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INTRANSITIVITY AND VAGUENESS

Published online by Cambridge University Press:  01 December 2008

JOSEPH Y. HALPERN
JOSEPH Y. HALPERN*
Affiliation:
Computer Science Department, Cornell University
*
*COMPUTER SCIENCE DEPARTMENT CORNELL UNIVERSITY ITHACA, NY 14853 E-mail:[email protected]
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Abstract

There are many examples in the literature that suggest that indistinguishability is intransitive, despite the fact that the indistinguishability relation is typically taken to be an equivalence relation (and thus transitive). It is shown that if the uncertainty perception and the question of when an agent reports that two things are indistinguishable are both carefully modeled, the problems disappear, and indistinguishability can indeed be taken to be an equivalence relation. Moreover, this model also suggests a logic of vagueness that seems to solve many of the problems related to vagueness discussed in the philosophical literature. In particular, it is shown here how the logic can handle the sorites paradox.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 1 , Issue 4 , December 2008 , pp. 530 - 547
Copyright
Copyright © Association for Symbolic Logic 2008

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References

BIBLIOGRAPHY

Aumann, R. J. (1976). Agreeing to disagree. Annals of Statistics, 4(6), 1236–1239.CrossRefGoogle Scholar
Bennett, B. (1998). Modal semantics for knowledge bases dealing with vague concepts. In Cohn, A. G., Schubert, L. K., & Shapiro, S. C., editors. Principles of Knowledge Re-presentation and Reasoning: Proceedings of the Sixth International Conference (KR ’98). San Francisco, CA: Morgan Kaufmann, pp. 234–244.Google Scholar
Black, M. (1937). Vagueness: an exercise in logical analysis. Philosophy of Science, 4, 427–455.CrossRefGoogle Scholar
Dummett, M. (1975). Wang's paradox. Synthese, 30, 301–324.CrossRefGoogle Scholar
Fagin, R., Halpern, J. Y., Moses, Y., & Vardi, M. Y. (1995). Reasoning About Knowledge. Cambridge, MA: MIT Press. [A slightly revised paperback version was published in 2003.]Google Scholar
Fine, K. (1975). Vagueness, truth, and logic. Synthese, 30, 265–300.CrossRefGoogle Scholar
Friedman, N., & Halpern, J. Y. (1997). Modeling belief in dynamic system. Part I: foundations. Artificial Intelligence 95(2), 257–316.CrossRefGoogle Scholar
Graff, D. (2000). Shifting sands: an interest-relative theory of vagueness. Philsophical Topics, 28(1), 45–81.CrossRefGoogle Scholar
Halpern, J. Y. (1997). On ambiguities in the interpretation of game trees. Games and Economic Behavior, 20, 66–96.CrossRefGoogle Scholar
Halpern, J. Y. (2005). Sleeping beauty reconsidered: Conditioning and reflection in asynchronous systems. In Gendler, T. S., & Hawthome, J., editors. Principles of Knowledge Representation and Reasoning: Proceedings of the Ninth International Conference (KR ’04). Oxford, Oxford Studies in Epistemology, Vol. 1, pp. 111–142.Google Scholar
Halpern, J. Y., & Fagin, R. (1989). Modelling knowledge and action in distributed systems. Distributed Computing, 3(4), 159–179.CrossRefGoogle Scholar
Halpern, J. Y., & Moses, Y. (1992). A guide to completeness and complexity for modal logics of knowledge and belief. Artificial Intelligence, 54, 319–379.CrossRefGoogle Scholar
Hempel, C. G. (1939). Vagueness and logic. Philosophy of Science, 6, 163–180.CrossRefGoogle Scholar
Kamp, H. (1975). Two theories about adjectives. In Keenan, E. L., editor. Formal Semantics of Natural Language. Cambridge, UK: Cambridge University Press, pp. 123–155.CrossRefGoogle Scholar
Keefe, R. (2000). Theories of Vaguness. Cambridge, UK: Cambridge University Press.Google Scholar
Keefe, R., & Smith, P. (1996). Vaguness: A Reader. Cambridge, MA: MIT Press.Google Scholar
Peirce, C. S. (1931–1956). In Hartshorne, C., and Weiss, P., editors. Collected Writings of Charles Sanders Peirce. Cambridge, MA: Harvard University Press.Google Scholar
Poincaré, H. (1902). La Science et l'Hypothèse. Paris, France: Flamarrion Press.Google Scholar
Raffman, D. (1994). Vagueness without paradox. The Philosophical Review, 103(1), 41–74.CrossRefGoogle Scholar
Soames, S. (1999). Understanding Truth. New York, NY: Oxford University Press.CrossRefGoogle Scholar
Sorenson, R. (2001). Vagueness and Contradiction. Oxford, UK: Oxford University Press.CrossRefGoogle Scholar
van Fraassen, B. C. (1968). Presuppositions, implications, and self-reference. Journal of Philosophy, 65, 136–152.CrossRefGoogle Scholar
Williamson, T. (1994). Vagueness. London/New York: Routledge.Google Scholar
Zadeh, L. A. (1975). Fuzzy logics and approximate reasoning. Synthese, 30, 407–428.CrossRefGoogle Scholar