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Re: [ontolog-forum] formal systems, common logic and lbase

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Sun, 25 Nov 2007 20:00:29 -0600
Message-id: <E2B4A543-A4B4-4FCE-AB3D-1E7363850676@xxxxxxxx>
On Nov 25, 2007, at 6:11 PM, rick@xxxxxxxxxxxxxx wrote:
> Yes, read them both. BTW - Do I have to pay to get access to CL now ?    (01)

We're waiting on ISO approval for the document to be made freely  
available.    (02)

>> They both give formal grammars and model theories of versions of  
>> first-order logic. They say nothing about axioms, they do not refer  
>> to "open ended schematic systems" (whatever those are: what ARE  
>> they, by the way?),
> Feferman doesn't say much about this. What he does say is "the  
> theory of operations employed is a version of the partial untyped  
> lambda calculus." He says a few other things that lead me to believe  
> he's thinking category theory...    (03)

Perhaps he is, but the untyped lambda calculus and its model theory  
can be fully characterized without any category theory (though folks  
who work in that extremely technical domain do avail themselves of  
category theoretic methods pretty freely).    (04)

>>> I believe Feferman's open ended schematic system implies  
>>> proposition b)
>>> and the evolution of formal systems towards logical environments.
>> What do you mean by a "logical environment"?
> Here's a pointer to the IFF logical environment, see figure 1 ...
> http://suo.ieee.org/IFF/metalevel/lower/ontology/ontology/version20021205.htm
>> BTW, the use of 'ascii-art' as in the above is best restricted to a  
>> non-proportional font. Your diagram is broken in any font I can  
>> find to view itin.
> Sorry, I put a graphic here ...
> http://www.rickmurphy.org/log-env.gif
> As I explained to Chris Menzel in a prior thread.    (05)

I'm afraid I never saw a response from you to my question about that  
graphic.    (06)

> This graphic represents a degenerate version of a logical  
> environment. Kent's, as referenced above is nicely done and well  
> developed in terms of transformations.
>> However, since it places CL and Lbase under something other
>> than 'Logics' (I'm not sure if its under 'Axiomatic' or "Natural
>> Language'), it is wrong, since these are in fact both logics.
> That's not what they say.    (07)

Then they (whoever they are) are wrong.  It depends on *exactly* how a  
logic is defined (there are several equally good notions), but CL is  
either a logic or a class of logics.    (08)

-chris    (09)

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