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

To: "rick@xxxxxxxxxxxxxx" <rick@xxxxxxxxxxxxxx>
Cc: ontolog-forum@xxxxxxxxxxxxxxxx
From: Pat Hayes <phayes@xxxxxxx>
Date: Mon, 26 Nov 2007 17:30:20 -0600
Message-id: <p06230905c370fde8135e@[]>
>  >> 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, letıs 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?    (01)

Er... what have they in common? By 'surface 
notation' I mean only a particular concrete 
syntax for a single given language. Examples of 
such concrete syntaxes for FOL are (using a 
familiar example text)    (02)

(forall ((x Man))(Mortal x))    (03)

<upside-down A> x. Man(x) <unicode 2283> Mortal(x)    (04)

:Man rdfs:subClassOf :Mortal .    (05)

[Every Man:] Mortal [Self]    (06)

(forall (?x)(=> (Man ?x)(Mortal ?x)))    (07)

:. A x: Man x .implies. Mortal x :.    (08)

mortal X ::- man X    (09)

and of course one can go on with dozens of 
examples. These are all saying exactly the same 
thing: they have identical semantics, and even 
the same 'abstract' syntactic form, but they are 
written in different surface notations which 
require different parsers. The colon character, 
for example, plays entirely different roles in 
the third, fourth and sixth examples 
(respectively an XML Qname indicator, a 
quantifier marker, and a scoping device in 
dot-notation). Omitting the ? before the x in the 
fifth example would produce a parsing error (in 
KIF), but this convention is irrelevant in the 
other cases. Etc..    (010)

CL is simply a standard for overcoming this 
theoretically uninteresting, but practically 
infuriating, barrier to communication, is all. 
And doing this took many man-years of effort and 
a determined, even draconian at times, approach. 
Writing standards is not easy, even when their 
content is moderately obvious.    (011)

>I've lumped in
>non-monotonicity, model theories and axiomatic semantics.    (012)

You seem to be making a kind of intellectual 
Jambalaya here. I have no clear sense of what it 
is that you are wanting to do with this mixture.    (013)

>  These might be
>a stretch at the empirical level, not to discount the good work already
>done by the folks a Kestrel on Specware, and given the solid work of
>Barwise, Goguen, Kent & others not so much news at the theoretical level.    (014)

Well, the Burstall/Goguen and Kent's is all very 
elegant as theory, but what is a lot less clear 
is, what is it a theory *of* ? None of it seems 
to have any clear connection with any actual 
practice. The Kestrel Specware material on the 
other hand is clearly useful, but only for very 
strongly typed frameworks and only for 
programming languages, neither of which seem to 
apply to our situation (or at any rate, not to CL 
or to ontology languages.)    (015)

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