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On Gupta-Belnap Revision Theories of Truth, Kripkean Fixed Points, and The Next Stable Set

Published online by Cambridge University Press:  15 January 2014

P.D. Welch
P.D. Welch*
Affiliation:
Department of Mathematics, University of Bristol, Bristol BS8 1TW, England. Graduate School of Science & Technology, Kobe University, Rokko-Dai, Nada-Ku, Kobe 657, Japan.
*
E-mail: [email protected]. Current address: Institut für Formale Logik, Währinger Str. 25, A-1090 Wien, Austria
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Abstract

We consider various concepts associated with the revision theory of truth of Gupta and Belnap. We categorize the notions definable using their theory of circular definitions as those notions universally definable over the next stable set. We give a simplified (in terms of definitional complexity) account of varied revision sequences—as a generalised algorithmic theory of truth. This enables something of a unification with the Kripkean theory of truth using supervaluation schemes.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 7 , Issue 3 , September 2001 , pp. 345 - 360
Copyright
Copyright © Association for Symbolic Logic 2001

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References

REFERENCES

[1] Antonelli, G. A., A revision-theoretic analysis of the arithmetical hierarchy, Notre Dame Journal of Formal Logic, vol. 35 (1994), pp. 204–208.CrossRefGoogle Scholar
[2] Barwise, Jon, Admissible sets and structures, Perspectives in Mathematical Logic, Springer-Verlag, 1975.CrossRefGoogle Scholar
[3] Belnap, Nuel, Gupta's rule of revision theory of truth, Journal of Philosophical Logic, vol. 11 (1982), pp. 103–116.CrossRefGoogle Scholar
[4] Burgess, John P., The truth is never simple, The Journal of Symbolic Logic, vol. 51 (1986), no. 3, pp. 663–681.CrossRefGoogle Scholar
[5] Chapuis, A., Alternate revision theories of truth, Journal of Philosophical Logic, vol. 25 (1996), pp. 399–423.CrossRefGoogle Scholar
[6] Friedman, H., Minimality in the -degrees, Fundamenta Mathematicae, vol. 81 (1974), pp. 183–192.CrossRefGoogle Scholar
[7] Gupta, A., Truth and paradox, Journal of Philosophical Logic, vol. 11 (1982), pp. 1–60.CrossRefGoogle Scholar
[8] Gupta, A. and Belnap, N., The revision theory of truth, M. I. T. Press, Cambridge, 1993.Google Scholar
[9] Herzberger, H., Notes on naive semantics, Journal of Philosophical Logic, vol. 11 (1982), pp. 61–102.Google Scholar
[10] Hinman, P. G., Recursion on abstract structures, The handbook of computability theory (Griffor, E., editor), Studies in Logic series, vol. 140, North-Holland, Amsterdam, 1999.Google Scholar
[11] Jech, T., Set theory, Pure and Applied Mathematics, Academic Press, New York, 1978.Google Scholar
[12] Kremer, P., The Gupta-Belnap systems S# and S* are not axiomatisable, Notre Dame Journal of Formal Logic, vol. 34 (1993), pp. 583–596.CrossRefGoogle Scholar
[13] Löwe, B., Revision sequences and computers with an infinite amount of time, Journal of Logic and Computation, vol. 11 (2001), pp. 25–40.CrossRefGoogle Scholar
[14] McGee, V., Truth, vagueness, and paradox: An essay on the logic of truth, Hackett, 1991.Google Scholar
[15] Moschovakis, Y., Elementary induction on abstract structures, Studies in Logic series, vol. 77, North-Holland, Amsterdam, 1974.Google Scholar
[16] Sheard, M., A guide to truth predicates in the modern era, The Journal of Symbolic Logic, vol. 59 (1994), no. 3, pp. 1032–1054.Google Scholar
[17] Visser, A., Semantics and the liar paradox, Handbook of philosophical logic (Gabbay, D. and Guenther, F., editors), Reidel Publishing Co., Dordrecht, 1989, pp. 617–706.Google Scholar
[18] Welch, P. D., On revision operators.Google Scholar
[19] Welch, P. D., Eventually infinite time Turing degrees: infinite time decidable reals, The Journal of Symbolic Logic, vol. 65 (2000), no. 3, pp. 1193–1203.CrossRefGoogle Scholar
[20] Yaqūb, A., The liar speaks the truth. A defense of the revision theory of truth, Oxford University Press, New York, 1993.Google Scholar