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. :-)
From: Pat Hayes [mailto:phayes@xxxxxxx]
Sent: Tuesday, February 27, 2007 7:37 AM
To: Horning, Jim
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,
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
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
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
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
OK, I screwed up my terminology. My first instinct
had been to use "subclass." I should have stuck with
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