See Also: Book Notes,

Conceptual Spaces:
The Geometry of Thought
Peter Gärdenfors
MIT Press, 2000 (Table Of Contents)

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: 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 space.

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 of rules).
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 views).
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. Simple!

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."

Other Notes:

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

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 was Kevin 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...

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