At 12:04 AM -0500 1/14/08, John F. Sowa wrote:
>Pat, Chris, and Wacek,
>
>I had overlooked that axiom because in CGs, there is no
>explicit operator for 'and'. A CGIF statement is just a
>set of concept and relation nodes with no markers between
>nodes (even blanks are optional). The conjunction of two
>statements is just a bigger set of nodes.
>
>PH> McCarthy claims that and-distribution applies to both:
> >
> > (ist c (p & q)) iff ( (ist c p) & (ist c q) )
>
>I would accept it also, (01)
I fail to see any reason to suppose it is true,
however. Do you have any *argument* or
*justification* for adopting it? (02)
> and I agree with Chris and Wacek
>that the suggested counterexample that involves time and
>a collection of events is unconvincing. (03)
Why? The relationship between ist and ist* is
symmetrical. They are duals. We could adopt
either as the real meaning of 'true in a temporal
context' and then the other would be defineable:
and only one of these strategies gives McCarthy's
axiom (the other gives the dual axiom, ie
transparency under DISjunction.) So what
justifies the choice of one rather than the other
as fundamental? Is there any linguistic evidence
for this? (04)
>
>It is similar to the following example that has been cited
>since antiquity:
>
> A true sentence when stated in the past tense:
>
> "Liz Taylor had seven husbands."
>
> A sentence that was never true in the present tense:
>
> "Liz Taylor has seven husbands." (05)
The point however is that the context approach to
temporal reference does not allow tenses: it sets
out to replace them by context-reference. Instead
of 'had' one says (ist Past ...'has'...). The
actual inner sentences are always in a 'present'
tense (actually, are tenseless.) So intuitions
arising from tensed language need to be examined
very carefully. (06)
>
>Re use of the word 'context' in knowledge representation:
>
>If you want to go back to the Ur-etymology, the word refers to
>something that is woven together (as in textiles). But even in
>classical Latin, it had a metaphorical extension to a weaving
>of words. The two basic meanings from a typical dictionary
>(Merriam-Webster) are
>
> 1. The parts of a discourse that surround a word or passage and
> can throw light on its meaning.
>
> 2. Milieu or environment. (07)
It is no good quoting dictionaries in discussions
like this. There are FAR more notions of
'context' than this. McCarthy gives the following
examples: (08)
= a set of beliefs, a belief state
= a conversational setting in which words or
phrasings are used specially, such as when a
surgeon says 'scalpel' to mean, 'put the number 6
scalpel into my hand'
= the 'world' of a work of fiction, eg the 'world' of Sherlock Holmes
= a temporary assumption made during the search
for a proof, as when proving (if A B) by assuming
A and then proving B. (09)
>
>The first sense is the more basic, and I interpret the second
>as a derivative sense that takes in more of the surroundings
>than just the words. (010)
Maybe it is derivative lexically, but it has a completely different meaning. (011)
>
>My recommendation is the following:
>
> 1. If you don't like the word 'context', then don't use it. (012)
That is not the point. The point is that others
use it to justify bad scholarship, claim
originality for old ideas, and repeat old
mistakes. (013)
>
> 2. But if you do think the word is sufficiently useful to be
> applied to formal knowledge representations, then state
> a clear, precise definition that is within the range of
> meaning in a conventional dictionary (such as M-W or
> any other well-edited dictionary you prefer). (014)
There is no such definition, and McCarthy (IMO,
correctly) says so explicitly. The only
definition is the context logic itself. (015)
>
> 3. My own preference is to focus on the phrase "parts of the
> discourse" and to state a formal definition in terms of
> some mechanism for selecting a chunk of text.
>
> 4. That is what I did for conceptual graphs. (016)
Wait. What have CGs have to do with a discourse?
The NL notions of context all seem to arise in
some kind of conversational or discourse setting:
but logics aren't used in such settings. They are
used to make assertions, not to have
conversations with. (017)
> I defined a
> context delimiter (represented by a box) as a container
> for some text (a set of graphs) that states whatever is
> is true in a context (as in McCarthy's ist predicate). (018)
That is completely circular. You havn't said what
"true in a context" means. How can anyone judge
whether any such claim is true, when you don't
say what you are talking about? (019)
>
> 5. In a mapping to and from IKL, I would map the contents of
> the CG context box to an IKL sentence s in "(that s)".
>
>I don't really care whether IKL uses the word 'context',
>since I am using it only for a syntactic mechanism in CGs.
>But as I said, the semantics of the contents of the CG box
>can be defined by axioms stated outside the box (or outside
>the IKL that-expression in a translation of the CG contents). (020)
And what are some of those axioms? Or even ONE of them? (021)
Pat (022)
>
>John
>
>
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