SUO: Language and Module Processing
All,
I have posted a file called "Language and Module Processing" at the address
http://suo.ieee.org/IFF/language-module-processing.html
and linked off the main SUO IFF page.
In this file I have offered a possible diagrammatic scenario for the
creation of the John Sowa's library of modules diagram
http://www.jfsowa.com/figs/suohier2.gif,
which (as John mentioned in a previous message) shows how the modules
derived from SUMO and OpenCyc could fit together.
There are six diagrams linked by five processing steps. The first two
processing steps occur in the *context of theories*, whereas the last three
processing steps occur in the *lattice of theories*.
The first diagram assumes two distinct ontologies SUMO and OpenCyc have been
resolved into several submodules resulting in two libraries of modules
within two lattices of theories for two distinct first order logic (FOL)
languages L_SUMO and L_CpenCyc, respectively. Recall that an FOL language is
the terminological content of an ontology consisting of relation symbols,
function symbols and constants with appropriate arities specified.
The first step forms the sum of the two FOL languages using the disjoint
union of the sets of relation symbols, function symbols and constants. This
results in the second diagram which has only one summed FOL language, but
consists of the two ontologies arranged as two distinct libraries of modules
in a single lattice of theories (recall that each FOL language determines
its own lattice of theories.
The second step involves two substeps: (1) specifying equivalent relation
symbols, equivalent function symbols, and equivalent constant symbols; and
(2) forming the quotient of the sum language modulo these equivalence
relations. This results in the third diagram which has only one quotiented
FOL language, but still consists of the two ontologies arranged as two
distinct libraries of modules in a single lattice of theories.
The third step works inside a lattice of theories. It forms a single library
of modules by summing the two previous libraries of modules. This results in
the fourth diagram which has the two ontologies arranged within one library
of modules in a single lattice of theories.
The fourth step accomplishes two objectives: (1) it extracts various
sub-sub-modules from the various sub-modules of the two ontologies; and (2)
it may create from scratch several generic modules that may be needed later.
This results in the fifth diagram which has the these generic modules
situated at the highest level below the top, with the two ontologies
arranged below these.
The fifth and final step creates a customized theory by forming the meet of
some of the original submodules from the two ontologies plus some of the
generic modules. The meet is formed by taking the union of the axioms in the
appropriate modules.
Please look this over and send me your comments.
Robert E. Kent
rekent@ontologos.org