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contex[s88,jmc]		Notes on contexts

holds(p,c)

value(e,c)

In the case of $holds$, we have little problem with the range, although
there might be some temptation to extend it beyond just two truth values
to some intensional entities.  In the case of $value$, the problem of
range arises immediately.  For many purposes, it can be short circuited to
some fixed set.  Maybe the range could itself be context dependent, and we
might imagine the range to be determined by some outer context, i.e. outer
to $c$.

However, the key question now is finding the simplest non-trivial
application of formalized contexts.  Maybe we can apply it to something
that Lakoff finds impossible for the objectivist viewpoint regarding
``The cat is on the mat''.

Here's a concrete simple problem to tackle.  Represent ``The cat is on
the mat'' by $holds(on(cat,mat),c17)$ and ``The mouse is on the mat''
by $holds(on(mouse,mat),c17)$.  Represent the general facts
about the tendency of cats to kill mice in some {\it suitable general} way.  Infer
$holds(future(dead(mouse)),c17)$ in by {\it suitable general}
 inference rules.  The italicized {\it suitable general} in the case of
the facts about cats killing mice means suitable for inclusion
in a general common sense database.  Thus it isn't suitable if it
can be shown that it is special to the example.  A similar criterion
is to be applied to the inference rules.  In both cases, some kind
of nonmonotonic reasoning is to be used, so that the generality does
not require the listing of exceptions.  However, the formalism must
tolerate exceptions, e.g. adding the fact that this cat is not hostile
to mice should cause the inference to fail without producing a contradiction.

Maybe we could get by with $holds(kill(cats,mice),c1)$, where $c1$
is a context in which the things that hold are things that
are habitual.

apr 23

We need to go from

holds(on(cat,mat),c1)

∧ holds(on(mouse,mat),c1)

∧ holds(eat(cats,mice),c0)

to

holds(will(eat(cat,mouse)),c1')

where  $c1'$ may be $c1$, but more likely it is $c1$ modified
in some way, e.g. by pointing out the previous assertions.
If we use an ultranatural deduction scheme we may be able to
go from

on(cat,mat) ∧ on(mouse,mat) ∧ eat(cats,mice)

to

will(eat(cat,mouse)),

but this involves the extension of logic corresponding to ultranatural
deduction, and a context is implicit (say $c1$).  Let's assume $c1$
refers to a particular situation in whicha specific cat, mouse, mat
and time are meant.

The formulation needs to be

a. general

b. elaboration tolerant

a. {\it general} meants that everything except $on(cat,mat)$ and
$on(mouse,mat)$ is in a form suitable for inclusion in  a database
of general common sense knowledge.

b. {\it elaboration tolerant} means tat the right thing happens if
we add any facts like

	1. this cat is friendly with mice

	2. the cat is stuffed to the gills

	3. the cat doesn't see, hear or smell the mouse

	4. the cat and mouse are porcelain figures

Remarks:

	1. Can we say

	$$mice=plural(mouse)$$

in a suitable context so that it follows that the sentence refers to
words and not things.  In the ``general English'' context the function
symbol $plural$ forces the desired interpretation.

	2. We are dealing with AI not the grammar of English or even
universal grammar.  We use English usage as a clue to how we want the
logic to work.