Re: [ontolog-forum] Ontologies and Algebraic Specifications

[Jairo Cardona Giraldo <cardona6i@xxxxxxxxx>]

Test (sorry)

----- Mensaje original ----
De: Elisa F. Kendall <ekendall@xxxxxxxxxxxx>
Para: [ontolog-forum] <ontolog-forum@xxxxxxxxxxxxxxxx>
Enviado: martes, 27 de febrero, 2007 16:07:16
Asunto: Re: [ontolog-forum] Ontologies and Algebraic Specifications

Jim --

I've been following the exchange with Pat, John Sowa, etc. commenting on your thoughts.  Would it be helpful to you if I could take one or more of the owl ontology components we've built in VOM, show you the OWL (pointing out which constructs correspond to quantifiers, etc., and translate it to FOL so that you can see what it would say in a first order representation?

I hadn't thought to do this previously, though I don't know why :).  Based on Steve's recent musings on the value or lack thereof of ontologies, at least for this application, I've thought seriously about providing the translation to FOL and augmenting that with additional axioms you can't say in OWL, then using -that- in JTP or some other FOL reasoner, possibly KM from the Univ. of Texas, which claims to be able to reason about actions using a situations mechanism, or the two in parallel, just to be a skeptic ... and to think about reasoning that includes hypothesis testing.

Just thinking about things out loud with you, since I've been stewing on these things in the background since I was in LA last week.

Best,

Elisa

Horning, Jim wrote:

Pat,

Thanks, that clarifies a lot.  Now let me see how I can do with the
"much, much greater than" message format that this list prefers.  :-)

Jim H.

  

-----Original Message-----
From: Pat Hayes [mailto:phayes@xxxxxxx] 
Sent: Tuesday, February 27, 2007 7:37 AM
To: Horning, Jim
Cc: ontolog-forum@xxxxxxxxxxxxxxxx
Subject: Re: Ontologies and Algebraic Specifications

    

...
  

- *traits* [modules/units/components] that are 
the concrete elements of discourse.  The body of 
a trait may refer to other traits and include 
*declarations*, *axioms*, and *consequences*. 
Axioms are mostly, but not exclusively, 
equations.
      

That seems very odd to me, speaking from the ONT 
side. There are many things one wants to say that 
just can't be put into equational form.
    

Yes, there are other things, and LSL has other
forms of axioms for those things that we found
to be important in specifying abstract data types
and functions.

I would like to know what other things it is
important to say in ontologies, and what forms
of axioms are best suited to saying them.
(LSL treats universally-quantified first-order
logical expressions as a special case of equations.)

...
  

- *units* [modules/units/component] that are the 
concrete elements of discourse.  The body of a 
unit may *import* from, and *export* to, other 
units and will include *type declarations* and 
possibly some *constraints*.
      

Hmm. Im not sure what you mean by a 'unit' here. 
(Common Logic has a 'module' construction, but 
that has a special purpose of limiting the 
'local' universe of discourse.)
    

All I was trying to say is that I believe most
ontologies are not written indivisibly as one
[block of text/diagram/formula/file/page], but
are written and presented in chunks (which might
be called different things in different ONT
languages).  This subdivision might or might
not have semantic significance in a particular
ONT language (e.g., scoping of names and
quantifiers).  These chunks have to be named
or identified somehow in other chunks; their
relations constitute a "gross anatomy" of
the presentation.
 
  

This seems to miss the central point, which is 
that an ontology is, at base, a theory; that is, 
a collection of sentences. Plus, maybe, some 
bells and whistles, but in many cases even those 
are re-understood as kinds of sentence (e.g. 
'imports'). Some languages have types which may 
in some cases require declarations, but these are 
not an essential part of the mix.
    

No, IMHO this is one of the points that I have
not missed.  However, I fear, some in this
community have overlooked it or gotten it wrong:
The presentation is not the same thing as what the
presentation denotes.  What I write in an ONT
language is not the same as the associated theory.
I don't care which one you call "the ontology,"
but you also need to have a name for the other one,
and any reader needs to know which you mean where.

  

Importing is a 
Web idea, and there is no such thing as 
"exporting" (AFAIK).
    

My mistake.  I thought the discussion I had seen
here of import and export related to ontologies.

E.g., John F. Sowa "I also added two special
kinds of statements:  'Import' for those types
that are specified elsewhere (I won't say
'defined'), and 'Export' for those types
specified in this file that may be used elsewhere."

If "ontology" means theory, then I agree that
it is not very useful to import and export theories,
and that import and export statements probably
don't make sense as part of theories.  That does
not mean that these constructs are not valuable
constructs in ONT languages, with or without the
Web.  Without them, the languages just won't scale.

  

Also, one of the most central and salient aspects 
of an ONT language is how it handles quantifiers, 
and what it can quantify over. You don't mention 
this anywhere, which I also find odd. Does Larch 
have quantifiers? (It is possible to treat 
quantification in terms of implicit universal 
quantification of variables and handling 
existentials by the deft use of functions, 
avoiding any need for an explicit quantifier 
scoping mechanism in the syntax. I'll make a 
guess that this is how Larch does it also.)
    

Absolutely correct.  This caused relatively few
problems in our domains.  How bad does it make
things for ontologies?

  

- *types* [classes/kinds/classes].
      

Be careful of terminology. "types" often is 
understood to imply that type membership is 
syntactically checkable or used to determine 
wellformedness. This is quite unusual in ontology 
languages. If you really do just mean classes, 
then yes, almost all ontology languages have this.
    

I was trying to indicate that I realized that there
were various notions of type and class and that each
ONT language probably picked just one of them.

...
  

Actually isA is usually understood as the 
relationship between an individual and its type; 
the relation between types is often called 
subClass. Yes, it may be entailed by other 
axioms. (Actually to be honest this varies 
between languages, and is a good hallmark of 
computational/deductive complexity.)
    

OK, I screwed up my terminology.  My first instinct
had been to use "subclass."  I should have stuck with
it.

...
 
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