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Reviewer: H. Van Dyke Parunak

Central to any computational account of cognition is the notion of a concept. Concepts are the building blocks of thought, and many of the classic problems of artificial intelligence (AI), including machine learning, nonmonotonic reasoning, and knowledge representation center around them. Mainstream AI is based on the “physical symbol system hypothesis” of Newell and Simon, which asserts that symbol manipulation is the necessary and sufficient means of intelligent action. In this framework, a concept is a symbol, to be manipulated in logical expressions. While common, this approach has led to a number of intractable problems, including the question of how one measures the similarity or dissimilarity between concepts, the problem of nonmonotonicity (how learning more about a concept can lead to the retraction of predicates that were previously held to be true of it), where new predicates come from, and, in general, how the link is established between symbols and the things they represent in the real world. One response to these difficulties is sub-symbolic processing, exemplified in connectionist systems. This approach views concepts as patterns of activation across a neural network. Given this view, conceptual similarity can be defined in terms of measurable distances between activation patterns, concepts can be learned by training, and, in general, the brittle structure of symbolic concepts can give way to a much more fluid representation. But it may be too fluid. How does a reasoner come to associate a diffuse pattern of activation with a bounded, well-defined concept__?__ How is it that people can learn concepts even in highly dimensional environments, in which learning is excruciatingly slow__?__ And how can a system generalize from patterns of activation corresponding to (say) robins, blue jays, and finches, to the higher-level concept of a bird__?__ Starting with a broad and thorough familiarity with the literature of cognitive science and AI, Gärdenfors proposes that concepts live neither at the high level of symbolic processing nor at the neural level, but at an intermediate, “conceptual” level. The fundamental structure of this level is the “quality dimension,” exemplified by temperature, weight, brightness, pitch, time, length, width, and height. The structure of such a dimension is determined directly by an agent’s sensory apparatus, thus addressing the symbol grounding problem. Some sets of dimensions are “integral,” in that a percept cannot be assigned a value in one dimension without being assigned a value in all dimensions in the set (for example, hue and brightness, or pitch and loudness). Such a set of dimensions forms a “domain.” Dimensions that are not integral with one another are said to be “separable.” A set of quality dimensions with a geometrical structure constitutes a “conceptual space.” Dimensions may be continuous or discrete, but they are ordered. That is, the agent can rank percepts along each appropriate dimension. This requirement permits the definition of the basic geometric relations of “betweenness,” and thus convexity. In this framework, a property (generally manifested in natural language as an adjective) is simply a convex region in some domain, while a concept (corresponding to a noun) is a set of regions in several domains, together with information about the relative salience and interrelations of those domains. The notion of convexity directly supports the experience of “prototypes” as central to a region, while the underlying geometrical structure yields an intuitive notion of conceptual similarity as a simple distance measure. Nonmonotonicity can be explained by deriving default properties from the center of a concept’s region, from which marginal instance may vary in non-salient ways. The author meticulously works out the implications of this model, using careful reasoning, his own experiments, and detailed reinterpretation of experiments by others. He constructs a detailed theory of semantics (including lexical problems, metaphors, and learnability), discusses how induction works in this model, and analyzes the computational aspects of this model as well. His argues that the symbolic and subsymbolic paradigms are not wrong, but they are incomplete, and his discussions (particularly of induction and computation) carefully analyze the contributions of each cognitive level to the problem at hand. The author is frank about the immature and underdeveloped areas of his own program, and fair and courteous to the myriad of authors whose work he analyzes. As a result, his book provides not only a compelling argument for a geometric model of concepts, but also a detailed overview of the philosophical, computational, cognitive, and linguistic literature dealing with representation. The result is a book that will stretch readers from many different disciplines and persuasions. The text is clear enough for the interested undergraduate or lay reader, yet detailed enough to enable researchers to pursue the agenda that the author lays out. No one who must deal with the problem of cognitive representation can afford to ignore this careful contribution to the discussion. Online Computing Reviews Service