Abstract
This paper, although self-contained and self-explanatory, can be considered complementary to the paper I presented in Las Palmas [1982a] at the Second World Conference on Mathematics at the Service of Man, The two papers deal with theories of proximity and dominance (in the context of social and behavioral inquiry) and they are complementary in the following senses:
-
(a)
In [1982a] we were interested in representing (“measuring”) proximity and dominance by intervals on the real line. The theories served as tools guaranteeing the existence of the required representations. In this paper the stress is on the theories themselves — their logic and their meaning. However, we ignore here theories requiring an informal mathematical language (which were quoted in [1982a] from works of other researchers such as Scott and Suppes [1958], Roberts [1969] and Krantz et al. [1971]) and limit ourselves to (parts of) those which can be axiomatized in a formal (two-valued or multi-valued) language. These theories can also be found in our [1981a] and [1981b].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bigelow, J.C.: Quantum Probabilities in Logical Spaces, Manuscript, Victoria University of Wellington.
Coombs, C.H.: 1964, A Theory of Data, John Wiley, New York. Dalla Chiara, M.L.: 1977, Quantum Logic and Physical Modalities, Journal of Philosophical logic 6, 391–404.
Giles, R.: 1974, A Non-Classical Logic for Physics, Studia Logica 33, 399–417.
Goldblatt, R.I.: 1974, Semantic Analysis of Orthologic, Journal of Philosophical Logic 3, 19–35. Gregson, R.A.M.: 1975, Psychometrics of Similarity, Academic Press, New York.
Katz, M.: 1980, Inexact Geometry, Notre-Dame Journal of Formal Logic 21, 521–535.
Katz, M.: 1981a, Difference Measurement Spaces, Journal of Mathematical Psychology 23, 195–213.
Katz, M.: 1981b, Lukasiewicz Logic and the Foundations of Measurement, Studia Logica 40, 209–225.
Katz, M.: 1981c, Two Systems of Multi-Valued Logic for Science, Proceedings of the 11th International Symposium on Multiple- Valued Logi, IEEE Computer Society Press, New York, 175–182.
Katz, M.: 1982a, Measures of Proximity and Dominance, Proceedings of the Second World Conference on Mathematics at the Service of Man, Universidad Politécnica de Las Palmas, 370–377.
Katz, M.: 1982b, Real-Valued Models with Metrie Equality and Uniformly Continuous Predicates, Journal of Symbolic Logic 47, 772–792.
Katz, M.: 1982c, The Logic of Approximation in Quantum Theory, Journal of Philosophical Logic 11, 215–228.
Krantz, D.H., Luce, R.D., Suppes, P. and Tversky, A.: 1971, Foundations of Measurement, Academic Press, New York.
Kruskal, J.B. and Wish, M,: 1978, Multidimensional Scaling, Sage Publications, Beverly Hills, CA.
Luce, R.D. and Raiffa, H.: 1957, Games and Decisions, John Wiley, New York.
Rabinowitz, G.B.: 1975, An Introduction to Non-Metric Multidimensional Scaling, American Journal of Political Science 19, 343–390.
Roberts, F.S.: 1969, Indifference Graphs, in F. Harary (ed.) Proof Techniques in Graph Theory, Academic Press, New York, 139–146.
Saati, T.L.: 1980, The Analytic Hierarchy Process, McGraw- Hill, New York.
Scott, D.S.: 1974, Completeness and Axiomatizability in Many-Valued Logic, in L. Henkin et al. (eds.), Proceedings of the Tarski Symposium (Proceedings of Symposia in Pure Mathematics 25), American Mathematical Society, Providence, R.I., 188–197.
Scott, D.S.: 1976, Does Many-Valued Logic Have Any Use? in S. Körner (ed.), Philosophy of Logic, Basil Blackwell, Oxford, 64–95.
Scott, D.S. and Suppes, P.: 1958, Foundational Aspects of Theories of Measurement, Journal of Symbolic Logic 23, 113–128.
Shepard, R.N.: 1974, Representation of Structure in Similarity Data: Prospects and Problems, Psychometrika 39, 373–421.
Tarski, A.: 1956, Logic, Semantics, Metamathematics (papers from 1923–1938), Claredon Press, Oxford.
Torgerson, W.S.: 1958, Theory and Methods of Scaling, John Wiley, New York.
Tversky, A.: 1969, Intransitivity of Preferences, Psychological Review 76, 31–48.
Tversky, A.: 1977, Features of Similarity, Psychological Review 84, 327–352.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1984 D. Reidel Publishing Company
About this chapter
Cite this chapter
Katz, M. (1984). Controlled-Error Theories of Proximity and Dominance. In: Skala, H.J., Termini, S., Trillas, E. (eds) Aspects of Vagueness. Theory and Decision Library, vol 39. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6309-2_4
Download citation
DOI: https://doi.org/10.1007/978-94-009-6309-2_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-6311-5
Online ISBN: 978-94-009-6309-2
eBook Packages: Springer Book Archive