The essence of conceptual spaces, as I understand it, is that we can define
concepts as regions in conceptual spaces. A conceptual space is defined
by axes representing qualities. What I am attempting to do in this web
page is to provide a little cheat sheet.
A simple example is a color space. It has three axis (unless perhaps
you are a tetrachromat). There are many ways to formulate what the three
axes are: http://www.physics.sfasu.edu/astro/color.html
Another example is taste: 4 axes?
Your choice of qualitative measures deeply affects how you understand
the world. 'Spose reality is an infinitely dimensional, then we have lots
of choices for axes. We simplify and correlate by using all that coordinate
transformation and axis projection stuff from 3D graphics! Heck Gardenfors
even uses Delauney Triangulation (or polyhedralization).
My clueless newbie confession: I wish "domain" were precisely defined
for Conceptual Spaces. That makes this 9-SEP-01 version a beta.
Criterion P, page 71
A natural property is a convex region of a domain in a conceptual
Criterion C, page 105
A natural concept is represented as a set of regions in a number
of domains together with an assignments of salience weights to the domains
and information about how the regions in the different domains are correlated.
Concept Combination, page 122
The combination CD of two concepts C and D
is determined by letting the regions for the domains of C,
confined by D replace the values of the corresponding regions
for D. (contrast class p. 119), for example the "stone lions"
outside the NYC library.
Six Tenets of Cognitive Semantics, page 160
i) Meaning is a conceptual structure in a cognitive system (not
truth conditions in possible worlds)
ii) Conceptual Structure are embodied (meaning is not independent
of perception or of bodily experience).
iii) Semantic elements are constructed from geometrical or topological
structures (not symbols that can be composed according to some system
iv) Cognitive models are primarily image-schematic (not propositional).
Image-schemas are transformed by metaphoric and metonymic
operations (which are treated as exceptional features on the traditional
v) Semantics is primary to syntax and partly determines it (syntax
cannot be described independently of semantics).
vi) Concepts show prototype effects (instead of showing the
Aristotelian paradigm based on necessary and sufficient conditions).
Process of Abstraction, page 191
Start with a collection of things. Identify and quantify individual objects.
The determine the clusters. Step three: abstract the clusters into dimensions.
Thesis L, page 201
"The cardinal semantic hypothesis for cognitive representations of words
has been thesis L, which states that basic lexical expressions in a language
can be represented semantically as natural concepts."
What I am attempting to do in this web page is to provide a little cheat
sheet for myself. If you find it interesting or especially if you find
it useful, or if you find it at all, let me know at email@example.com
I may not be totally objective since I rely so heavily on my spatial
sense, but I believe this book captures the essence of how we can represent
knowledge in some sensible fashion. It only took me eight months to finish
it, which is better than Sowa's Knowledge Representation book which I gave
up on about half way thru. It was a good book, but it did not speak to
me. The last book that took me months to read, AND I actually finished
Kelly's Out Of Control (see book notes at top).
metonym & metaphor - metaphor is the same shape of concepts
applied to a different domain. Metonym, the pen in "the pen is mightier"
is a metonym symbolizing the printing press and the end of the iron age
CYC, the common knowledge project,
is going open source with premium service extra. This features:
What does read mean in each of the following: red book, red oak, red wine,
red hair (before red hair dye!), red skin, red soil, Redwood, red scare,
red sky at night...
6,000 concepts: an upper ontology for all of human consensus reality.
60,000 assertions about the 6,000 concepts, interrelating them, constraining
them, in effect (partially) defining them.
For me, the beauty of Conceptual Spaces is not every concept has to
maintain an absolute relationship with each other, they only need to be
consistent when they both appear in the same Conceptual Spaces. It makes
the ontology problem local.
9-SEP-01 jch aka YON - Jan C. Hardenbergh
- See other book notes