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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: Fri, 30 Nov 2007 17:34:25 -0600
Message-id: <p0623090ec37642b85fd1@[]>
>Christopher Menzel wrote:
>>  On Nov 25, 2007, at 6:11 PM, rick@xxxxxxxxxxxxxx wrote:
>>>>  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.
>>  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.
>Well, it's subtitle is ": a framework for a family of logic based
>languages." And the introduction says CL "is a logic framework intended
>for information exchange and transmission."    (01)

I know, I wrote it. Being intended for 
information exchange is not incompatible with 
being a logic or even with being a version of FOL.    (02)

>If you're citing this ...
>as a normative definition of a logic, then CL contains some things in
>addition to what's in that definition (ex. Section 6.3 and annex A)    (03)

That reference begins:    (04)

"Typically, a logic consists of a formal or 
informal language together with a deductive 
system and/or a model-theoretic semantics."    (05)

which fits exactly with Annex A (or B or C, or 
the main body of the text, for that matter.) 
While the importing semantics in 6.3 is new, it 
still satisfies the above description since we 
give a model-theoretic semantics and a formal, if 
'abstract', syntax.    (06)

>its called a framework.    (07)

In the subtitle. We called it a 'framework' 
because, strictly speaking, it provides for an 
open-ended variety of 'languages' (in a strict 
logician's sense of 'language'), since it allows 
for a variety of concrete syntaxes (all different 
'languages' in the strict sense: in fact, each of 
them is a while family of languages) for the same 
abstract syntax. Which is of course part of the 
point. But you will note that a *single* abstract 
syntax is provided, and a *single* model theory 
specified for that single abstract syntax, and 
all the conformance conditions are referred to 
that *single* specification.    (08)

>  So, I have to conclude its more than a logic.    (09)

This conversation is going on too long. There is 
little to be gained by citing decorative text at 
us that we wrote, in an attempt to refute our 
position. At most, you will get us to admit that 
we may have made a poor choice of words. The ISO 
spec is quite tightly written, and I think its 
meaning is abundantly clear.    (010)

>If by class of logics, you mean a) framework; b) family of languages;
>and c) for network transmission, then I'm good with that.    (011)

"Framework" has no exact meaning. The term 
"family of languages" is accurate, but might be 
misleading. In the strict sense of 'language' 
used in many logic textbooks, then indeed CL is a 
family of languages; but they are all equivalent 
to one another when considered as logics, and are 
all [**] versions of FOL. And yes, of course it 
is intended for network transmission: that has 
been a guiding principle behind all these efforts 
since the first KIF draft over a decade ago.    (012)

Pat    (013)

[**] As Chris has pointed out, this is not 
STRICTLY true. There are actually - for technical 
reasons - three 'families' defined in the spec: 
CL itself, the family of segregated sublanguages 
of CL, and the family of compact sublanguages of 
CL. Classical FOL is both compact and segregated. 
But still, this is a much narrower range of 
possibilities than is often called a 'family': it 
excludes for example modal, indexed, hybrid, 
tensed, linear, multivalued, paraconsistent, 
nonmonotonic, higher-order (of any degree), 
typed, sorted and many other kinds of logic, and 
anything which is not a logic (such as any 
programming language). The non-compact CL 
language is not strictly FO: it is in fact a 
finite rendering of an infinitary sublanguage of 
L-omega-omega1 (it allows some recursively 
defined infinite conjunctions/disjunctions but 
only finite quantifiers. See
which uses the now obsolete term 'SKIF' for the language.)    (014)

>>  -chris
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