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Re: [ontolog-forum] Scheduling a Discussion [was: CL, CG, IKL and the re

To: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Patrick Cassidy" <pat@xxxxxxxxx>
Date: Thu, 3 Jan 2008 02:38:25 -0500
Message-id: <00bd01c84ddb$a043beb0$e0cb3c10$@com>
  Concerning your comment:    (01)

[Pat Hayes] >> If anyone can
> suggest a single axiom which relates propositions or sentences to
> contexts, and is true both when this means the proposition is true at
> or in that time, and also when it means the proposition is entailed
> by a set of beliefs, I would be delighted to be shown it. I have made
> this challenge repeatedly to proponents of 'contexts' for many years,
> and have yet to be given an answer.    (02)

I suspect this isn't quite what you had in mind, but it seems relevant here:    (03)

I use for my own purposes a very simple notion of "Context" reflecting a
similar attitude to what you express:    (04)

> Thus, the term "context"
> has no single meaning: it is used simply to refer to anything (or
> sometimes everything) which can influence meaning but which is
> outside the scope of the current theory. It is always defined
> negatively    (05)

Which, as I understand it is similar to the view describe by Graeme Hirst in
his paper "Context as a Spurious Concept":
duzSzpubzSzghzSzHirst-CICLing-2000.pdf/hirst00context.pdf    (06)

But contexts, whatever they are, have to be dealt with.  With a general
relation "isTrueInContext" and reified statements (here without the "that"
operator, for simplicity), one can then use time intervals, events,
situations, belief systems, fictional, hypothetical, counterfactual, or any
other situation that can affect the truth of a statement and call it a
    (isTrueInContext (livesIn SherlockHolmes London) SherlockHolmesStories)    (07)

Such "ist" statements can be nested to any level:    (08)

    (isTrueInContext (isTrueInContext (livesIn SherlockHolmes London)
Year1887) SherlockHolmesStories)    (09)

 . . .  or one can create an aggregate context (reified here for simplicity)    (010)

    (isTrueInContext (livesIn SherlockHolmes London)
Year1887inTheSherlockHolmesStories)    (011)

What that means is that anyone is free to assert any time interval, belief
system, etc., or combination thereof as an instance of the Type "Context".
Cyc defines 12 independent "dimensions" of context, and I can visualize
other dimensions as well.    (012)

The problem is that in general, what is true in one context (thus defined)
is not necessarily true in any other context.  That makes it hard to use
*any* assertions outside a context, if it is only explicitly specified to be
true in that context.  A lattice of theories or contexts will, of course,
allow any given context to inherit some assertions from an included context.
One special thing about time intervals as contexts is that, assuming that
one is dealing with the "real world" as the outermost context, what is true
in a particular time interval has a definable probability of being true in
subsequent time intervals.    (013)

So if we have:
  (isTrueInContext (hasLocation PodunkCentroid Lat40Lon80) Year 2000),
. . . one can specify a probability (in this case fairly high) that the
  (isTrueInContext (hasLocation PodunkCentroid Lat40Lon80) Year 2001)
. . . is also true (i.e., if the town doesn't expand that year).
The probability in this case can be derived from the historical observations
on how often cities (perhaps finely classified) change their geographical
boundaries.  Buildings may also move (large ones less often).  Mountains are
a lot less likely to move.    (014)

Each assertion for each different type of relation and object will have a
different function describing the probability that it will remain true over
time, but some regularities will be recognizable (e.g. the density of pure
water at a certain temperature and pressure is likely to be the same
forever).  People move around a lot, so the location of a person can only be
relied on within regions that expand as fast as a car or plane can move -
though more information or probabilities will reduce the likely rate of
change.    (015)

Finding some general way to reason with such a notion of context when more
than one context is of interest is a problem for which I have no idea at
all, other than (for time contexts) to specify in the ontological definition
of each type of entity how rapidly specific assertions may lose their truth
value over time for that type of thing.  This sounds like a lot of work, but
it is in fact what people learn as their understanding of the world grows,
and it enables them to make "commonsense" predictions of what will be true
later from what is true now.  I am not at all sure that we can avoid
representing that kind of detail, unless we are using only a specific
application that doesn't need it.    (016)

PatC    (017)

Patrick Cassidy
cell: 908-565-4053
cassidy@xxxxxxxxx    (018)

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