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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: Mon, 26 Nov 2007 09:56:31 -0600
Message-id: <p06230905c37097ff1cef@[192.168.1.2]>
>Pat Hayes wrote:
>>>  Hi Pat and all
>>>
>>>  remind me please
>>>  what is CL for? what does it add to FOL or previous existing things?
>>
>>  If FOL were a single formal language with a single, uniformly
>>  accepted, universally used, syntax, then CL would add nothing. But it
>>  isn't. Almost everyone who writes about FOL or uses it, uses a
>>  slightly different notation. Everyone knows they are all equivalent,
>>  and logically proficient users can switch (or even muddle) notational
>>  conventions with impunity, and often do so; but for information
>>  exchange between programs this is a nightmare. The point of CL (and
>>  earlier, of KIF) was to provide a single standard interchange
>>  notation for first-order logic.
>
>But as a model of a formal system, this approach falls short of what's
>already been defined by information flow, the information flow framework
>and category theory.    (01)

I think we are talking about different topics. 
Category theory is just a mathematical technique. 
It isn't obvious, in fact, that category theory 
IS the best mathematics to talk about 
inter-translation between formalisms. And there 
are many other such attempts at over-arching 
theoretical frameworks for such discussions, such 
as Burstall and Goguen's notion of 'institution' 
(also based in category theory) and the actual 
system SpecWare deployed by Kestrel systems. IMO, 
none of this ideas are ready for standardization 
yet: it is to early in this very ambitious 
research area to be trying to fix an 
international standard.    (02)

>  These approaches have been more fully developed
>especially as related to transformation.    (03)

Though I agree the IFF framework is very 
impressive, it hasn't yet (AFAIK) actually been 
applied to any detailed examples of real-life 
formal languages and the issues that arise in 
trying to relate them.    (04)

>Also, the design principles of
>these approaches also better approximate how knowledge and behavior get
>played out in distributed systems.    (05)

We simply don't know enough to know if this is true or not, IMO.    (06)

But anyway, this isn't what the common logic initiative set out to do.    (07)

>
>>  The original intention was to adopt a single surface syntax upon
>>  which everyone would agree: but when it became apparent that even the
>>  ten or so members of the working group could not agree, this idea was
>>  abandoned, and instead a system of a common 'abstract syntax'
>>  allowing for many different 'surface syntaxes' (aka dialects) was
>>  adopted. If you check the conformance conditions in the ISO spec,
>>  they require that each dialect specification provide a mechanizable
>>  process to parse that dialect into the abstract syntax categories.
>>
>
>But thats only part of the answer    (08)

Its the answer to the question we set out to 
answer. Im not sure what question you are trying 
to answer.    (09)

>and getting from source to target is
>the hard part. Where there's intersection or union (composition) between
>the source and target, great. Where there's additional information
>(refinement) the fun begins. Seems though that a formalization of
>transformation is what should be strengthened, first by recognition of
>its importance as a central design principle, that affects behavior,
>then to support the mechanics of transformation even just as a pattern
>language.    (010)

Well, all I can say is, good luck. I don't think 
we are even in a position yet to say exactly what 
"transformation" means well enough to create a 
mathematical theory of it. There is a danger here 
of being prematurely impressed by conventional 
mathematics, and letting the math drive the 
thinking rather than using it (as it should be 
used) simply as a tool. So, for example, let me 
ask you: WHY do you think that formalisms and the 
transformations between them would form a 
category? Is it because categories are, well, 
really neat: or is because of some intuition you 
have about the formalisms and the 
transformations? (Such as, that translations 
always have an inverse, perhaps?) Where does that 
intuition come from?    (011)

As for software support for language 
transformations, there is now lots of technology 
available, ranging from Specware-style 
proprietary industrial-scale systems to open 
standards such as XML Schema.    (012)

>
>>  This should have been a simple exercise, but standardization
>>  processes tend to run very slowly and often in circles, so this
>>  limited goal took several years. Along the way, some of us (mostly
>>  Chris Menzel and myself) noticed that traditional textbook
>>  formulations of FOL contained a number of restrictions which were not
>>  in fact strictly necessary, and almost as a exercise in pure
>>  mathematics[1] set out out to see how far we could go in removing
>>  them, and what effect this might have on the resulting logic.  This
>>  involved using a very neat mathematical trick which Chris showed to
>>  me, of how to generalize the traditional FO model theory. Shortly
>>  afterwards I became involved in the W3C RDF and OWL standardization
>>  efforts, and realized that this same mathematical trick could be
>>  applied to RDF and OWL, and would solve a number of small, technical
>>  but stubborn problems that were plaguing the W3C working groups,
>>  making RDF somewhat more intuitive (and simpler) than it would
>>  otherwise be. So the RDF, and then the OWL, specs were written using
>>  this same trick in their model theories, making the entire family of
>>  languages (RDF, OWL, CL and now IKL) semantically compatible in a
>>  rather strong sense. So this is another achievement of the CL work,
>>  realized in CL and used very centrally in IKL and OWL/RDF. But this
>>  is indeed rather a technical matter: it might be compared to having
>>  an engine which uses a new fuel additive, where the user of the logic
>  > is like the driver of the automobile. The driver doesn't need to know
>>  how its done exactly, but the engine responds better.
>>
>
>Is there a paper available on this ?    (013)

Several. There are pointers in    (014)

http://ontolog.cim3.net/file/resource/presentation/PatHayes_20061026/OntologyWorkshopSlides.html    (015)

>So far it just sounds like
>abstraction which is ok on the way up, but leave you hanging on the way
>down.    (016)

I only follow this metaphor very vaguely, maybe 
not at all. What are 'up' and 'down' here?    (017)

BTW, it may well be that CL does not solve *your* 
problem. I believe that is what we have been 
trying to tell you.    (018)

Pat    (019)

>
>>  Hope this helps.
>>
>>  Pat
>>
>>  [1] Although not entirely, as removing unnecessary syntactic
>>  restrictions was a large part of how we could home in on an
>>  appropriate 'abstract' syntax which would be universal for all
>>  surface forms.
>>
>>>  thanks
>>>  PDM
>>>
>>>  On Nov 22, 2007 10:38 PM, Pat Hayes <phayes@xxxxxxx> wrote:
>>>>   >Hi Pat
>>>>   >
>>>>   >thanks for bringing this up
>>>>   >
>>>>   >It think CL could be very useful as KR for  NLP applications
>>>>
>>>>   OK, that wasn't clear from your earlier emails, which seemed (?) to
>>>>   be saying that CL *was* NLP.
>>>>   But why say CL instead of FOL? CL *is* FOL, after all. And people
>>>>   have certainly thought of using FOL as KR for NLP, in fact that was
>>>>   one of the very first ideas ever tried. It doesn't work (to sum up
>>>>   about a decade of research in a small sentence.)
>>>>
>>>>   >The facts that you have developed the spec and never thought of all
>>>>   >possible applications of CL are not mutually exclusive from my point
>>>>   >of view
>>>>
>>>>   Oh, indeed. But this particular application isn't a new idea.
>>>>
>>>>   >Welty indeed confirmed that there is not work done in this area
>>>>   >that he knows of
>>>>
>>>>   Not using CL as such, no, because CL is a very new standard. But
>>>   > using FOL, there has been a lot. And there is nothing in CL which
>>>>   takes it beyond FOL in any way useful for NLP. (Are you sure he
>>>>   wasn't talking about IKL? The new idea in IKL is indeed worth
>>>>   investigating for this kind of application, and I know Welty is
>>>>   interested in this, but IKL goes way beyond CL in expressive power.)
>>>>
>>>>   >- but unlike you he did not rule out the possibility
>>>>   >of further investigation
>>>>   >(part of his lessons learned, I guess, never say never)
>>>>   >
>>>>   >I will send you a copy of the paper
>  >>>
>>>>   Please do.
>>>>
>>>>   Pat
>>>>
>>>>
>>>>   >
>>>>   >cheers
>>>>   >PDM
>>>>   >
>>>>   >
>>>>   >On Nov 22, 2007 9:23 AM, Pat Hayes <phayes@xxxxxxx> wrote:
>>>>   >>  >Rick
>>>>   >>  >thanks for interpreting your thoughts.  I am becoming increasingly
>>>>   >>  >interested in CL, although I am still working out how it relates to
>>>>   >>  >other formalisms, and how can I use it
>>>>   >>  >As discussed briefly with Welty last week, it appears obvious to me
>>>>   >>  >that CL is at core of NLP,
>>>>   >>
>>>>   >>  I have no idea what you and Welty were
>>>>   >>  discussing, but I can assure you that CL has
>>>>   >>  almost nothing to do with NLP (assuming you mean
>>>>   >>  by this, Natural Language Processing.) I know
>>>>   >>  that Welty knows better than to make such a
>>>>   >>  statement, so I presume you may have
>>>>   >>  misunderstood him.
>>>>   >>
>>>>   >>  CL is really a very limited, technical project: a
>>>>   >>  version of first-order logic with a very
>>>>   >>  forgiving syntax and a slightly modified
>>>>   >>  semantics (modified in order to accommodate the
>>>>   >>  syntactic freedom), stated as a 'standard' (i.e.
>>>>   >>  with explicit conformance conditions spelled out)
>>>>   >>  and allowing for a variety of alternative surface
>>>>   >>  syntactic forms. The CL ISO documentation gives
>>>>   >>  three such surface forms in detail, and others
>>>>   >>  are possible. But these are all just syntactic
>>>>   >>  variations on first-order logic, all with a
>>>>   >>  common semantics. First-order logic is not NLP.
>>>   > >>  (Some very early NLP work assumed that NL is a
>>>>   >>  'rich' version of a logic, but that idea has been
>>>>   >>  thoroughly refuted by now. Certainly the
>>>>   >>  languages that humans actually speak are not
>>>>   >>  logics, and cannot be fully understood without
>>>>   >>  taking a large number of non-logical
>>>>   >>  considerations into account.)
>>>>   >>
>>>>   >>  Pat Hayes
>>>>   >>
>>>>   >>  PS. In case you feel that I am merely blustering
>>>>   >>  here, I would point out that I authored the CL
>  >>>  >>  specification (apart from Annex B, which was
>>>>   >>  written by John Sowa), so I do have something of
>>>>   >>  an inside view both of what it says and of the
>>>>   >>  presumptions and ideas on which it is based.
>>>>   >>
>>>>   >>
>>>>   >>  >so I am interested
>>>>   >>  >in your suggestion as a possible way forward in that direction
>>>>   >>  >thanks
>>>>   >>  >PDM
>>>>   >>  >
>>>>   >>  >>  Given the current structure of CL & LBase, I believe
>>>>  proposition a) is
>>>>   >>  >>  where CL & LBase are now: a natural language description of the
>>>>   >>  >>  constraints to which the axioms of an open ended schematic
>>>>  system would
>>>>   >>  >>  adhere. Proposition b) presumes that we structure a
>>>>  logical environemt
>>>>   >>  >>  as illustrated below.
>>>>   >>  >>
>>>>   >>  >>                 Logical Environment
>>>>   >>  >>                         |
>>>>   >>  >>         -----------------------------------------
>>>>   >>  >>         |       |               |               |
>>>>   >  > >>  Languages    Logics          Models         Theories
>>>>   >>  >>                                                  |
>>>>   >  > >>                                         -----------------
>>>>   >>  >>                                          |                |
>>>>   >>  >>                                      Axiomatic    Natural Language
>>>>   >>  >>                                                          |
>>>>   >>  >> 
>>>>-------------------
>>>>   >>  >> 
>>>>|                  |
>>>>   >>  >>                                                LBASE
>>>>  Common Logic
>>>>   >>  >>
>>>>   >>  >>  I believe Feferman's open ended schematic system implies
>>>>  proposition b)
>>>>   >>  >>  and the evolution of formal systems towards logical environments.
>>>   > >>  >>
>>>>   >>  >>  Rick
>>>>   >>  >>
>>>>   >>  >>
>>>>   >>  >>
>>>>   >>  >>  paola.dimaio@xxxxxxxxx wrote:
>>>>   >>  >>  > Thanks a lot Rick
>>>>   >>  >>  > havent had the chance to read the 
>>>>docs yet, but it sounds like a
>>>>   >>  >>  > fundamental question, although 
>>>>shifts in thinking paradigms may be
>  >>>  >>  >>  > unsettling and painful
>>>>   >>  >>  > I do think that CL is going to stimulate the transition
>>>  >from NLP to AI
>>>>   >>  >>  > (so many acronyms)
>>>>   >>  >>  > and I have come to accept the possibility of a passive
>>>>  logical schema
>>>>   >>  >>  > but I am still reading
>>>>   >>  >>  > (and reading and reading)
>>>>   >>  >>  > I am interested in exploring your a) and b) propositions
>>>>   >>  >>  > what happend to this chap Feferman? did he get any traction?
>>>>   >>  >>  > will catch up with the reading and continue with this
>>>>  discussion at
>>>>   >>  >>  > the first opportunity
>>>>   >>  >>  > cheers
>>>>   >>  >>  > PDM
>>>>   >>  >>  >
>>>>   >>  >>  >
>>>>   >>  >>  > On 11/17/07, rick@xxxxxxxxxxxxxx <rick@xxxxxxxxxxxxxx> wrote:
>>>>   >>  >>  >>
>>>>   >>  >>  >>
>>>>   >>  >>  >> All:
>>>>   >>  >>  >>
>>>>   >>  >>  >> Folks might enjoy the Soloman Feferman lecture Goedel,
>>>>   >>Nagel, Minds and
>>>>   >>  >  > >> Machines. After recounting an exchange
>>>>   >>  >between Godel and Nagel circa 1956,
>>>>   >>  >>  >> Feferman describes the implications of the minds vs.
>>>>   >>machines dichotomy
>>>>   >>  >>  >> ensuing from the exchange. To avoid the
>>>>   >>  >>impass resulting from the dichotomy,
>>>>   >>  >>  >> Feferman proposes the redefinition of a formal system to an
>>>>   >>"open ended
>>>>   >>  >>  >> schematic axiomatic system." He claims this
>>>>   >>  >>redefinition is a constructive
>>>>   >>  >>  >> step towards an "informative, systematic
>>>>   >>  >>account at a theoretical level of
>>>>   >>  >>  >> how the mathematical mind works that
>>>>   >>  >>squares with experience."  He stresses
>>>>   >>  >>  >> the importance of a subject neutral theory
>>>>   >>  >>of operations with basic schemata
>>>>   >>  >>  >> for language, arithmetic, set theory that would amount to a
>>>   > >>version of an
>>>>   >>  >>  >> untyped lambda calculus. Feferman concludes by rejecting
>>>>   >>any effective
>>>>   >>  >>  >> machine representation of mind as
>  >>>  >>  >>contemplated by Nagel, Penrose & others.
>>>>   >>  >>  >>
>>>>   >>  >>  >> So, what does this mean to Common Logic and
>>>>   >>  >>LBase ? Seems to me that efforts
>>>>   >>  >>  >> like Common Logic and 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.
>>>>   >>  >>  >>
>>>>   >>  >>  >> Rick
>>>>   >>  >>  >>
>>>>   >>  >>  >> 
>>>>_________________________________________________________________
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>>>>   >>  >
>>>>   >>  >--
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>>>>   >>  >School of IT
>>>>   >>  >www.mfu.ac.th
>>>>   >>  >*********************************************
>>>>   >>  >
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