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Frederick ,
You aksed if I could provide references (preferably Web
pointers) to the discussions of
mathematical structures you mention?
Here's a start- the Conference on Galois Connections
2001. Abstracts are at:
a sample abstract is:
Galois connections, concept lattices, and related structures in fuzzy
logic
by
Radim Belohlavek
Dept. Computer
Science, Palacky University, Tomkova 40, 779 00 Olomouc, Czech Republic
The main purpose of the talk is to present a theory of Galois connections,
concept lattices, and related structures from the point of view of fuzzy logic.
Fuzzy logic and fuzzy set theory originated by Zadeh in 1965 has been
substantially developed recently. Contrary to classical logic that works with
two truth values (0 and 1), fuzzy logic works with an ordered scale of truth
values (truth degrees). This makes it possible to grasp the intuition that
propositions of natural language are not always fully true or fully false;
rather, they are true to a certain degree (examples: "100 is a big number", "it
is very cold"). Formalization of this idea leads to logical calculi for
so-called approximate reasoning and to the theory of fuzzy sets (classical logic
and set theory are special cases). "Fuzzy approach" has been applied to various
disciplines and theories; there are numerous commercial applications of fuzzy
logic. We show a way to generalize the theory of Galois connections, concept
lattices, and related structures to fuzzy setting. The generalization is
well-motivated: from the point of view of the theory of concept lattices, the
present generalization makes it possible to handle vagueness in data
(object-attribute relations, formal concepts etc.). The issues that will be
discussed are: the notion of a fuzzy Galois connection; fuzzy Galois connections
induced by binary fuzzy relations; relationship between fuzzy Galois connections
and (non-fuzzy) Galois connections; fixed points of fuzzy Galois connections and
the notion of a fuzzy concept lattice; fuzzy closure operators and closure
systems; fuzzy order, the structure of fixed points of fuzzy Galois connections,
and the main theorem of fuzzy concept lattices; some issues that are degenerated
in classical case (logical precision, similarity). Briefly discussed will be the
connection of the present approach to other approaches (fuzzy concept lattices:
A.Burusco+R.Fuentes-Gonzales, S.Pollandt; fuzzy closure operators: Italian and
Spanish groups) and some directions of future research.
There's a Concept Lattices and Application worksop. The 2004 info is
at:
http://www.cs.vsb.cz/cla/2004/
and there's a 2005 conference coning uo.
http://cla2005.inf.upol.cz/about.html
Gary
-----Original Message-----
From: Frederick B.
Kintanar [mailto:fred@ntsp.nec.co.jp]
Sent: Wed 3/23/2005 2:38 AM
To: Gary Berg-Cross
Cc: Rob Freeman; John F. Sowa;
cassidy@MICRA.COM; West, Matthew R SIPC-OFD/321; SUO WG; cg@CS.UAH.EDU
Subject: Re: Inconsistent models, mapping, interoperability, and
the SUO
Gary Berg-Cross wrote:
> One this discussion of
building a lattice from studying word sets, such as
>
> >
Actually, I've started work on a prototype lattice that uses
> WordNet's
noun
> > classes. So far, I have a first order Q&A function
to move from one
> node
> > in the lattice to another. I
think the same thing is needed for the
> verbs,
> > but haven't
gotten that far.
>
> Doesn' the work on "Formal Concept Analysis "
(FCA) at
> Karlsruhe build concept lattices something like this? For
exaple
> Philipp Cimiano, Steffen Staab, & Julien Tane tested an
assumption that :
>
> "verbs pose strong selectional restrictions
which could be used to
> build a conceptual hierarchy on the basis of
the inclusion relations
> between the extensions of the selectional
restrictions of all the
> verbs. Tthe verbs themselves
provide intensional descriptions for
> each concept
(in "Deriving Concept Hierarchies from Text by Smooth
> Formal Concept
Analysis"). They have a small concept lattice example
> in the
paper.
>
> I've also seen discussion of mathematical structures
related to FCA
> (e.g. concept lattices, Galois connections, closure
structures,
> attribute implications) that seems to be something worth
considering
> here if people are building applications.
>
Hi
Gary,
Could you provide references (preferably Web pointers) to the
discussions of
mathematical structures you mention? I haven't gotten
around to
studying FCA
in detail, but I am interested in relating Galois
connections to the
informorphisms
of Barwise & Seligman, also used
in Robert Kent's Information Flow
Framework
that is one of our starter
documents for an SUO.
Part of IFF's emphasis is on coming up with
meta-ontologies where mapping
between inconsistent models is possible in a
principled way. The work of
Kalfoglou and Schorlemmer, working on the
mapping and merging of "populated
ontologies" may provide a relevant
technique.
*/"IF-Map: an ontology mapping method based on Information
Flow theory"/*
/*Y.Kalfoglou*/, M.Schorlemmer.
http://www.ecs.soton.ac.uk/~yk1/ifmap-jds03.pdf
*/"Ontology
mapping: the state of the art"/*
/*Y.Kalfoglou*/, M.Schorlemmer
http://www.ecs.soton.ac.uk/~yk1/kalfoglou_schorlemmer_ontomapKER03.pdf
Cheers,
Fred
Frederick
Kintanar
NEC Telecom Software Philippines
Cebu City
>
**Regards,
>
>
>
>
Gary
>
> -----Original
Message-----
> *From:*
owner-standard-upper-ontology@listserv.ieee.org on
behalf
> of Rob
Freeman
> *Sent:* Tue 3/22/2005 9:52
PM
> *To:* John F.
Sowa
> *Cc:* cassidy@MICRA.COM; West, Matthew R
SIPC-OFD/321; SUO WG;
>
cg@CS.UAH.EDU
> *Subject:* Re: Inconsistent
models, mapping, interoperability, and
> the
SUO
>
>
John,
>
> On Tuesday 22 March 2005 23:14,
John F. Sowa wrote:
>
>
> > Before spammers started to play
games with it,
> > Google's page-rank
algorithm was the best guide
> > to finding
useful sites among the trash. Some such
>
> techniques can be adapted to any method for
storing
> > and retrieving data, including
the lattice. You
> > can add metadata
to each theory that says who's
> > using it,
for what purpose, and with what
success.
>
> Seeking meaning in a pattern
in the connections of your lattice,
> like
Google's
> page-rank algorithm, which seeks
meaning in the pattern of connections
> between
pages on the Web.
>
> Yes, that's
nice.
>
> Seeking patterns in use would be
one strategy. Another would be to
>
seek
> patterns in response to a
query.
>
> Which takes me to Rich's
initiative.
>
> On Tuesday 22 March 2005
23:32, Rich Cooper wrote:
>
>
> > Actually, I've started work on a
prototype lattice that uses
> WordNet's
noun
> > classes. So far, I have a
first order Q&A function to move from
> one
node
> > in the lattice to another. I
think the same thing is needed for
> the
verbs,
> > but haven't gotten that
far.
>
> Rich. Why use WordNet? Why not
use words? That way you can handle
> your
query
>
"natively".
>
> As you seek paths from
word-to-word you will travel node-to-node,
> and
describe
> a pattern in your lattice, which can
be interpreted meaningfully a
> bit
like
> the patterns of Google's page-rank
algorithm, as John suggests.
>
>
-Rob
>
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