Re: SUO: Re: "Monolithic" Ontology
Leo,
A few sounds bites in response below. These views have been aired
before, repeatedly, so I'll resist the temptation to reply to all the
replies this will probably generate, although I'd be happy to discuss
further with you individually.
At 06:00 PM 3/5/2002 -0500, Leo Obrst wrote:
>Pat,
>
>I had a longish message for you earlier, but my mailer died, so I'll
>just address some of your points, since I now more clearly understand
>what you are asking. Unfortunately, this still may be longish.
>
>See below.
>
>Leo
>
>Patrick Cassidy wrote:
> >
> > John --
> > I was hoping that the definitions I provided would be
> > clear as to intent, but I didn't realize that you already had
> > a different definition of "terminological ontology". Apparently
> > my attempt at clarifying the meanings failed. I think
> > the distinction is worth recognizing, so I'll try again.
> >
> > What I have in mind what would be (I think) in your
> > terms, a "formal ontology", but without any commitment as to which
> > of the concepts actually have instances in the real world. Your
> > definition says (in part):
> >
> > > Examples of formal ontologies include theories in science
> > > and mathematics
> >
> > IF one reads this definition to mean that a formal ontology
> > **may have** but does not necessarily have real-world instances,
> > then what I think would serve as a useful "monolithic" standard
> > would be a **formal ontology**, but it would be agnostic as
> > to which of the defined concepts would subsume specific
> > real-world instances, e.g. my Honda Accord.
> > Your use of "theory" seems to coincide with "mathematical
> > theory". A formal ontology without real-world instances would
> > be such a mathematical theory. I am using "theory" in the
> > sense of "theory of the real world" (definition 1 in the Random
> > House Unabridged). The important point is to distinguish a formal
> > ontology which has no real-world instances from one which does
> > have real-world instances. I will be happy to use whatever terms
> > you think most perspicuous to label these different concepts.
> > The former would qualify as a mathematical theory, I believe,
> > but not as a theory of the real world.
>
>I view all that we are doing here in SUO and as ontology engineers as
>really concerned about creating "data world theories" (or perhaps
>"information theories") in the sense that these ontologies are
>information world surrogates for commonsense theories of the real world.
>We want our systems (software products, documents, etc.) to embody
>approximately real-world-like semantics. Now, "commonsense theories" may
>have to be enlarged a bit to also include regular "real world"
>mathematical and scientific theories (obviously the former, but largely
>the latter too), especially if you have a need for a quite accurate,
>declarative "best" "data theory" of quantum mechanics in your system
>(document, community, etc.)
>
>What this means: eventually all of our ontologies will have instances
>(or we hope, as ontologistss). Data/information surrogate instances.
>That's the point. And we can quibble about whether "mathematical
>theories" have real-world instances: I think they do, but then I tend to
>be a realist. There are other philosophical positions where that answer
>is not so clear-cut. But we really are in the business of building
>ontologies (in the information space, as engineering products) so that
>our generic notions have real ("information", not physical) instances.
>
> > I am of course familiar with terminologies, which is
> > precisely why I used the term "terminological ontology" to
> > emphasize the inclusion of axiomatizations. Since this conflicts
> > with your definitions, please replace "terminological ontology" by
> > "formal ontology" in my previous note.
>
>You just have to be careful, since there are "terminological logics" out
>there (aka description logics): they try to classify axioms into a
>subsumption hierarchy(ies). In addition, there is a distinction between
>"term" and "concept" which is sometimes (often?) made: the former is a
>word or phrase (in this context), the latter is the semantic notion
>behind the word (in general; don't want to get into THAT debate here).
>
> > To illustrate the distinction that I think is valuable, consider
> > alternative formal ontologies:
> >
> > 1. Entity 2. Entity
> > / \ / \
> > Object Process Object Process
> > / \ / \
> > SolidObj LiquidObj NaturalObj Artifact
> >
> > Theory 1. might have my Honda under "SolidObj" in ontology 1.
> > Theory 2. might have my Honda under "Artifact" in ontology 1.
> >
> > Suppose instead we had a "monolithic" formal ontology:
> >
> > 3. Entity
> > / \
> > Process Object
> > / | \ \
> > SolidObj Artifact LiquidObj NaturalObj
> >
> > Theory 3 would have my Honda as an instance of both "SolidObj"
> > and "Artifact". This would be consistent with both theories
> > 1 and 2, and in fact those who use both 1 and 2 may find the
> > merged ontology equally adequate for their own purposes.
> > Other theories using formal ontology 3 might have my
> > Honda as an instance of only one of those concepts. Unless
> > more detailed definitions were included, we would have no
> > way of knowing which theory best represents the real
> > world, even if they all used the same monolithic ontology 3.
>
>Even if more detailed definitions were included, we still might have NO
>way of knowing which theory represents the real world: 1, 2, 3. That is
>the point. For example: perdurantist vs. endurantist. Half the people on
>this list will argue for one, the rest for the other. Who's right? NO
>ONE KNOWS: there is no final answer (at least to this point), just
>argumentation and applicability, the latter meaning something like
>"depends on your application".
I agree, there is no One True Ontology. I believe there are many, and
we're just trying to find one.
>So the point of a non-monolithic set
>(lattice?) of logically integrated ontologies is that YOU, the ontology
>application developer or community shared-semantics developer (or
>metadata developer) pick the theories that are appropriate to you.
The problem is then that "Y'ALL" ontologists have to find a way to
translate between them if you want to communicate. That's a hard problem,
so it's better to try to get agreement up front. That's the point of this
effort. People are free to disagree but it amazes me that folks (not you)
keep participating in this group as spoilers, even when they disagree with
the fundamental purpose of the effort.
>This is what ultimately distinguishes us from philosophical formal
>ontology: we are interested in ontology engineering, i.e., semantic
>foundations for applications. We ARE interested in formal ontology,
>i.e., what kinds of being/becoming constitute the real world, but more
>directly we are interested in the "data/information surrogate" of that:
>how might I phrase and structure the semantics of the real world which I
>seek to model for my systems (communities, documents, etc.)? Which
>means, ultimately, we need to decide things for particular uses, though
>the philosophical questioning and argumentation goes on, perhaps without
>resolution.
>
> >
> > This is of course the simplest case, with no logical conflicts.
> > But we can also create a monolithic ontology with mutually
> > contradictory concepts (e.g. definitions of time), either
>
>You have to be care here again, because it may be that in your logical
>language, you in fact CANNOT have (do not WANT to have) mutually
>contradictory concepts (that is one problem of monolithic ontologies,
>unless they have a very refined notion of ontologies, i.e., like that
>based on possible world semantics, which is usually a modal logics
>notion). Of course, that is also a FEATURE of logic in general, i.e., we
>really do want logical consistency. You are probably talking more about
>the underlying knowledge representation language for these ontologies.
>
> > of which might be selected by different ontologists as the
> > best way to represent the real world (in the monolithic
> > ontology the different definitions would have to have
> > different names). Asserting that the "time" of the real
> > world is an instance of one or the other of those definitions
> > would then constitute (in my terminology) different
> > "theories" of real-world time.
>
>Yes, in fact, this is what the "lattice of theories" approach advocates.
>
> >
> > My point is that having all of the potential theories
> > defined within a single self-consistent formal ontology
> > is more useful than just concatenating different ontologies
> > or trying to find mappings between ontologies which use
> > different sets of higher-level concepts and therefore
> > cannot be precisely related.
>
>No, you cannot have all theories defined within a single self-consistent
>formal ontology. Why? Because one theory may have X as an axiom, another
>theory may have NOT X, which makes the two theories inconsistent. If,
>however, you have a quasi-modal framework (yes, pun intended, or a
>belief-maintenance system which is probably modal), then you might have
>two (mutually inconsistent) theories which are in the same framework but
>very "far" apart. I think the IFF intends to be such as framework, but a
>logical framework based on category theory.
>
> >
> > That is the kind of monolithic ontology that I think
> > is feasible, but useful.
> >
> > I strongly disagree with this assertion:
> > [JS]
> > > The number of legitimately useful theories is infinite. Trying to
> > > reduce that infinity is not only impossible, but counterproductive.
> > I think it likely that many ontology users would be quite
> > content to use any reasonably comprehensive standard ontology
> > rather than try to develop an idiosyncratic one. There are
> > doubtless some who develop peculiar ontologies because their
> > view of the world truly differs from that of others, but
> > I expect that most of the differences in existing ontologies
> > arose simply due to an absence of an accepted standard, rather
> > than principled differences about how reality should be
> > represented (I don't count preferences -- especially in the
> > absence of any reason to compromise -- as principled differences).
> > The existence of a monolithic formal ontology (without
> > instances) would be one step forward, and with that in place,
> > over time it may turn out that one particular self-consistent
> > subset of those concepts finds wide use and becomes a de
> > facto standard "theory of the real world".
>
>I agree with your comment about ontology users. I advocate this, i.e.,
>"experts" defining an upper, otherwise everyone and their grandmother
>will, which is the state we are in generally right now. I know of many
>grandmother designed ontologies. They are usually called UML object
>models. Luckily (or perhaps not, given our real intent here), they are
>purely documentation and there is no conformance mapping between them
>and the systems which implement them (so kind of oxymoronic).
>
>Forget about the ontology without instances. All ontologies (at least
>those addressing universals, and a couple other qualifications) expect
>to have individuals or instances (or particulars). That's the point. Of
>course the clear-cut distinction between universals and individuals may
>break down, and in fact has in description logics, for example.
>Formerly, DLs made a distinction between T-boxes and A-boxes, which is
>largely your distinction between Terminology (universals, generic
>ontology) and Assertions (about instances/individuals, particulars). But
>they don't really make this much anymore. I happen to think that
>ontology includes generalizations/distinctions about universals AND
>particulars.
>
> >
> > I also have some question about this assertion:
> >
> > > A lattice of all possible theories is possible without any agreement
> > > whatever.
> >
> > Two theories that have different sets of top-level concepts and
> > different sets of relations may have nothing in common. If this
> > fits the definition of a "lattice of theories" then a lattice is
> > no better than a catalog. More useful would be a "subsumption
> > lattice", but this would require a substantial degree of commonality,
> > i.e. the existence of some "base theory" or at least a common middle
> > and a lot of relations (or distinctions) in common.
> >
A subsumption lattice would indeed be useful. In fact, SUMO already has
that. While I believe that a single, useful, consistent lattice of
theories is possible, and sufficient, I would certainly welcome people who
believe otherwise creating formal theories which are inconsistent with
others in SUMO. That exercise would make concrete what the actual
inconsistencies are. For the most part, those supposed inconsistencies
have only been conjectured, rather than precisely described in logical
axioms sufficient for having a substantive and informed discussion about
whether they are in fact irreconcilable.
Adam
> > Pat Cassidy
> >
> > ====================================
> >
> > John F. Sowa wrote:
> >
> > >
> > > Pat,
> > >
> > > Your points are related to topics that we discussed in the ANSI
> > > workshops on ontology during the years 1996 and 1997:
> > >
> > > PC> I am using the phrase "terminological ontology" to mean a
> > > > real honest-to-goodness ontology which has well-defined concepts.
> > > > The "terms" are merely the labels attached to each of these
> > > > well-defined concepts.
> > >
> > > The problem is that none of the things called "terminologies" really
> > > have "well-defined concepts". To be defined sufficiently for computer
> > > processing, they must be supplemented with axioms and definitions in
> > > some formal, logical notation (KIF or CGs, for example).
> > >
> > > PC> It is distinguished from a **theory** in that a theory includes
> > > > instances, i.e. assertions that certain real-world objects, processes,
> > > > or events are instances of specific concepts in the terminological
> > > > ontology.
> > >
> > > No. A theory is simply a set of axioms and their logical consequences.
> > > It may include specific instances, but many, if not most theories do not
> > > mention instances in their axioms. However, to be useful, a theory must
> > > be applicable to actual instances.
> > >
> > > PC> Different theories will place the instances under different
> > > > concepts in the terminological ontology (i.e. the instances will
> > > > conform to differently defined concepts).
> > >
> > > Yes and no. If the terminological ontology is defined precisely,
> > > any or all theories that are compatible with it should apply to special
> > > cases of its concepts. What you are talking about would only be true
> > > of terminological ontologies that are not well defined (which, however,
> > > is true of most of them).
> > >
> > > PC> If there are examples of well-defined terminological ontologies
> > > > which proved in some way deficient by virtue of trying to be
> > > > inclusive, I would much appreciate the war-stories associated with
> > > > such cases, or a pointer.
> > >
> > > Anybody who has tried to do NL processing of real texts (any newspaper
> > > would do) has discovered such thorny problems in almost every sentence.
> > > The terminologies are not deficient "by virtue of trying" but by the
> > > impossibility of succeeding in being truly inclusive. If you want
> > > examples, I suggest that you try using a machine-translation system on
> > > ordinary news reports. The easiest one to try is BabelFish:
> > >
> > > http://babelfish.altavista.com/
> > >
> > > PC> The great benefit I expect to come from this is for different
> > > > ontology groups to be able to see whether they could effectively
> > > > use other definitions to describe the instances they are most
> > > > concerned about. This is, I believe the first step in reducing
> > > > the number of different definitions of what is intended to be
> > > > the same concept. If we cannot eliminate the use of different
> > > > theories (as is widely believed), we can nevertheless reduce the
> > > > differences between ontologies to a minimum. We may even find
> > > > that some particular consistent combination of the concepts in the
> > > > ontology is believed by a majority of users to suit their purposes.
> > >
> > > The number of legitimately useful theories is infinite. Trying to
> > > reduce that infinity is not only impossible, but counterproductive.
> > > In many cases, however, it is possible to find ways of relating
> > > theories that are compatible, if only their definitions were suitably
> > > transformed (something like a co-ordinate transformation in geometry).
> > > That can be done, but it should be automated, not done by hand. For
> > > further discussion of how it can be automated, see the following slides:
> > >
> > > http://www.jfsowa.com/talks/negotiat.htm
> > >
> > > In these slides, I don't cover all the possible transformations, but I
> > > suggest some that have proved to be useful. The main point of the talk
> > > is that trying to do the translations by hand is a waste of time and
> > > automated or at least semi-automated tools are much more appropriate.
> > >
> > > PC> I would expect a lattice of theories to be possible only when
> > > > there is at least the level of agreement on basic concept definitions
> > > > that would be exemplified by a unified terminological ontology.
> > >
> > > A lattice of all possible theories is possible without any agreement
> > > whatever. However, it is useful to index the lattice with the terms
> > > of a terminological ontology (as defined below).
> > >
> > > The distinction between a terminological ontology and a formal or
> > > axiomatized ontology is one that we discussed in our workshops.
> > > Following is my definition (which is based on those discussions):
> > >
> > > terminological ontology.
> > > An ontology whose categories need not be fully specified by axioms
> > > and definitions. An example of a terminological ontology is WordNet,
> > > whose categories are partially specified by relations such as
> > > subtype-supertype or part-whole, which determine the relative
> > > positions of the concepts with respect to one another but do not
> > > completely define them. Most fields of science, engineering,
> > > business, and law have evolved systems of terminology or nomenclature
> > > for naming, classifying, and standardizing their concepts.
> > > Axiomatizing all the concepts in any such field is a Herculean task,
> > > but subsets of the terminology can be used as starting points for
> > > formalization. Unfortunately, the axioms developed from different
> > > starting points are often incompatible with one another.
> > >
> > > formal ontology.
> > > A terminological ontology whose categories are distinguished by
> > > axioms and definitions stated in logic or in some computer-oriented
> > > language that could be automatically translated to logic. There is
> > > no restriction on the complexity of the logic that may be used to
> > > state the axioms and definitions. The distinction between
> > > terminological and formal ontologies is one of degree rather than
> > > kind. Formal ontologies tend to be smaller than terminological
> > > ontologies, but their axioms and definitions can support more
> > > complex inferences and computations. The two major contributors to
> > > the development of formal ontology are the philosophers Charles
> > > Sanders Peirce and Edmund Husserl. Examples of formal ontologies
> > > include theories in science and mathematics, the collections of
> > > rules and frames in an expert system, and specification of a
> > > database schema in SQL.
> > >
> > > For completeness, my glossary also includes a definition of a
> > > prototype-based ontology and a mixed ontology, which includes examples
> > > of all of the above. The complete glossary is Section 6 of the
> > > following article:
> > >
> > > http://www.jfsowa.com/ontology/ontoshar.htm
> > >
> > > For more on these and related topics, see the Guided Tour of Ontology:
> > >
> > > http://www.jfsowa.com/ontology/guided.htm
> > >
> > > For a more recent discussion of the fundamental philosophical issues,
> > > see the following paper (Section 7 goes into more detail about the
> > > relationships between terminological and formal hierarchies):
> > >
> > > http://www.jfsowa.com/pubs/signproc.htm
> > >
> > > I also agree with the point that Jon Awbrey made:
> > >
> > > JA> But first, a recurrent personal note. It's a funny thing, I
> > > > suppose, but no matter how often one says that one believes that
> > > > progress in a particular task is possible, just not in a particular
> > > > direction, others who are dead set on that direction will tend to hear
> > > > it as a denial of the possibility of progress in general. Let us then
> > > > recognize this as what is often called a "persistent phenomenon".
> > >
> > > What I am suggesting is that there is a very good reason why a precisely
> > > defined dictionary of all possible concepts has not been written: it
> > > violates the fundamental nature of language to be adaptive, flexible,
> > > and infinitely extensible. The normal use of natural languages depends
> > > on the option of extending or modifying the meaning any word in any
> > > and every possible utterance. As Peirce said, "meanings grow."
> > >
> > > I am not suggesting that we should give up, but what we must do is
> > > to change direction: provide a formal framework that would support
> > > an open-ended number of theories that would be indexed by the words
> > > of a terminological hierarchy (or actually N hierarchies, where N is
> > > the number of languages to be supported). For further details, see
> > > the final section of the signproc.htm paper.
> > >
> > > John Sowa
> > >
> > >
> >
> > --
> > =============================================
> > Patrick Cassidy
> >
> > MICRA, Inc. || (908) 561-3416
> > 735 Belvidere Ave. || (908) 668-5252 (if no answer)
> > Plainfield, NJ 07062-2054 || (908) 668-5904 (fax)
> >
> > internet: cassidy@micra.com
> > =============================================
>
>--
>_____________________________________________
>Dr. Leo Obrst The MITRE Corporation
>mailto:lobrst@mitre.org Intelligent Information Management/Exploitation
>Voice: 703-883-6770 7515 Colshire Drive, M/S W640
>Fax: 703-883-1379 McLean, VA 22102-7508, USA
Adam Pease
Teknowledge
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