Computing with concepts

We are defining an approach regarding the development of some RDF constructions to be used as a model of allocation of resource activities. One setting is the school administration of school resources. This is a small but significant setting. The other settings are

· FARES (Formal Analysis of Risk in Enterprise Systems) being developed as part of a State of Michigan Department of Homeland Security project.

· The Roadmap proposals

We know the importance of model building because we have cognitive models that we experience as tacit knowledge. School administrators have tacit models also, of course. These models are flexible and change as they are "used" in thinking about school activities.

“Formal” model building activity can be uncertain because natural concepts have uncertainty. Concepts have a certain quality that we, our society, do not see in mathematical models about physics or engineering.

Ontology can be understood as being similar in some ways to mathematics, and yet different. One can appreciate the limitations of classical mathematics. One can recognize that there is an issue with respect to complexity in decision-making. So even within advanced training in mathematics, one can appreciate that this limitation exists and one can look to machine-ontology as a replacement for formal mathematics.

In models of social activity we have systems like UML and object oriented programming, which can be sold as "everything one needs" and yet fails to achieve the flexibility and malleability that we know first hand from direct, personal, experience with our tacit models about those things we are very familiar with.

Knowledge management practices support the use of ontology as models of complex social situations.

The discipline of knowledge management has created some understanding about the uncertainty of building models about activities. The phrase “best practices” of a “community of practice” conveys a good beginning to this discussion. We can build on this understanding as we look for parts of the class of activities that school administrators do. Computational means, such as database use, can be provisioned with ontology models.

Modeling building with RDF depends on representing all single pieces of information as a triple

< subject, verb, object >

So administrator views a list of employees is represented in a particular structure.

<subject> administrator

<verb> views

</object>

</verb>

</subject>

is one way to represent this RDF triple. However, the W3C standard allows us to represent it in a more compact form as

< administrator, views, a list of employees >

The property, “views” is treated here as “has property of being about the view”. “Views” then is a relationship between administrator and a list of employees. The administrator might also have other relationships to other “things”.

< administrator, hires, an applicant >

< administrator, reviews, a list of applicants >

etc

These relationships are forced into a specific finite set of “activities” that administrators do, because the socialization process creates expectations.

The complete set is composed of the elements of a model about the activities of an administrator. Note that this set of activities can undergo change because of the nature of the social world’s expectations. So a new activity may “all of a sudden” be enforced by new social expectation. A change in any well-established activity may “all of a sudden” be enforced by social expectation. These changes can be reflected in the set of activities represented loosely in a small RDF repository.

Two issues remain to be considered. The first has to do with how the set of RDF elements is used as a computational means expressed over sets of data, such as lists of applicants and lists of employees. The second has to do with the imposition of a type of “grammar” by the RDF standard and the potential need to remove the grammar and encode only co-occurrence with relational typing.

The first issue can be demonstrated within a short period of time based on the task related to modeling the allocation of resources activity.

The second issue allows us to compare the Orb (Ontology referential base) standard with the RDF standard. The Orb is a set of triples, but this time there is no “imposition” of meaning other than through an naming of things, a and b, that co-occur and a typing of the set of relationships that might exist between the two things.

< object1, relationship, object2 >

So object1 may be “administrator”. Relationship may be “views”, and object2 may be “list”.

The object “list” may have a domain and range function like mathematical functions. Likewise “administrator” might be a specific selected range element from the set

{ “administrator”, “teacher”, “student”, “parent”, “governmental authority” }

The relationship also has a domain and range. So “views” may be a selected range element form the domain set:

{ “views”, “decides about”, “hires”, “fires”, “reviews” }

A high level “upper abstract” concept can then be defined:

< “administrator”, “activity”, “result of activity” >

The uncertainly comes when one asks any one of the questions,

· is this enumeration of concepts complete?

· Is this enumeration of concepts “correct”?

· Is this enumeration of concept clear?

These are the 3Cs; { complete, consistent, clarity } .

The 3Cs provide guiding principles as one embarks on the modeling of complex social activity. Oh, and by the way, all social activity is in fact “complex” and not reducible to classical mathematical models.

The 3Cs have a parallel to formal mathematics, like geometry. Geometry is developed by looking for a descriptive enumeration of a smallest set of concepts that can be clearly expressed and have independence from each other and yet “span” the complete universe of discourse. To achieve this goal, mathematics allows itself to undergo an abstraction process. This same abstraction process is provided in the upper differential ontology framework abstract layer.

The differential ontology framework can be applied to various domains and can be used to provide clear, complete and consistent subject matter indicators. This is being demonstrated in several projects.

The simplicity of differential ontology framework comes as a comparison to artificial intelligence. Differential ontology framework is used to enhance individual human ability to make sense of a set of signs about concepts, in a context that is experienced in real time as part of everyday life.

Roadmap