### The Complexity of Revision

Gian Aldo Antonelli
Source: Notre Dame J. Formal Logic Volume 35, Number 1 (1994), 67-72.

#### Abstract

In this paper we show that the Gupta-Belnap systems and are . Since Kremer has independently established that they are -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.

First Page:
Primary Subjects: 03B60
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1040609294
Mathematical Reviews number (MathSciNet): MR1271698
Digital Object Identifier: doi:10.1305/ndjfl/1040609294
Zentralblatt MATH identifier: 0801.03021

### References

[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.
Mathematical Reviews (MathSciNet): MR1256415
Project Euclid: euclid.ndjfl/1093633907
[2]Belnap, N., and A. Gupta, The Revision Theory of Truth, Mit Press, Cambridge, Ma, 1993.
Mathematical Reviews (MathSciNet): MR1220222
Zentralblatt MATH: 0858.03010
[3]Hinman, P., Recursion-Theoretic Hierarchies, Springer-Verlag, Berlin, 1978.
Mathematical Reviews (MathSciNet): MR499205
Zentralblatt MATH: 0371.02017
[4]McGee, V., Truth, Vagueness, and Paradox: An Essay on the Logic of Truth, Hackett, Indianapolis, 1991.
Mathematical Reviews (MathSciNet): MR1066695