Luis, Jean Marc, Ben, List,
It would probably at this point be valuable for those who are not
familiar with Marty's work (and who are not fluent in French as I
certainly am not) to at least take a look at the Summary in English of
his Foliated Semantic Networks: Concepts, Facts, Qualities posted at :
http://www.univ-perp.fr/see/rch/lts/MARTY/semantic-ns/
The first page of the Summary is the Abstract of the paper and is copied
below my signature while the entire Summary is of interest.
Gary
Foliated Semantic Networks: Concepts, Facts, Qualities
by Robert Marty
Abstract
This paper suggests a general perception-based theory of representation
within the framework of the phenomenology of C. S. Peirce (named by him
"phaneroscopy") by means of the generalization of R. Wille’s basic
lattice-concepts theory of objects and their attributes.
We first summarize Peirce's main categorization of all n-adic relations
into three fundamental kinds: Firstness, Secondness and Thirdness (i.e.,
relations requiring monads, dyads and triads, respectively, in their
definitions). His "reduction thesis" reduces all relations of higher
adicity into these three kinds.
We then use elementary Category Theory to develop "relation-structures"
of concepts, relations and higher order relations, based entirely on
experienced simple "qualities of feeling." A relational algebra results
which includes semantic nets as relation-structures. In terms of this
algebra we use Peirce's "reduction theorem" in order to build a
"foliation" of all conceptual/relational-structures by means of levels
("sheets") algebraically defined. This provides a canonical "normal
form" for networks of n-adic relations. This can be done to existing
semantic network formalisms to help make sense of phenomenologically
confused components.
Analogously to Wille's lattice-concepts theory connecting objects and
attributes, we define "representation-contexts" connecting two
corresponding classes of phenomena formalized in terms of Category
Theory by diagrams in a category we call relational structures provided
with natural transformations as morphisms. This leads us to a foliated
conception of semantic networks with each concept and relation assigned
to a particular phenomenological level. Thus a foliated network
represents not only a state of things but also the mode of connection of
the network with the state of things. One consequence of foliation is
that we now have a method for relational subsumption using the
generalization-hierarchy of relations.
In addition to the insight afforded by this formal analysis, we also
obtain a lattice of representation-relations which may be
computationally used as an IS-A hierarchy sub-element for the purpose of
automatic inference, in all subject-domains involving representation.
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