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

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Chris Menzel <cmenzel@xxxxxxxx>
Date: Sun, 30 Dec 2007 11:55:08 -0600 (CST)
Message-id: <alpine.OSX.1.00.0712301128010.11105@xxxxxxxxxxxxxx>
On Sun, 30 Dec 2007, John Black wrote:
> on Thu. Dec. 27, 2007 at 11:28 AM, John F. Sowa wrote:
> JS>I agree with the points that Chris and Pat made about contexts,
>> but I'd like to add a few comments.
>> JB>> I had thought that time was yet another type of context. Is it
>>>> different somehow?
>> PH> You CAN treat time as a context, if you like contexts. But that
>>> is not the only way to tackle a logic of time: the modal temporal
>>> logics pre-date context logics by about 60 years.
>> I agree.  A context approach to time can be reduced to a
>> noncontextual approach by adding an extra argument for time to every
>> relation.  For example, consider the sentence
>>    At time t, the cat Yojo was on a mat.
>> In a context approach, you could translate that to a conceptual graph
>> of the following form:
>>    [Time: *t]<-(PTim)<-[Situation: [Cat: Yojo]->(On)->[Mat] ]
> And this is one of the main attractions for me about Conceptual
> Graphs. The enclosing 'Situation:' concept looks a lot like a context
> to me. But CL and thus CGIF are not "context logics". What does it
> take to make a logic a context logic if not just that you can express
> such contexts?    (01)

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.)  On the
semantic side, the meanings of those constructs will be *fixed* in every
interpretation of the language.  Ideally, there will then be a complete
proof theory for the language, i.e., a proof theory whose theorems are
exactly the sentences of the language that are true in every
interpretation of the language.  CL and CGIF and not context logics in
this sense.  However, in both it is of course possible to formulate
axiomatic *theories* of contexts, just as it is possible to formulate
theories of numbers, sets, or physics.    (02)

> The other big attraction of CGs to me is the attractive possibility
> that the graphical display of CGs may facilitate the solution of
> certain types of reasoning problems. I am particularly interested (for
> no particular practical reason, just am) in the possibility of
> reasoning about the kind of knowledge problems described in "Reasoning
> About Knowledge" by Fagin, et al.
> http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=8240
> If I did this right, it means: a person *j knows that a person *h knows that
> he, *j, knows that Yojo the cat is named "Yojo". Textually, it gets very
> complicated to look at. Would it be simpler for a human if this was visible
> graphically?    (03)

That's of course a matter for psychological research.  There's been a
fair amount of work on graphical reasoning where an answer to the
question might be found.    (04)

> And does it make any difference to a machine?    (05)

None, surely, with respect to all the well-known theoretical limitations
on automated reasoning, as those limitations are all
representation-independent.    (06)

Chris Menzel    (07)

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