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Spring 1996 The Price of Universality
Edith Hemaspaandra
Notre Dame J. Formal Logic 37(2): 174-203 (Spring 1996). DOI: 10.1305/ndjfl/1040046086

Abstract

We investigate the effect on the complexity of adding the universal modality and the reflexive transitive closure modality to modal logics. From the examples in the literature, one might conjecture that adding the reflexive transitive closure modality is at least as hard as adding the universal modality, and that adding either of these modalities to a multi-modal logic where the modalities do not interact can only increase the complexity to EXPTIME-complete. We show that the first conjecture holds under reasonable assumptions and that, except for a number of special cases which we fully characterize, the hardness part of the second conjecture is true. However, the upper bound part of the second conjecture fails miserably: we show that there exists a uni-modal, decidable, finitely axiomatizable, and canonical logic for which adding the universal modality causes undecidability and for which adding the reflexive transitive closure modality causes high undecidability.

Citation

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Edith Hemaspaandra. "The Price of Universality." Notre Dame J. Formal Logic 37 (2) 174 - 203, Spring 1996. https://doi.org/10.1305/ndjfl/1040046086

Information

Published: Spring 1996
First available in Project Euclid: 16 December 2002

zbMATH: 0865.03032
MathSciNet: MR1403817
Digital Object Identifier: 10.1305/ndjfl/1040046086

Subjects:
Primary: 03B45
Secondary: 03D15, 03D35

Rights: Copyright © 1996 University of Notre Dame

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Vol.37 • No. 2 • Spring 1996
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