re: facts of reality, context, possible worlds

>I think our emails are getting too long (8 pages for the last one).

Agreed.

>   Therefore, I am temporarily ignoring most of the questions in your 
>last email, and focusing on the most important issues.
>
>1. RDF triples and facts of reality
>a. I said
>I tried to bridge the gap between the RDF document and the KR 
>document by associating RDF "sets of triples" with KR "proposition 
>list" with "facts of reality".
>b. You said
>I think that association might be mistaken, which may be giving us 
>so much trouble. Certainly one should not identify RDF triples with 
>'facts of reality'.
>c. My response
>If RDF triples are not related to the facts of reality, then they 
>have no value for anyone.

They are (hopefully) related, but they are not identical. The 
relationship between them is exactly what the model theory is about.

>The purpose of the Semantic Web is to provide man and machine with 
>easy access to the facts of reality.

I would characterize it somewhat differently. The purpose of the SW 
is to make propositional content available to machine processing on 
the Web. Indeed, most of the time, that content will *correspond to* 
the facts of reality; but those facts themselves cannot be accessible 
to machines. One cannot send a fact over an optic fiber; one can only 
send symbols; a syntax of some kind. Now, exactly how a formal syntax 
can specify real facts is a good question: as I said above, getting 
that correspondence clear is what model-theoretic semantics is about.

>
>2. context
>a. I said
>You are not getting rid of the context, you are making it explicit.
>b. You said
>Then it is no longer contextual. If I say 'it is raining' at 3 pm on 
>5 Dec 2002, then the time of my utterance is part of its context. If 
>I say 'it is raining at 3pm on 5 Dec 2002', then my utterance needs 
>no temporal context, and in fact it would be meaningless to ask what 
>its temporal context was, ie when it was true. As far as time is 
>concerned, it has been removed from the context space: its just 
>simply true or false. Making information explicit *removes* it from 
>the context.
>c. My paraphrase of 2b
>Context is all relevant knowledge not explicitly given in the statement.
>d. the KR alternative
>Context is all relevant knowledge,

The problem is that if you really mean 'all' here, then this is 
open-ended. It is usually impossible to state ALL relevant knowledge. 
Contexts, of course, are indeed often defined in an open-ended way 
like this, which is one reason why the concept is so blurry.

>and is explicitly specified in the proposition.  The details of 
>"proposition" are given in [1],]2].  For now, think of a proposition 
>as
>     at context { statement }
>For this particular example, here is an outline of the context 
>[3],[4] (you can add yourself to the context)
>     at view=tabula rasa {
>         definition of rain
>         definition of fall

Most natural-kind terms like this do not have definitions.

>         at space=some city, time=3 pm on 5 Dec 2002 {
>             rain do fall done
>         }
>     }
>
>3. possible worlds
>a. You said
>Of course there IS only one world, but semantics has to be concerned 
>not just with the way the world actually is, but with the ways that 
>it COULD be given what we are able to say about it. It is impossible 
>ever to say enough to pin down the actual world in full detail; and 
>since a reasoner has no access to the actual world other than 
>through sentences of the formal language, it has to as it were 
>survey the possible ways that the world might be, given what is said 
>about it. (You might find Tarski and Quine good authors to read on 
>this topic, they both have the issues very clear. I speak of course 
>as a disciple of theirs ;-))
>b. My paraphrase of 3a
>The real world is too hard, so we'll deal with imaginary worlds.

Bad paraphrase. The point is not that the real world is too hard, but 
that it is too large. So we have to deal with partial descriptions; 
and partial descriptions, by their very nature, allow other 
interpretations. There's nothing 'imaginary' about a misunderstanding 
arising from incomplete information.

>c. the KR alternative
>It is not necessary to pin down the actual world in full 
>detail.  You can select the appropriate level of detail, depending 
>on your purpose, and express it in KR propositions.

Sure, so KR is a syntax, as I suspected. In which case it needs a 
semantics. Just saying that it 'corresponds to the facts' doesn't cut 
it.

Pat

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