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Re: [ontolog-forum] Ontologies and Algebraic Specifications

To: "Pat Hayes" <phayes@xxxxxxx>
Cc: ontolog-forum@xxxxxxxxxxxxxxxx
From: "Horning, Jim" <Jim.Horning@xxxxxxxxxx>
Date: Tue, 27 Feb 2007 12:49:49 -0800
Message-id: <07DE34877A2D084F872D43939AE59DC071D7F6@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx>
Pat,    (01)

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.  :-)    (02)

Jim H.    (03)

> -----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.    (04)

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.    (05)

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.)    (06)

> >- *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.)    (07)

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.    (08)

> 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.    (09)

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.    (010)

> Importing is a 
> Web idea, and there is no such thing as 
> "exporting" (AFAIK).    (011)

My mistake.  I thought the discussion I had seen
here of import and export related to ontologies.    (012)

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."    (013)

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.    (014)

> 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.)    (015)

Absolutely correct.  This caused relatively few
problems in our domains.  How bad does it make
things for ontologies?    (016)

> >- *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.    (017)

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.    (018)

> 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.)    (019)

OK, I screwed up my terminology.  My first instinct
had been to use "subclass."  I should have stuck with
it.    (020)

...    (021)

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