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

To: "rick@xxxxxxxxxxxxxx" <rick@xxxxxxxxxxxxxx>
Cc: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Tue, 27 Nov 2007 11:03:12 -0600
Message-id: <p06230901c371fa83adc7@[]>
>Christopher Menzel wrote:
>>  On Nov 25, 2007, at 6:10 PM, rick@xxxxxxxxxxxxxx wrote:
>>>  ...
>>>>>  Seems to me that efforts like 
>>>>>http://cl.tamu.edu/Common Logic and 
>>>>>   would either have to a) be defined within this type of an open 
>>>>>  ended system, let's say as the natural language description of the 
>>>>>  constraints to which the axioms that make up the theory of such a 
>>>>>  system would adhere; or b) evolve into an open ended system that 
>>>>>  exhibits characteristics of transformation across languages, 
>>>>>  logics, models and theories.
>>>>  No, neither. Common logic is simply a modernized Net-savvy 
>>>>  restatement of first-order logic, in an attempt to get past the 
>>>>  interoperability problems arising from the huge variety of surface 
>>>>  notations in use.
>>>  But Feferman's talking about openness of language and you're saying 
>>>  surface notation. What's the difference?
>>  I have no idea what Feferman was talking about, but whatever it was, I 
>>  am quite certain it is irrelevant to CL. CL, as Pat indicates, is an 
>>  answer to a problem -- the difficulty of getting knowledge bases that 
>>  use different notations for (perhaps some fragment of) first-order 
>>  logic to interoperate.  It's an engineering solution to a practical 
>>  problem.  That's it.  There are some cool features to CL, but the idea 
>>  is Not That Deep.
>I guess not !
>Here's what Feferman's talking about ...
>http://math.stanford.edu/~feferman/papers/dettruth.pdf    (01)

Are you sure this is the right reference? This is 
all about a canonical theory of truth, attempting 
to get past the limitations of the Tarski 
hierarchy. Very interesting (and very technical) 
stuff, but nothing much to do with open-ended 
axiomatic systems or mappings between theories, 
as in IFF or institution theory. Feferman's 
system is entirely an extension of Peano 
arithmetic, a first-order theory.    (02)

>Looks like Feferman and McGee's writings on open ended axiomatic systems
>have been around since the early 90s.
>I can accept that choices were made to limit the scope of the CL
>specification    (03)

No, you have the wrong idea. CL wasn't the result 
of 'limiting' any scope: it was a project with 
its own goals and purposes, unrelated to whatever 
you are thinking about. It isn't IFF-lite.    (04)

>, but I remain unconvinced that there's no connection
>between what Feferman's writing about and CL.    (05)

I don't know how to convince you without you 
first taking a graduate course in foundations of 
mathematics, but if you have the above reference 
right, perhaps you could just take it on 
authority? They really have nothing at all to do 
with one another. (The IKL project, now, may 
indeed have some possible relationship to 
Feferman's stuff, since IKL can define its own 
truth-predicate.)    (06)

>I now have access to my printed copy of CL. For example, 3.8 says "a
>dialect by definition is also a conforming language." And section 7.1
>says "These are really conditions on a specification of a language or
>notation..."    (07)

But all of this is (as should be clear from the 
surrounding context) referring to CL itself, and 
hence limited to FOL. "Dialect" and "conforming" 
are actually technical terms defined in the 
glossary of the document, in ISO fashion.    (08)

One point that may be relevant here is that this 
word "language" has many meanings. In its use in 
"formal language" (AKA "formal system"), it still 
has many meanings. In one sense, all those 
various surface syntaxes for FOL are *different* 
languages. IN fact, in the logic-standard sense, 
each choice of nonlogical vocabulary defines a 
different formal language. When we wrote the CL 
spec, we wanted to say that CL was a single 
language with a variety of 'dialects', and a 
single abstract grammar. This is a different 
sense of 'language', more like a programming 
language. So the word is often used rather 
loosely, as it is in places (like your first 
citation) in the CL spec.    (09)

>  >> Interesting, thanks for the info, anything you could refer me to so 
>>>  I can read up on this ?
>>  On LBase as a precursor to Common Logic?  On the incompleteness 
>>  (better, perhaps, incompleteability) of arithmetic?  On the 
>>  completeness of first-order logic?
>Completeness of FOL.    (010)

Read any logic textbook that has a chapter on semantics or model theory.    (011)

Pat    (012)

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