Wednesday, April 27, 2005
On the discussion of data
regularity à On the Stephenson Cyber Attack
Taxonomy à
Discussion about descriptive logics and future advancement in mathematics
Kent and Bryan
Regarding the paper at
http://www.w3.org/2004/12/rules-ws/paper/56/
I would pose a type of side question to the others in the group. Perhaps this can be discussed tomorrow and Thursday at
http://www.w3.org/2004/12/rules-ws/registered
(which is in 2005 by the way – mislabeled URL.)
The position paper talks about the need to create data federation and semantic alignment between RDF knowledge bases and other knowledge bases.
Let us set aside the question of what “other” knowledge bases refer to.
The claim is that the OWL sameAs and equivalentTo assertions are really needed and that they are needed in a dynamic environment where the rules using these assertions are changing. These two requirements seem to be suggestive of the “weakening of set and category theory” that I have talked about in my on-line book following the work by former Soviet computational semiotics.
The question is regarding the kinds of changes that can occur IF the Semantic Web logic is to “stay in fidelity to” the natural reality that is modeled by the ontology? My example will bring the pragmatic axis into light and suggest that the discussion up to now has been unreasonably focused in classical notions of logic (and not on real model modeling – like modeling the intentions of terrorists).
My work, following the work of others that I cite, suggests that ontology formalism needs a weakening of category theory and set inclusion. The suggestion follows long discussions with people like Werbos, Zadeh and Grossberg over the past two decades.
This need to weaken set and category theory is, perhaps, because the notions sameAs and equivalentTo are limited.
The limitation of these notions remains even if one gets perfect interoperability, i.e., if one had some means to enforce a standardization between RDF knowledge bases and say Ballard’s Mark 3 or Orb encoding. Perhaps we are talking about standardization with Cyc Corp ontology?
In any case, we seem to be talking about a crisp notion of set membership and category membership.
Although the SAIC ASC position paper suggest what I am also suggesting, that something is needed (not related to the notion of interoperability) and this is a power to model changes where we have degeneracy (multiple possible evaluations in standard logics.) I argue that this “response degeneracy” is exactly what situational logics need and yet are not provided when one uses descriptive logics. I have said something about this at: [43]
<quote>
Using DOF, the empirical
work from semantic extraction processes is transferred to a formal encoding of
1) explicit description of
concepts (using words and relationships to other concepts)
2) metadata related to
ambiguation/disambiguation issues related to “that” concept
3) cultural use,
reconciliation, issues related to “that” concept
</quote
An example might help.
Suppose we use a type of voting procedure where a profile element has a vote of 1, that a to be categorized element is to be included in a category, if the profile element is also in the category profile (see voting procedure )
In this voting procedure, each element of the profiles are regarded as “the same as” or “equivalent to” . But over time and as the intentionality of active real natural systems, like a terrorist cell, change; the natural categories themselves undergo what are truly complex transformations.
Example: the category of risk of a particular type – for example a risk that a distributed attack is occurring via the importation of various elements of a biological treat. The ontological elements, perhaps – as we suggest – due to modifications of ontological primitives as if metabolic in nature – change in real natural event expression. Formative and differential ontology was developed to reflect this fact. I see almost nothing in the W3C OWL work that seems to address this issue. I now that some people feel that my observation is not appropriate – by then point only to very complicated notation and no grounding in complex systems theory. For them, it seems to me, it is formalism all the way down. (metaphor to the creationist story of “turtles all the way down”) (smile). This problem of formalism is addressed with citation at: ( link )
The solution that differential ontology framework gives is two fold:
1) Temporarily we use ontology encoding as only a set of described concepts with properties, attributes and relationships to other concepts – no inferred “new” knowledge that is computed by inference engines. We leave inference to a human observation of the proper subsetted concepts. The paradigm is human centric.
2) 2Following the model form SchemaLogic (www.schemalogic.com) the terminology used in an ontology is equipped with reconciliation metadata. With the metadata we allow the uncertainties – and the indeterminacy (really occurring in natural systems) to have some means to compute rules based on the notion that concepts can be pointed at with subject matter indicators (SMI), and thus in some limited sense we can use these pointer structures to help us get a good set of concepts represented as a situational scoped ontology individual.
The Roadmap gives additional detail.
Including additional work on how frameworks and semantic primitives offer a means to instrument any extension of set theory and category theory so that the real world complexity is properly addressed.
Please note Douglas Clark’s paper
http://www.w3.org/2004/12/rules-ws/paper/46/
Also
I enjoyed reading
http://www.w3.org/2004/12/rules-ws/paper/124/
but again note that the issues of complexity and fidelity between DL or FOL and real world is avoided in most cases in most of the other papers. This has serious practical issues when government project attempt to base global analysis of risks based on ontology inference.
Again I point out the notion that
there is a
This school has just as rich
grounding in scientific and mathematical literatures as does AI and the
Thank you for reading and yes I know, this stuff is difficult to grasp.