statements, this follows trivially from notmal logical
reasoning, but here it needs to be stated by quantifying over propositions and
by having a function on propositions which mirrors conjunction: (012)
(forall (P Q)(iff ((AND P Q)) (and (P)(Q)) )) (013)
(forall (P Q)(iff (during (AND P Q) T)(and (during P T)(during Q T)) )) (014)
and similarly for all the other connectives. I leave handling "inner"
quantifiers as an exercise for the reader :-) (015)
Pat (016)
PS. BTW, did I ever send you my ideas on how to reduce IKL to CL by eliminating
"that" constructions recursively? I would be interested in your reactions. (017)
> ...
>
> Tara
>
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