Tuesday, February 15, 2005
Reasoning over types
Parts I – III of the Adi structural ontology.
The DHS Ontology Case.ppt
Center of Excellence, proposal
New Tutorial on Orb technology à
A discussion on the protégé email list is a good one and points to some excellent language in regards to
"reasoning over types"
The Glass Bead Games are designed to stand up and detail the thought about various issues, and the thoughts about using ontologies to reason with are on a number of people’s minds.
Our group prefers to point at the notion of reasoning over types with the language "algebraic logical forms" verses "arithmetic logical forms". The distinction simply uses a metaphor that uses the differences and similarities between elementary arithmetic and elementary algebra (of the types that school children learn). The reasoning over types has the property that the logical atoms are in fact “concepts” and concept subsets. The reasoning involved touching a certain set of concepts, associations, properties, and/or attributes.
But this distinction might not be acceptable to everyone. What the issues are, in talking about logical forms, is not so easy to discuss because there are strongly held viewpoints about what computational inference is, or is not.
We are looking for some community agreement on this terminology - and realize where there may be some sources of terminological reconciliation issues.
If one "reasons" using class constructions, existing within a formal ontology, then one would like to say that this is a type of algebra. This seems useful to us, and thus should be accepted as merely being useful to someone.
In this algebraic logic the notion of domains and ranges (for concepts, properties, attributes) does "extend" the Aristotle - type deductive "inferences".
But reasoning in this way does not involve induction, nor first hand measurement of real world event structure. This is also true of the arithmetic – type logic.
Because all we have is a very limited notion of inference, we have to make sure of our concepts about "reification", "validity" or "fidelity" between the reasoning process and the natural world. The Soviet cybernetics community (Pospelov, Osopov, Finn) would say,"One has to "check" the results of computational reasoning against direct measurement in the world".
But at a deeper level the notion of type is almost always exactly the notion that a category has been identified. We use the language "categorical Abstraction" or cA to indicate a naturally occurring categorical primitive - which "comes" into existence via a process in the "non-abstract" real world. See work on semantic primitives by Sowa, Ballard, Pospelov, Adi.
The sought for "behavioral ontologies" are then informed by the set of cA atoms and the event chemistries that one observes through measurement (of things in the world).
The difference between an instance and a type is hard to settle on within communities that differ on whether AI has established a polemic about the nature of intelligence. Because the AI polemic is so strong, and so incorrect, it is often useful to distinguish between
1) the value that comes from concept representations (ie ontologies) and algorithms; and
2) the assertion that machines are sentient, or capable of knowing.
So, on to the important stuff . . .
One may think of type as being something shared by the instances having that type. One can also reflect on when an abstraction has occurred. Types, and categories, are always abstractions, and "leave something behind in the abstraction process" - (paraphrase from A. H. Whitehead).
Reasoning over specific instances is a reasoning that depends on some set of rules that can compute in predictable ways using the specific instances as the logical atoms.
(Side note: this unfortunate use of the term "individual" in OWL discussion makes the reference to "data" even more difficult, unless one accepts this term "individual" as the same as "instance data".)
Instance data that has associated with concepts expressed in some ontology (OWL, KIF, TM, or other), might live outside of our ontology architecture.
Then we may have real time data streams, whose "flow" is to be "understood" by a specific computational resource, in the form of an OWL, KIF, or TM ontology having some type of constraint language.
Action-perception cycles are then needed to maintain truth, since formal reasoning by itself is often found to be making sense of the world in a false fashion.