SUO: Re: Language And Module Processing (LAMP)
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Robert, SUO WG, ...
I would like to start thinking about this by beginning with simple term logics.
Let's say we have two formal languages Lex_1, Lex_2 over the same alphabet A,
so that Lex_1, Lex_2 c A*, and these understood as the basic lexicons of terms
that are available as building blocks for every higher level. For example, we
might be thinking of something like the following:
Lex_1 = {..., "thing", "object", "vehicle", "truck", "semi_truck", "trunk", ...}
Lex_2 = {..., "thing", "entity", "vehicle", "lorry", "articulated_lorry", "boot", ...}
The quotient idea is very important. It is yet another one of the ways that we have
of talking about constraints, or controlled variety, or information, or lawfulness.
I can think of at least two different ways that quotients come up. Very roughly,
we might think of these as "denotative" and "connotative" information.
For example, we might suspect that "thing"_1 and "object"_1 in Lex_1 mean the same thing,
or we might suspect that "object"_1 in Lex_1 and "entity"_2 in Lex_2 mean the same thing.
There are many way to test these sorts of hypotheses. Proceeding "empirically",
like the ever-popular "field linguist", we could go out into the "field", find
informants Inf_1 and Inf_2 for Lex_1 and Lex_2, respectively, and query them
about the instances of a suitable universe X to which they would apply the
terms of Lex_1 and Lex_2.
For example, suppose we collect data that falls
into the pattern of the following scattergram:
o-------------------------------------------------o
| X . . . . . . . . . . |
| . . . . . |
| . . o-----------o . o-----------o . . |
| / \ / . \ . |
| . / . o \ . |
| / /.\ . \ . |
| . / / . \ . \ |
| o . o . . o o . |
| . | | . | | . |
| . | vehicle_1 | . . | vehicle_2 | . |
| | | . . | | . |
| . o . o . o . o |
| . \ \ . / / . |
| . \ \ / / . |
| . \ . o . / . |
| . \ . / \ / . |
| . . o-----------o . o-----------o . . |
| . . . . . . . . . |
| . . . . . . . . . . |
o-------------------------------------------------o
This would make it reasonable to say, approximately speaking,
that "vehicle"_1 denotes the same things in X as "vehicle"_2,
on the evidence of Inf_1 and Inf_2. Observe that the weight
of the counter-evidence is measured by the relative frequency
of the outlying instances, those in the "symmetric difference"
of the extensions of the terms: Symdiff (Vehicle_1, Vehicle_2).
The "denotative" or "extensional" type of quotient operation
amounts to ignoring the outliers and the regions of the universe
that they occupy, collapsing the topology into the following form:
o-------------------------------------------------o
| X |
| |
| o-------------o |
| / \ |
| / \ |
| / \ |
| / \ |
| o o |
| | vehicle_1 | |
| | = | |
| | vehicle_2 | |
| o o |
| \ / |
| \ / |
| \ / |
| \ / |
| o-------------o |
| |
| |
o-------------------------------------------------o
Jon Awbrey
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> 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.
> >
> > 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 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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