Pat Hayes wrote:
> In our IKL formalism we extend FOL (actually
> CLIF, but that is not important) with a
> proposition-naming construction written (that
> <sentence>), so for example
>
> (that (forall (x)(implies (P x)(R x a))))
>
> is the proposition which is true just when the sentence
>
> (forall (x)(implies (P x)(R x a)))
>
> is true, in any interpretation. Thus, the
> proposition that is denoted by the naming
> expression depends on the interpretation of the
> nonlogical symbols in the embedded sentence, as
> one would expect. (01)
I have a slight, and possibly unimportant, concern with the 'when'. (02)
In IKL, you have means to represent contextual content using the
relation ist (is true in). It is also possible to accommodate for a
name to name different entities in different contexts. Under a
particular interpretation, a particular sentence may name different
propositions. (03)
For example, if (04)
(not (= a b))
(= (tnb 'c' c1) a)
(= (tnb 'c' c2) b) (05)
then the sentence (06)
(p c) (07)
names different propositions in the contexts c1 and c2. It may be that (08)
(ist c1 (that (p c)))
(not (ist c2 (that (p c)))) (09)
The same sentence (p c) names different propositions in c1 and c2, and
these propositions are true and false, respectively. The concern with
'when' is that there is no apparent temporality here, and the contexts
need not be temporal -- it may be different speakers with different
understanding of 'c'. (010)
The 'when' would perhaps be more appropriate in cases such as (011)
(= (tnb 'a' t1) (tnb 'a' t2))
(ist t1 (that (p a)))
(not (ist t2 (that (p a)))) (012)
where (p a) does name the same proposition in t1 and t2, but the
proposition is true or false, depending on the (intended to be temporal
-- but how does ikl know?) context. (To be careful, I would perhaps
need to ascertain also that (= (tnb 'p' t1) (tnb 'p' t2)).) (013)
In other cases, 'where' would be better than 'when'. In general, 'is
true just when' would be better replaced by 'is true just in every context'. (014)
This relates me to my earlier comment on that logic is atemporal, even
if you accommodate for time in this or other way: all assertions happen
to be true at the same time (the real time of the interpreter), even if
a 4d model with time instants or intervals as separate entities is
adopted. Of course, unless you allow for time indexicals that would
allow the interpreter to connect the assertions to its real time, but
then you reach out of a fixed model (or the model must include the
interpreter); in that case, (015)
(ist #now (that (p a)))
(not (ist #now (that (p a)))) (016)
might both be true. (017)
vQ (018)
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