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
>http://www.w3.org/TR/lbase/LBase
>>>> 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. (01)
I guess not ! (02)
Here's what Feferman's talking about ... (03)
http://math.stanford.edu/~feferman/papers/dettruth.pdf (04)
Looks like Feferman and McGee's writings on open ended axiomatic systems
have been around since the early 90s. (05)
I can accept that choices were made to limit the scope of the CL
specification, but I remain unconvinced that there's no connection
between what Feferman's writing about and CL. (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)
>
>> I've lumped in non-monotonicity, model theories and axiomatic
>> semantics.
>
> Into what? And what does it even mean to say you've lumped together
> (a) a formal property of certain logics (b) all mathematical theories
> of meaning and (c) formal axiomatizations of specific semantic theories? (08)
We're not connecting here because you missed this prior message in which
I refer you to the logical environment of IFF. (09)
http://ontolog.cim3.net/forum/ontolog-forum/2007-11/msg00156.htm (010)
This answers your arcs question as well as he structural relationships. (011)
>>> LBase is (was,better, as it seems to have been widely ignored) an
>>> earlier attempt to do this for the W3C family of semantic web
>>> languages. Goedel's incompleteness result, which gave such a shock
>>> to foundations of mathematics, has no relevance to the completeness
>>> of first-order logic (which was also first proved by Goedel, by the
>>> way.)
>> 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? (012)
Completeness of FOL. (013)
> -chris
>
>
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