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• W2018462672 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." @default.
• W2018462672 created "2016-06-24" @default.
• W2018462672 creator A5071803397 @default.
• W2018462672 date "1996-04-01" @default.
• W2018462672 modified "2023-09-26" @default.
• W2018462672 title "The Price of Universality" @default.
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• W2018462672 doi "https://doi.org/10.1305/ndjfl/1040046086" @default.
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