Notre Dame Journal of Formal Logic 37 (2):174-203 (1996)

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
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DOI 10.1305/ndjfl/1040046086
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References found in this work BETA

Properties of Independently Axiomatizable Bimodal Logics.Marcus Kracht & Frank Wolter - 1991 - Journal of Symbolic Logic 56 (4):1469-1485.

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Citations of this work BETA

Why Combine Logics?Patrick Blackburn & Maarten de Rijke - 1997 - Studia Logica 59 (1):5 - 27.
Complexity of Intuitionistic Propositional Logic and its Fragments.Mikhail Rybakov - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):267-292.
Zooming in, Zooming Out.Patrick Blackburn & Maarten de Rijke - 1997 - Journal of Logic, Language and Information 6 (1):5-31.

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