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2.6 Concept Refinement
In general a concept description can have some additional components beyond
the syntactic and semantic components of a simple concept description:
- Refinement
- An important component is a list of other concept
descriptions that it refines. That is, all of the requirements
of the listed descriptions are incorporated into this description,
which means that in order for an abstraction to belong to the concept
it must belong to all of the concepts on the list (and it must
also satisfy the requirements stated in the syntactic and semantic
components of the present description).
We might also say that the concept description inherits from
the concept descriptions it refines. However, inheritance has come
to have a fairly specialized meaning in computer science, particularly
in object oriented programming, so we shall generally avoid the
term here, using "refinement" instead.
In concept webs, a concept description should contain hypertext links
to each of concept descriptions that it refines.
- Use
- Similarly, a concept description may include a list of
(names of or links to) other concept descriptions that it uses
in stating the description. The difference between use and refinement
is that the meaning of the symbols in the concept descriptions on
the use list is not changed, whereas symbols in the concept
descriptions on the refines list generally have their meanings modified
by additional requirements (stated in the present description or coming
from other descriptions on the refines lists).
We can think of the concepts mentioned on the uses list as being
incorporated intact as parts ("sub-assemblies") of the current concept.
We do not (intentionally) permit circular chains of
refinement or use. Thus refinement and use relations on concept
descriptions are hierarchical; in terms of graph theory, they form an
acyclic graph. Concept descriptions may nevertheless contain other
links besides refinement and use links, and there is no requirement
of noncircularity among the total set of connections.
Thus we shall use the term conceptual hierarchy
when referring to the acyclic graphs of refinement and use, but also
speak of the concept graph or concept web in
reference to a set of concept descriptions and all of their connections.
Hierarchical development of concepts through refinement and use is
what makes it possible to build up descriptions incrementally, rather
than having to state long, flat lists of requirements for complex
concepts. It is the main support for categorization and other related
conceptualization mechanisms, including generalization (removing
requirements--going up the refinement hierarchy) and specialization
(adding requirements--going down the refinement hierarchy).
musser@cs.rpi.edu