SUO: Re: IFF base constructs
----- Original Message -----
From: "West, Matthew R SITI-ITPSIE" <matthew.west@shell.com>
To: "Standard-Upper-Ontology (E-mail)" <standard-upper-ontology@ieee.org>
Sent: Monday, September 29, 2003 1:59 AM
Subject: SUO: IFF base constructs
> Dear Robert,
>
> You recently informed us of a recent paper of yours,
> "Semantic Integration in the IFF". In this you pointed out,
> amongst other things, that the IFF provided a set of base
> constructs such as tuples.
>
> Could you provide the full list of constructs available in
> the IFF to those constructing ontologies?
Dear Matthew,
Briefly, the IFF aims to support, through its terminology and
axiomatizations, the philosophy, techniques and basic constructs of both
Information Flow (IF) and Formal Concept Analysis (FCA). Please see the
books:
* Jon Barwise and Jerry Seligman.Information Flow: The Logic of Distributed
Systems. Cambridge Tracts in Theoretical Computer Science 44. Cambridge
University Press. 1997.
* Bernhard Ganter and Rudolf Wille. Formal Concept Analysis: Mathematical
Foundations. Heidelberg: Springer. 1999.
I cannot provide a "full" list of constructs, since the IFF is open to new
ideas. I can only list what is axiomatized at present or will be in the near
term. In particular, the IFF aims to support the ideas behind *channel
theory* from the theory of IF, and the ideas behind *conceptual scaling*
from the theory of FCA. In addition, the IFF extends both IF and FCA to the
level of category theory (CT). In particular, the IFF offers the idea of a
*diagram of theories* (or logics) to represent the notion of a library of
modules. Of course. underlying any of the operations to construct ontologies
are elements from set theory and category theory, such as: set, class,
collection, function, (binary) relation, composition, identity, product,
sum, etc. And also, I must include elements of first order logic, such as:
language, variable, entity, relation, expression, language morphism,
expression function, language interpretation, theory, axiom, theorem,
closure, theory morphism, model, instance hypergraph, type language,
satisfaction, model morphism, fiber model function, truth classification,
prologic, (normal) logic, etc. Here are some particular examples:
----------------------------------------
IF
IF Concept:
classification
theory
local logic
normal logic
channel
information flow
IF Operation:
construction of the (regular) theory of a classification
construction of the classification generated by a theory
sums and quotients of theories and logics
moving theories (direct and inverse image) along a (type) function
moving logics (direct and inverse image) along an infomorphism
etc.
----------------------------------------
FCA
FCA Concept:
formal context = classification
concept lattice
FCA Operation:
left and right derivation operators
extent and intent of a concept
smallest concept with an object in its extent
largest concept with an attribute in its intent
meet and join of concepts
subsuming
a tree hierarchy as a classification
an endorelation as a classification
a preorder as a classification
a partial order as a classification (ordinal scale)
the 1-dim ordinal scale for a total order
the nominal scale for a set
the Boolean scale for a set (powerset classification)
construction of the concept lattice of a classification
projection of the classification of a concept lattice
direct sum of a collection of classifications
semiproduct (categorical sum) of a collection of classifications
direct product of a collection of classifications
apposition of a collection of classifications with a common set of instances
subposition of a collection of classifications with a common set of types
etc.
----------------------------------------
CT
CT Concept:
diagram of theories
CT Operation:
sum of a collection of theories
quotient of an endorelation of theories
surjective morphism of an endorelation
endorelation of a morphism
inclusion morphism of a subtheory
meet of a homogeneous diagram of theories
fusion of a diagram of theories
sum of a collection of diagrams of theories
etc.
----------------------------------------
In summary, unpopulated ontologies can be represented as IFF theories, and
populated ontologies can be represented as IFF logics. Libraries of modules
can be represented as diagrams of theories (or logics). Collections
(discreet diagrams) of theories can be summed. Endorelations of theories can
be quotiented. The theories indexed by a diagram can be moved to the LOT
over the fusion base language. The meet of a homogeneous diagram of theories
can be constructed. The colimit of a diagram of theories can be constructed.
When relevant consistency checks can be done, we can test a diagram of
theories to see whether it is monocosmic or polycosmic. For a discussion of
how a sort hierarchy fits into the IFF, see the SUO list message
(2003 June 29) "Reply: Pattern analysis in a lattice of theories"
http://grouper.ieee.org/groups/suo/email/msg10194.html.
The paper that you mentioned above
"Semantic Integration in the IFF" (2003)
CEUR Workshop Proceedings Vol. 82
http://sunsite.informatik.rwth-aachen.de/Publications/CEUR-WS/Vol-82/
has a collection of operations that might be used to maintain a diagram of
theories (aka, a system or ontologies or a library of modules).
In short, the IFF can represent the operations needed in John Sowa's process
of "building the hierarchy" as explained in the SUO list messages:
(2003 May 16) "Building the hierarchy"
http://grouper.ieee.org/groups/suo/email/msg09453.html
(2003 May 17) "Reply: Building the hierarchy"
http://grouper.ieee.org/groups/suo/email/msg09466.html
Robert E. Kent
rekent@ontologos.org