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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