Saturday, December 17, 2005
Lattice of ontologies
Pro: It is suggested that the work of Tarski
establishes a foundation to ontological engineering. This suggestion is made based on certain schools of thought that
have been associated with classical artificial intelligence and with first
order logics.
Con: Reservations have been noted by a number of
scholars, including Roger Penrose and Robert Rosen. These two authors’ works can be examined to see what the issues
are regarding non-computability, and non-representation-ability of classical
logic.
Recommendation: A review of the literature shows that
biological engineering and generic science has been attempting to build an
engineered solution for basic research on structure and function within
biological form. This form has been
expressed in the Foundational Model of Anatomy. The model is part of a large “semantic network” of over 775,000
concepts, called Unified Medical Language System. The query discussed in
http://sigpubs.biostr.washington.edu/archive/00000135/
focused on the part to
whole relationship, specifically queries that do depend on ontological
attributes, properties, relationships, subsumption and facets. Again, however the logic is mostly external
to the ontology (which is encoded in Protégé 2000) using a frame, or KIF, type
paradigm.
One of the
vocabularies from the UMLS is MeSH. In
the description (at the link) one sees that concept descriptions is considered
sufficient and that no extensive logical apparatus is present. Query does allow computer code, of
course. But the search is by descriptor
names or by searching for term names.
Logic is simple and external.
The recommendation is
thus that sets of well-defined concepts from the UMLS, or some subpart of it, should
be studied so that a minimal core is extracted to form the conceptual content
of a smallest ontology, when compared with a lattice to be constructed over
this smallest ontology.
The objective of the recommendation
is to create a lattice of ontological structures each one with an ordering
relationship that depends on some implementation of Tarski’s recursive
notation.
Penrose’s “The Road to
Reality” (2004) is specific in avoiding any discussion of his work in quantum
cognitive neuroscience. Perhaps this is
way we find no mention of Tarski or foundation of logic in “The Road To Reality”. But in “The Emperor’s New Mind” (1989), spends
the first third of the book on logic.
Chapter two is on algorithms and Turing machines, and includes the
Church-Turing thesis. Church’s lambda
calculus is given a clear presentation on pages 66 – 70. Tarski is not mentioned. The concept of a lattice of models or theory
is also not mentioned. Fiber bundles
are, and are mentioned in a way the suggest some of the literature on slots and
fillers and facets.
Thus there is some
hope that a mapping can be developed that tests the foundational elements of
Penrose and Tarski/Sowa lattice of ontology.
We know that very
large communities of genetic researchers are using microarray hardware and
analytic methods (mostly forms of latent semantic indexing on “attributes” of
measured phenomenon from gene expression – such as expression rates and protein
concentrations. This is where we would
propose to test a lattice of ontologies.
(see [316] )
The tie back to
Penrose is via the fiber bundle formalism, and what seem to be natural
relationships to the frame based reasoning available in KIF.