[Inquiry] Relations In General

[Jon Awbrey]

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RIG.  Note 1

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3.4.31.  Relations In General

In a realistic computational framework, where incomplete and inconsistent
information is the rule, it is necessary to work with genera of relations
that are gradually more relaxed in their constraining characters but that
still preserve appropriate measures of analogy with the original species
of relations that are found to prevail in perfect information contexts.

In the present application, the kinds of relations of primary interest are
functions, equivalence relations, and other species of relations that are
defined by their axiomatic properties.  Thus, the information-theoretic
generalizations of these structures lead to partially defined functions
and partially constrained versions of these specially defined families
of relations.

The purpose of this Section is to describe the kinds of generalized functions
and other generic orders of relations that are needed to extend the discussion
of sign relations to a more realistic level of computational and data-theoretic
analysis.  In this connection, to frame the problem in concrete syntactic terms,
I need to adapt the "equivalence class" notation for two different generalizations
of equivalence relations, to be defined below.  But first, a number of preliminary
topics need to be treated.

Jon Awbrey

| Title:    Inquiry Driven Systems:  An Inquiry Into Inquiry
| Author:   Jon Awbrey <jawbrey at oakland.edu>
| Version:  Draft 10.01
| Created:  23 Jun 1996
| Revised:  04 Apr 2003
| Advisor:  M.A. Zohdy
| Setting:  Oakland University, Rochester, Michigan, USA
| Outline:  3.  The Medium and Its Message
| Outline:  3.4.  Reflective Interpretive Frameworks

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