Notre Dame Journal of Formal Logic

The Complexity of Revision

Gian Aldo Antonelli

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In this paper we show that the Gupta-Belnap systems ${\bf S}^\char93 $ and ${\bf S}^*$ are $\Pi^1_2$. Since Kremer has independently established that they are $\Pi^1_2$-hard, this completely settles the problem of their complexity. The above-mentioned upper bound is established through a reduction to countable revision sequences that is inspired by, and makes use of a construction of McGee.

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Notre Dame J. Formal Logic Volume 35, Number 1 (1994), 67-72.

First available in Project Euclid: 22 December 2002

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Primary: 03B60: Other nonclassical logic


Antonelli, Gian Aldo. The Complexity of Revision. Notre Dame J. Formal Logic 35 (1994), no. 1, 67--72. doi:10.1305/ndjfl/1040609294.

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  • [1]Kremer, P., ``The Gupta-Belnap systems $\bf S^\#$ and $\bf S^*$ are not Axiomatisable," The Notre Dame Journal of Formal Logic, vol. 34 (1993), pp. 583--596.
  • [2]Belnap, N., and A. Gupta, The Revision Theory of Truth, Mit Press, Cambridge, Ma, 1993.
  • [3]Hinman, P., Recursion-Theoretic Hierarchies, Springer-Verlag, Berlin, 1978.
  • [4]McGee, V., Truth, Vagueness, and Paradox: An Essay on the Logic of Truth, Hackett, Indianapolis, 1991.