Re: [ontolog-forum] Next steps in using ontologies as standards

["Ali Hashemi" <ali.hashemi@xxxxxxxxxxx>]

Hmmmm.

Maybe we can first agree on the problems at hand, and see if we can find a compromise that can result in action.

We're all in agreement that ontologies present an opportunity to capture and streamline a lot of the work being done by disparate groups of people.

Our experience shows that there is a large amount of work being redone and wheels being reinvented as a result of the inability to communicate across domains.

One overarching problem is that many subject matter experts lack the requisite background in logic to specify an ontology for their domain easily.

Compounding this problem of articulation is the fact that there is a multiplicity of languages out there and it is unclear (to many) which is the most suitable formalism.

Following all these preliminary problems before an ontology is actually formulated, there is the semantic mapping problem of how to reuse each of these ontologies.

Pat C envisions gathering people from various domains and trying to determine, via consortium, the (a?) base common ground.
John S and others note that these efforts are time consuming, and there is rarely if ever consensus within a domain, let alone across disparate fields.

I personally have a number of criticisms of RDF and OWL, namely that they are not expressive enough, rely too much on metaforms (Danesi 2002), resulting in a significant amount of semantics being left external to the system of representation. This makes the reuse of ontologies specified in RDF and OWL a nightmare.

I will focus the rest of the message on ontologies with at least first-order expressiveness; if it is not applicable to your needs, I apologize.

----

If the problems outlined above more or less accurately capture the current state of affairs, then I think we need a two pronged approach - both bottom-up and top-down.

Top down means that there is likely a large subset of FOL axioms that are reused in various guises among different domains. I'm being agnostic about whether they are primitives, or atomic blocks. But i am making a conjecture that there exists a large body of FOL theories and more specifically sets of models (Tarski sense) that are reused.

If the above seems too abstract, let me make one quick appeal to philosophy before getting to engineering. Whenever we choose a language of representation we inadvertently end up highlighting certain aspects of the phenomena under consideration at the expense of others. In the context of FOL, i conjecture that these patterns that we will see emerge again and again correspond to those noted by mathematical logicians and computer scientists. These theories correspond to (but are not limited to): symmetries, groups, partial orderings, geometries.  They really relate, at a fundamental level, how abstract symbols in the language connect to one another in interesting patterns.

It doesn't really matter at this stage if i'm right about these theories being somehow "fundamental" (i use the word loosely) or not. They are however among the most well understood, characterized and developed FOL theories we have, though they haven't yet been represented as ontologies. (Side note: Michael Gruninger's Semantic Technologies Laboratory is building a Common Logic repository which will include these theories, I've already done one for partial orders.)

This might correspond to the top-down approach.

--

Similarly, we need to enable SME's to express their intuitions in a language that is expressive enough (has enough of the semantics in the language of representation) to allow useful semantic mappings to be generated. This means that we need tools for ontology design, to get what people think they know out, and tools for semantic mapping to connect their ideas to one another.

This is the "bottom-up" component.
--

The idea would then proceed thusly:

Let's imagine a single domain. There are various stakeholders in the domain each with a particular view of what is. Before the consortium phase, to me, it makes sense to have each stakeholder specify their knowledge not as the domain ontology, but to see how they compare (are similar and different) to others.

If we grow a repository of logical theories at the same time as domain specific theories, the interplay between the two will direct and guide a more unified and streamlined ontology community.

That is to say, as each actor in each domain specifies their knowledge, they map into a central repository to see what structures they've been using, and more importantly in what ways they're extending those axioms.

In this way, the logical structures provide a core which does not capture all but a large enough subset (i think it's an open question whether it does form a complete cover as a foundation). The repository would then grow dynamically depending on how the ontologies people have specified map into it. In fact, it would likely grow in accordance with "abstraction layers" depending on the type of ontology being mapped in, but let's leave that for a later discussion.

Getting back to standards. Instead of having 15, 50, 100 people trying to define a single concept, they have instead defined X concepts. Quite likely there will be a good deal of overlap between their ideas, and some significant and important differences. But lo and behold, we have a mechanism by which to compare and contrast their ideas. We can specify how concept A is consistent with B and where they diverge.

There's still a problem of which concept is the right one for the standard. But it's also been greatly facilitated for two reasons. First, the problem has been transformed back to that of any standard, not of an ontology any more. The knowledge of people (as they understand it) has already been specified. It's a question of picking the appropriate specifications. But (perhaps) more interestingly and beneficially, the different senses of a concept have also been articulated and mapped to one another through a centralized repository.

Thus there is no one correct idea of time or shipment or customer. That doesn't mean we can't use them together, but simply that we need to know how their models interact with one another, and to what degree (in what ways) we might use the varying concepts in different ontologies.

Anyhow, the above is only a sketch of an approach to the standards problem. Some thoughts to chew on? Tear it apart :D.

---

Ref:

(Danesi 2002) M. Danesi, "Abstract Concept-Formation as Metaphorical Layering." Studies in Communication Sciences 2/1 pages 1-22, 2002.

On Tue, Jan 20, 2009 at 2:34 AM, John F. Sowa <sowa@xxxxxxxxxxx> wrote:

 

I'll summarize your proposal:

 1. Find a set of primitive concepts that are common to all
    natural languages.  These would be similar to the defining
    vocabulary of Longman's dictionary for students who are
    learning English as a second language.

 2. Use those primitives to define a much larger vocabulary of
    terms and thereby relate them by means of those primitives.

This idea is not bad for writing a dictionary that is intended
to be used by students who *already* learned the concepts in
their native country and just need to learn the English words
for them.  Just look at a typical definition:

  energy.  The power which does work and drives machines:
     atomic/electrical energy | the energy of the sun.

If the students had already learned the concept, this kind
of definition would enable them to relate the English word
'energy' to their previous knowledge.  But for an ontology,
this definition is worthless.  In physics, the words 'energy',
'work', and 'power' express three different, but related
concepts that are defined by different formulas.  For an
ontology, the above definition would be worse than useless
-- because it happens to be false.  Almost every definition
in that dictionary is either false or hopelessly vague.

PC> The whole point of creating an FO by a large consortium

 > is precisely to be certain that the views representing many
 > different interests and ways to express knowledge are taken

 > into account...

A consortium or committee is good for evaluating proposals,
but they can't solve the unsolvable.  Just look at the way
the Newtonian concepts of space, time, mass, and energy
evolved in the progression to relativity and quantum mechanics.

Those words are used in all three theories (and many other
variations).  But those words are *not* defined in terms of
primitives.  They are related to one another by various
equations.  Furthermore, the equations in the three theories
are not only different; they are contradictory.  There is
nothing that remotely resembles defining primitives.

That observation is true for every formal ontology.  There
are no primitives.  There are just equations (or other
kinds of formulas) that relate the terms.  The words in
one theory and its successors are frequently the same
or similar.  But the equations that relate them are
very different.

There's a fundamental reason why it's impossible to use any
subset of natural language vocabulary as ontological primitives:
NL words are intended to be used in a open-ended number of ways,
but ontological terms are absolutely precise within the scope
of a particular theory.

That distinction creates an inherent conflict:

 1. There are common ideas expressed in the basic vocabularies
    of many different languages, as many people such as Len Talmy
    and Anna Wierzbicka have shown.  But the corresponding words
    are vague, with many different *microsenses* that vary from
    one "language game" to another.

 2. Formal ontologies and scientific theories require sharply
    defined terms that denote values that can be measured
    precisely.  Those terms are defined only within a formal
    theory (or language game), and any paraphrase in the words
    of #1 is at best a vague approximation.

The Longman's defining terms (or anything similar, such as
Wierzbicka's primitives) are inherently vague.  They cannot
be used to define ontological terms that must have a precise,
formally defined sense.

John


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