Wacek, (01)
My preference about formalisms of any kind is to minimize any
discussion of their "meaning" in any terms other than the ones
used to explain the formal operations. (02)
vQ> I mean, I agree to explain the meaning of a formula in IKL
> (or any other logic) by means of referring to the model. (03)
That is all the meaning that is relevant to understanding the
formalism. Anything else is a discussion about possible ways
of using the formalism for some application. (04)
vQ> In the particular case above, it seems clear to me that you
> take it wrong, and that Pat objects rightfully. (05)
Pat and I agree on the formalism. I think that both of us made
a mistake of using words outside the IKL framework when we were
responding to various questions and comments on this thread. (06)
Following is the passage in which I strayed over the line by
mixing talk about the use of the formalism with talk about the
formalism itself: (07)
JFS> 1. The IKL model theory defines an evaluation function Phi,
> which for any proposition p, determines a truth value Phi(p).
>
> 2. Inside a nested context, however, the proposition p could
> have a truth value that is different from the value Phi(p)
> that would be determined outside any nested context. (08)
I suggest that point #2 above be replaced with #2' below: (09)
2'. Some IKL user, however, might define a function TVal(p),
which, inside some "that-clause", could return a value T or F
that may be different from the value Phi(p). (010)
The function TVal(p) belongs to the user's ontology, not to the
IKL model theory. The people who state the axioms that define
TVal can say anything about it they please. (011)
In this sense, the ist(p,C) predicate is something defined by
John McCarthy, and Pat was explicating JMC's terminology. Pat
was not saying anything about IKL itself. (012)
John (013)
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