Re: SUO: RE: Abstractions and Embodiments
Dear Matthew,
I used FCA as an example of what can be done.
The principle is more important than any particular
tool that may be used.
MW: I have some concerns about FCA, but that is mostly
about the sorts of graphs it produces, rather than
the principles involved. The graphs are not subtype/
supertype graphs, although they are easily confused
with those, so whilst I think the distinctions are
important I am less enamoured of the graphs FCA
produces.
FCA is constructed from a table, which can be
interpreted in several different ways. Under one
interpretation, the column headings represent
monadic predicates and the row headings represent
concept types, which are defined as conjunctions
of some combination of the predicates. The result
of applying the FCA algorithms produces a lattice,
which is a version of a type-subtype hierarchy.
As an example, see the beverage example in my
tutorial on math & logic:
http://www.jfsowa.com/logic/math.htm#Lattice
The FCA algorithms only accommodate type-subtype
constructions for concepts definable by conjunctions
of monadic predicates. That is my major criticism,
but there are other ways of getting around such
limitations and other algorithms that can be used.
John