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Title: Conceptual Spaces: The Geometry of Thought by Peter Gardenfors ISBN: 0-262-07199-1 Publisher: Bradford Book Pub. Date: 20 March, 2000 Format: Hardcover Volumes: 1 List Price(USD): $45.00 |
Average Customer Rating: 5 (4 reviews)
Rating: 5
Summary: An eye opener
Comment: For anyone interested in the cognitive topics, machine learning and artificial intelligence, this book is an eye opener. The point of view it presents attempts to put an order in what "meaning" really means.
Drawbacks of the book? The lack of conceptualization when it comes to dynamic concepts (treated very superficially). Also, the theory is deficient when modeling the functional aspects of concepts (a "sin" already recognized by the author).
But considering the pioneering character of this piece of art, these drawbacks are just compelling invitations for further research in the field.
Rating: 5
Summary: A new model of thought
Comment: Profound piece of work. I am not a cognitive scientist, and this book is a bit technical, but it is still within reach of the motivated lay person.
Gardenfors puts forward a a model to explain cognition that he calls "conceptual spaces." These conceptual spaces are at a level of abstraction in between the symbolic (used by AI types) and connectionist (Neural Nets). But what makes his conceptual spaces interesting and plausible is the position he takes that in this conceptual space, most reasoning is done by evaluating the analog of a distance between two aspects of a perception. Or, we find things to be similar if they are "geometrically" (measurably) closer on some limited number of dimensional scales.
This is easy to follow for things like colors, but he doesn't stop there. He goes on to describe how this explains a wide variety of perceptions, as well as how we form and reform categories and concepts, and shows how this informs semantics and the process of induction.
My only criticism is that some of the illustratios would have been more powerful in color.
Rating: 5
Summary: Excellent! Conceptual Spaces make sense to me.
Comment: 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. For example, color spaces are conceptual spaces, as is the tasting combos of sweet, bitter, salty.
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).
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!
I especially liked the notion that a metaphor is taking the spatial relationship of a cluster of concepts in one domain and using them in a new domain to help understand the new domain.
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Title: Knowledge Representation: Logical, Philosophical, and Computational Foundations by John F. Sowa ISBN: 0534949657 Publisher: Brooks Cole Pub. Date: 17 August, 1999 List Price(USD): $81.95 |
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Title: Basic Category Theory for Computer Scientists (Foundations of Computing) by Benjamin C. Pierce ISBN: 0262660717 Publisher: MIT Press Pub. Date: 07 August, 1991 List Price(USD): $23.00 |
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Title: Formal Concept Analysis: Mathematical Foundations by Bernhard Ganter, Rudolf Wille ISBN: 3540627715 Publisher: Springer-Verlag Pub. Date: 01 January, 1999 List Price(USD): $49.95 |
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Title: Visualizing the Semantic Web by Vladimir Geroimenko, Chaomei Chen ISBN: 1852335769 Publisher: Springer Verlag Pub. Date: 17 January, 2003 List Price(USD): $87.95 |
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Title: Conceptual Structures: Information Processing in Mind and Machine (The Systems programming series) by John F. Sowa ISBN: 0201144727 Publisher: Addison-Wesley Pub. Date: 01 July, 1983 List Price(USD): $38.60 |
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