SUO: Re: Language and Module Processing
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Robert,
Second pass ... this time I will focus on the obstacles that I see.
Robert E. Kent wrote:
>
> 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.
I looked at these pictures. The following questions come to mind:
1. What's actually in the boxes labelled
"SUMO", "S_1", "S_1", "S_3", ...,
"OpenCyc", "O_1", "O_2", "O_3", ...?
2. In order to think about order-flipping dualities (of the galois kind),
it usually helps me to draw both of the lattices that are involved,
so let me make an ascii stab at that:
M_X = X T_L = L
full set, full set,
all models in space X. all "descriptors" in L.
o o
| . . |
| . . |
M_1 |_| M_2 o . . o T_1 |_| T_2
/ \ . . / \
/ \ . . / \
/ \ . . / \
M_1 o o M_2 . T_1 o o T_2
\ / . . \ /
\ / . . \ /
\ / . . \ /
M_1 |^| M_2 o . . o T_1 |^| T_2
| . . |
| . . |
o o
M_0 = {} T_0 = trivial theory,
null set, no information above
no models. what's already given.
I will get some coffee and think about that.
Jon
> 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
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