Université de Perpignan

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.