Analogy and structure
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Bibliographic Information
Analogy and structure
Kluwer Academic Publishers, c1992
- : acid-free paper
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"This book serves as the mathematical basis for Analogical modeling of language (Kluwer, 1989)"--Back cover
Includes bibliographical references (p. 366-370) and index
Description and Table of Contents
Description
Analogy and Structure provides the necessary foundation for understanding the nature of analogical and structuralist (or rule-based) approaches to describing behavior. In the first part of this book, the mathematical properties of rule approaches are developed; in the second part, the analogical alternative to rules is developed. This book serves as the mathematical basis for Analogical Modeling of Language (Kluwer, 1989). Features include:
A Natural Measure of Uncertainty: The disagreement between randomly chosen occurences avids the difficulties of using entropy as the measure of uncertainty.
Optimal Descriptions: The implicit assumption of structuralist descriptions (namely, that descriptions of behavior should be corrected and minimal) can be derived from more fundamental statements about the uncertainty of rule systems.
Problems with Rule Approaches: The correct description of nondeterministic behavior leads to an atomistic, analog alternative to structuralist (or rule-based) descriptions.
Natural Statistics: Traditional statistical tests are eliminated in favor of statistically equivalent decision rules that involve little or no mathematical calculation.
Psycholinguistic Factors: Analogical models, unlike, neural networks, directly account for probabilistic learning as well as reaction times in world-recognition experiments.
Table of Contents
Introduction. Part I: Structuralist Descriptions. 1. Measuring the Certainty of Probalistic Rules. 2. Systems of Rules. 3. The Agreement Density for Continous Rules. 4. Maximum Likelihood Statistics. 5. Optimal Descriptions. 6. Simplest Descriptions. 7. Preferred Derivations. 8. Analyzing the Effect of a Variable. Part II: Analogical Descriptions. 9. Problems with Structuralist Descriptions. 10. An Analogical Approach. 11. A Natural Test for Homogenety. 12. Statistical Analogy. 13. Defining Other Levels of Significance. 14. Actual Examples. 15. Analogical Analyses of Continuous Variables. 16. Behavioral Factors. Concluding Remarks: A Final Analogy. References. Index.
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