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Re: [ontolog-forum] CL, CG, IKL and the relationship between symbols in

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Mon, 31 Dec 2007 21:42:44 -0500
Message-id: <4779A8A4.1000802@xxxxxxxxxxx>
Pat and Chris,    (01)

I sympathize with your negative views about various proposals
for versions of context logic.    (02)

PH> Two points. First, it is absolutely not clear what counts
 > as a 'kind of context'. IMO the very idea of "context" is
 > so ill-defined as to be meaningless as an theoretical tool
 > of analysis.    (03)

Yes.  That is why I use the word 'context' in a very precise
way:  a context is a box (or other enclosure) that delimits
some statement or conjunction of statements that make some
assertion about the many different kinds of things that people
have called contexts.    (04)

CM> ... can you give an example of the sort of thing you think
 > CL/IKL can't represent but CG+box can?    (05)

I'll give an example, and I'd  be very happy if you can show
that IKL can represent it.  Consider the following sentence:    (06)

    Tom convinced Sam that it's impossible for
    a cow to jump over the moon.    (07)

To avoid getting into formal details, I'll put brackets around
parts of that sentence to show where the context boxes would go:    (08)

    [Tom convinced Sam that [it's impossible for
         [a cow to jump over the moon] ] ].    (09)

The outer box delimits the clause that says    (010)

    "Tom convinced Sam that p"    (011)

where p is a statement in a nested box that can be treated
as an unanalyzed unit when examining the outer clause of the
sentence.  The verb 'convince' is an intensional verb that
introduces some axioms (preconditions and postconditions)
about how p is related to Tom's beliefs before and after the
convincing.  And the beliefs would be in another context box,
which would be updated in the next time step (more context
boxes) as a result of the convincing.    (012)

The statement p has the form "not possible q" where q is
another statement "a cow jumps over the moon".  The box that
contains p requires different axioms about alethic modalities.    (013)

CM> A context logic would have to do the same [state axioms] for
 > the primitive syntactic apparatus it uses to represent contexts.    (014)

I agree, but I do not envision a single "context logic", but
a mechanism that allows open-ended sets of axioms for various
kinds of contexts.  Every intensional verb, such as 'convince',
'seek', or 'fear' (and there are thousands of such verbs), would
have a different collection of axioms that would specify how the
statements in the nested box were interpreted.    (015)

CM> Well, they *are* all different [languages], aren't they?
 > Each metalevel contains truth predicates and other appropriate
 > semantic apparatus for all the preceding levels.    (016)

Look at the English sentence above.  Each of the three bracketed
clauses is treated differently, but nobody says that they are
different languages.    (017)

CM> Seems like an opportunity to educate to me.    (018)

I agree.  The main question is whose terminology is more misleading.
My recommendation is to avoid the word "language" as too overloaded,
especially when you start using logics to represent NL semantics.
I prefer to talk about different metalevels with different axioms
for interpreting the nested levels.    (019)

CM> If they do, then you disabuse them of their confusion.    (020)

I realize that Tarski was not confused, but his unfortunate
choice of terminology creates confusion.  As I said, I would
replace his word 'language' with 'level' or 'metalevel'.    (021)

CM> Well, seems to me you get exactly the same thing at the limit
 > of the Tarskian hierarchy.  You get a single language that
 > encompasses all the finite 'levels'.    (022)

In that sense, I would agree.  But the simplest thing to do is
to talk about levels instead of languages.    (023)

John    (024)

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