Azamat and Dick, (01)
AA> These questions [about model theory] are caused by undervaluing
> the role of natural language in machine semantics.
>
> It is of use to remember that natural language is the most
> universal representation language. (02)
I have the highest regard for the value of natural languages and
their universality for all the purposes of human communication.
No artificial language ever defined can replace them. In fact,
I would claim that every artificial language so far defined
can, at best, replace NLs for just a tiny range of purposes. (03)
AA> There are no meaningful statements or rules in formal languages
> which can not be expressed in natural languages, but there is a
> multitude of significant statements and rules which can not
> be expressed in formal languages. (04)
I certainly agree. But those restrictions on artificial languages
are very important because they make it easier to implement and
use those languages within their limited range of usefulness. (05)
I would compare NLs to our human hands and artificial languages
to the various tools we use. We can turn a screw with our hands,
but a screwdriver is easier to use. We can break a stick with our
hands, but a saw makes a cleaner cut. We can measure distances
with our fingers and feet, but a ruler is more precise. For each
of those purposes, we can invent a special tool that is more
suitable, but there is no single tool ever invented that is as
versatile as our hands. (06)
AA> If semantic interoperability and translation imply exchanging
> invariant semantic patterns, it is about the semantics of natural
> language in the first place. For the real world semantic machines
> will be natural language machines. (07)
I claim that we can never achieve the goals of artificial intelligence
until we get our computer systems to "understand" natural languages
at some reasonable level. But even then, restricted languages will
still be important for many applications. (08)
Just look at the progress that was made in mathematics and physics
by the inventions of special notations for algebra, calculus, and
analytic geometry. Mathematical languages were designed as
supplements to NLs for supporting thinking, reasoning, and
communication by people with other people. (09)
RHM> ... everything I've read about [model theory] seems
> completely backwards. You take a sentence out of context,
> and imagine all the possible contexts which might be the
> actual context of that sentence. (010)
No. When logicians translate NL sentences to logic they
do exactly what you are doing with mKR: they make the
implicit context explicit by adding additional information,
which is also stated in some form of logic. (011)
RHM> I take exactly the opposite approach.
> 1. A proposition is created by a human being.
> 2. He/she has an actual context, within which
> he/she creates a sentence.
> 3. Every sentence has one actual context.
> 4. The aim of mKR is to express that one
> actual context. (012)
As a matter of fact, logicians make the same assumptions as
your #1, #2, and #3, and they have the same goal as your #4.
But they do so with notations that are more precisely defined
than mKR. (013)
For example, somebody might say "It is raining." The implicit
context of that utterance is the time and place of the speaker
and listener. A logician would translate that to some statement
in logic that says, in effect, "At time t and at location x,
rain is falling." (014)
That is what you have been doing with mKR. But most of us
in this forum have been complaining that your notions of
'space', 'time', and 'view' (and many other topics) have
been far too vague. (015)
What do you mean by space? A particular point specified in
a given coordinate system? Some extended region of space?
How is it specified? (016)
What do you mean by time? A point in time? An extended
interval? How is it specified? How do you relate time
and space in a 3D or 4D specification? (017)
What do you mean by view? A literal visual view, as
determined by a camera at a specific location with a
specific direction, focus, and resolution? A more
metaphorical notion? How do you define and specify it? (018)
Your descriptions have been far too vague to enable
two independent programmers to construct compatible
implementations of what you have been saying about mKR. (019)
John (020)
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