Thursday, December 15, 2005
Communications on lattice of theories
John
Rather than "infinite number of models", if we were to say "unlimited number of models" would this be in line with what you want to say? Does the lattice that you speak of have a possible specific realization in a context (as part of a future complex web service negotiation) where a specific but finite in number set of partially ordered theories/models has been made available for computational exchanges?
If unlimited is a sufficient concept, than we have the possibility that in the present moment, a web service will construct (perhaps as an aggregation from a small set of primitives) a specific lattice of "small finite state machines" in one to one correspondence to a set of partially ordered formal constructions). This is what I belief Richard Ballard's Mark 3 is going to do. This is also how the polylogic-based system developed Erez Elul is doing. It is also, what Klausner has done.
These constructions would then be available as a specific (standard compliant) set of resources available as part of web service realization.
In this case, the concept of "infinite" must be a potential but not actual computational structure.
Side question: Is it possible to have two different (completely unrelated by any order / metric) infinite lattices?
I agree that the concept of infinite is a valuable one, but one that might be “merely” constructed by human ability to create (induce) abstract formal systems. I also agree that there appears to be a continuum in our existence, particularly with respect to the reality of being able to divide distance into smaller units. So the problem of representing reality is an open question – still. But what can we do to create standards for web services?
I have been trying, again over the past week, to focus on what pragmatics means in term of goals and possibilities that biological systems (at least) have in any specific moment. A good place to look to see actual implication issues is in how the Unified Medical Language System (UMLS) is being used by the pharmaceutical, medical and gene research communities.
My reading materials on this are Mork et al (2003), and Planet et all (2001). (references are in the hyperlinks from
http://www.ontologystream.com/beads/nationalDebate/309.htm
Oh, that one might say that the later Wittgenstein's work was more elegant (even if he himself was not completely satisfied, than the Tractatus. The criterion for "elegance" varies. The Tractatus was neatly organized and expressed - perhaps as no or few other works of logic-philosophy-literature ever was. But the later work (and I talk about the Blue and the Brown Books when I think about the later work) was elegant in that it more clearly (perhaps than only a few other works) identified the issues that logical positivism could not completely and consistently deal with. The later work was satisfying in a way that the Tractatus was not. Yes?
I hope that this working group will try to address these following issues
1) On the sufficiency of current standards: The sufficiency of RDF to model that part of reality where response degeneracy exists - as in decision support where more then one future actually is potential (or more than one reality is actually potential) (or where this theoretical concept of an infinite number of lattices has more than one (disjoint) realization).
2) Semantic dimension is complex: If RDF is seen as being sufficient only within a specific boundary (such as in dealing with simple relationships between data elements, then how does one address the semantic dimension when humans are interacting in a crisis - for example.)
3) The separation of the ontology concepts from first order logic specification: How first order logics might be separated from existing OWL programs and systems IN SUCH A WAY that the logic can be recombined easily. This does not seem to be technically difficult to separate the logic in a program that exists independent from the specification of concept, attributes, relationships and properties (and perhaps "aspects").
4) Development of curricular elements for knowledge science: How can the ontology community leadership develop a non-philosophical treatment of the full range of structural (ie fixed and engineered) as well as open (flexible and not fully engineered) services? Is it possible to make the separation between engineered systems and open systems philosophically clean as well as reflected in the standards, so that the current confusion goes away? Can this treatment be provided as university curriculum?