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Saturday, December 17, 2005


 The BCNGroup Beadgames



Challenge Problem  à



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




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.