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Re: [ontolog-forum] Time representation

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Mon, 21 Jan 2008 02:18:09 -0500
Message-id: <47944731.7020906@xxxxxxxxxxx>
John B.,    (01)

Some answers to your questions:    (02)

 > 1. Is the interpretation of [Proposition: p'] true if p' is true
 > and false otherwise?    (03)

Actually, it's more primitive than that.  It's true if p' is a
proposition and false if p' is not a proposition.    (04)

In effect, a conceptual graph g is true or false by itself (just
as any formula in any version of logic).  But when you surround
g by a box with a type label, the only thing that is asserted
is that g is of that type.  (If it's not of that type, as in
[Situation: g], then type coercion causes g to be interpreted
as a statement of a proposition that describes the situation.)    (05)

That corresponds to what the QUOTE operator does in Lisp:  it
prevents the following expression from being evaluated.  In order
to force the evaluation in Lisp, it's necessary to use another
operator called EVAL:    (06)

    (EVAL (QUOTE s)) is equivalent to s by itself.    (07)

In conceptual graphs, the Asrt (assert) relation has that effect:    (08)

    (Asrt [Proposition: g]) is equivalent to writing g by itself
       on a 'sheet of assertion' (Peirce's term).    (09)

 > 2. What about the [Situation *s] graph? This is true if there
 > in fact existed a situation on 20 January 2008 that made
 > proposition p' true?    (010)

That concept node, by itself, simply says that there exists a
situation, and s is used to label it.  It maps to the following
formula in CLIF:    (011)

    (exists (s) (Situation s))    (012)

To say that there existed a situation on that date that made p' true,
you would write    (013)

    [Situation: *s p'] (PTim ?s "20 January 2008")    (014)

By type coercion, the concept node on the left would be expanded:    (015)

    [Situation: *s] [Proposition: *x p'] (Dscr ?s ?x)
       (PTim ?s "20 January 2008")    (016)

This says that there exists a situation s, there exists a proposition x
stated by the graph p', the description of s is x, and the point in time
of s is 20 January 2008.  Following is the corresponding IKL:    (017)

    (exists (s x) (and (Situation s) (Proposition x) (= x (that p))
       (Dscr s x) (PTim s "20 January 2008"))    (018)

 > 3. In the context framework you mentioned the other day, with the
 > triples, you defined (T1,X,T2) as a T1 = a bounded text, X = a
 > context, and T2 = axioms showing the relation of T1 to X.
 > What would be an example of an axiom that relates  p' to
 > (PTim ?s, "20 January 2008")? Does this simple example need any?    (019)

The graph p' would correspond to the text T1.  The situation s would
be the context X, in terms of which the T1 is interpreted.  The text
T2 would be some axioms stated in some version of logic (which could
be stated in conceptual graphs, IKL, or any other suitable notation)
that would say how the PTim relation is supposed to relate any
situation to any date (of which s and "20 January 2008" are examples).    (020)

John Sowa    (021)

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