Conceptual spaces

Peter Gärdenfors

 

Contents

Preface
Chapter 1: Dimensions	
1.1 The problem of modeling representations	1
1.1.1 Three levels of representation	1
1.1.2 Synopsis	4
1.2 Conceptual spaces as a framework for representations	6
1.3 Quality dimensions 	9
1.4 Phenomenal and scientific interpretations of dimensions 	12
1.5 Three sensory examples: color, sound and taste	14
1.6 Some mathematical notions	21
1.6.1 Betweenness	22
1.6.2 Equidistance	24
1.6.3 Metric spaces	25
1.6.4 Euclidean and city-block metrics 	26
1.6.5 Similarity as a function of distance	28
1.7 How dimensions are identified	29
1.8 Integral and separable dimensions	33
1.9 On the origins of quality dimensions	38
1.10 Conclusion	43
Chapter 2: Symbolic, conceptual and subconceptual representations
2.1 An analogy for the three kinds of representations	47
2.2 Symbolic representations	51
2.2.1 Computationalism	51
2.2.2 The limitations of symbolic representations	54
2.3 Subconceptual representations	60
2.3.1 Connectionism	60
2.3.2 Representations in connectionist and related systems	62
2.4 Conceptual representations	64
2.5 Connections to neuroscience	73
2.6 Comparisons	79
2.6.1 Harnad's three-level theory	79
2.6.2 Two other theories	82
2.7 The jungle of representations	85
Chapter 3: Properties
3.1 Program	88
3.2 Properties in intensional semantics	90
3.3 Criticism of the traditional view of properties	93
3.4 Criteria for natural regions of conceptual spaces 	99
3.5 Natural properties	104
3.6 Reconsidering the problems	112
3.7 The relativism of conceptual spaces	115
3.8 Connections to prototype theory	122
3.9 Voronoi tessellations of a space	127
3.10 Higher-level properties and relations	133
3.10.1 Relations and properties	133
3.10.2 Shapes	136
3.10.3 Actions and functions	141
3.11 Conclusion	143
Chapter 4: Concepts
4.1 Concepts vs. properties	145
4.2 Modeling concepts	147
4.2.1 Concepts with features in several domains	147
4.2.2 Essential properties and the theory-theory of concepts	152
4.3 The role of similarity in concept formation	158
4.3.1 Similarity as a theoretical construct	158
4.3.2 Similarity as shared properties	161
4.3.3 Tversky's criticism of similarity determined from distances	163
4.4 Combining concepts	167
4.4.1 The primary model	167
4.4.2. Comparisons with other theories	173
4.4.3 The effect of contrast classes	175
4.5 Learning concepts	179
4.6 Non-monotonic aspects of concepts	185
4.7 Concept dynamics and non-monotonic reasoning	191
4.7.1 Change from general category to subordinate	191
4.7.2 Change in salience	193
4.8 Objects as a special kind of concepts	195
4.9 Four geometric categorization models	198
4.10 The shell space	207
4.11 Experiments	211
4.11.1 Experiment 1	212
4.11.2 Experiment 2	215
Chapter 5: Semantics
5.1 What is a semantics?	219
5.1.1 Questions for a semantic theory	219
5.1.2 A classification of semantic theories	222
5.1.3 The relation between the conceptual structure and the world	227
5.1.4 Lexical meaning vs. truth conditions	229
5.2 Six tenets of cognitive semantics	232
5.3 Analyses of some aspects of lexical semantics 	245
5.4 An analysis of metaphors	256
5.4.1 The spatial analysis	257
5.4.2 Relations to other cognitive theories of metaphors	261
5.4.3 Contrast classes, pragmatics and metaphors	265
5.4.4 Can domains be separated?	270
5.5 The learnability question	274
5.6 Communicating referents	278
5.6.1 Freyd's analysis	279
5.6.2 Three levels of abstraction: from object to cluster to dimension	281
5.6.3 Adjectives and dimensions	285
5.7 Can meanings be in the head?	288
5.8 Conclusion: the semantic program	297
Chapter 6: Induction
6.1 Three levels of induction	299
6.2 The symbolic level	303
6.2.1 Logical positivism and its enigmas	303
6.2.2 An example from machine learning	308
6.3 The conceptual level	313
6.3.1 Induction and natural properties	313
6.3.2 Comparison with Carnap	316
6.4 The role of theoretical concepts	319
6.5 The subconceptual level	326
6.5.1 Observation vs. perception	326
6.5.2 Generalizing within a domain with the aid of artificial neuron networks	329
6.6 Correlations between domains	334
6.7 Conclusion: what is induction?	342
Chapter 7: Computational aspects
7.1 Computational strategies on the three levels	344
7.1.1 Symbolic computations	345
7.1.2 Conceptual computations	347
7.1.3 Associationist calculations	353
7.1.4 Reduction of dimensions: from subconceptual to conceptual representation	356
7.1.5 The necessity of conceptual computations	360
7.2 Conceptual spaces as emergent systems	363
7.2.1 "Fast" and "slow" features of a system	363
7.2.2 Emergent inferences	365
7.3 Smolensky's treatment of connectionism	367
7.4 Not all computation is done by Turing machines	372
7.5 A system for object recognition	375
7.6 Conclusion	377
Chapter 8: In chase of space
8.1 What has been achieved?	379
8.2 Connections between levels	382
8.3 Conclusion: the need for a new methodology	385
Notes
References

 

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