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

To: "John F. Sowa" <sowa@xxxxxxxxxxx>
Cc: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Mon, 31 Dec 2007 00:31:35 -0800
Message-id: <p06230906c39e431dfc73@[]>
>I agree, but there is an issue about policy and terminology.
>CM> What makes a logic a context logic is that a notion of context
>  > is taken as a logical *primitive*.  What this means syntactically
>  > is that appropriate constructs (designed intuitively to express
>  > a notion of context) will be required elements of the language
>  > of the logic.  (An example is McCarthy's "ist" operator in his
>  > context logic.)
>In natural languages, different kinds of contexts tend to have
>very different axiomatizations, and people frequently make
>statements that relate different contexts in different clauses
>of the same sentence.    (01)

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. So I have no idea 
how a claim like this could possibly be substantiated. But even 
leaving that aside, if indeed a single sentence involves many 
contexts for its various clauses, then that is actually a 
counterexample to the notion of context logics, since it is a 
hallmark of a context logic that it relates an entire sentence to a 
context (in most cases, in fact, an entire theory is asserted "in" a 
context.) Context logics cannot handle finer-grained 
contextualizations than a sentence.    (02)

>  Any kind of context logic that is going
>to be used for analyzing and reasoning about NLs has to support
>something like that.    (03)

There are no context logics which support "things like that", as far 
as I know. Certainly the context logics described by McCarthy, Guha, 
Lenat and others, which use "ist" to relate contexts to sentences, do 
not.    (04)

>Common Logic does not support such things, and even IKL is too
>homogeneous to support them.    (05)

Well, its not clear what one means by 'support'. CL can *describe* 
such things axiomatically, and in fact we did so in the IKL work, 
using 'contextual names'. To me, this ability illustrates one way in 
which the IKL approach is superior to the use of a special context 
logic.    (06)

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