# KEHOME/knowledge/TheoryFormalConceptAnalysis/fca.txt
# 9:30 am 1998/1/26
# new systax Sep/29/2002

#================================#
# KR vs. Formal Concept Analysis #
#================================#

# Reference:
# "Formal Concept Analysis", Chapter 11 of
# B.A. Davey and H.A. Priestley,
# "Introduction to Lattices and Order",
# Cambridge University Press, 1990

1. isomorphic context
=====================
For the simplest case, the contexts are isomorphic.
FCA
  A context, x, is a triple (object,attribute,relation)
  where
  object is a set {g, ...}
  attribute is a set {m, ...}
  relation is a map {g has m, ...}
KR
  # context x is a concept-hierarchy
  at view=x
  existent  isc object,attribute,relation #concept
  object    isc g, ...                    #concept
  attribute isc m, ...                    #concept
  relation  isc "g has m", ...            #concept

2. new concepts
===============
FCA
  Match attributes
  to determine lattice of all possible concepts.
KR
  Match attributes (integrate/differentiate)
  to determine new hierarchy.
  This new hierarchy is a new context.

3. algebraic variables
======================
FCA
  ?
KR
  Concepts may be viewed as simple algebraic variables
  in the usual sense.  For example, given
    Dutchess, Reno isu dog
    Dutchess has color=black; Dutchess do bark done
    Reno has color=white; Reno do bark done
  then the statements
    dog has color
    dog do bark done
  are both meaningful.  The meaning is obtained
  by substituting
    dog -> Dutchess
  or
    dog -> Reno