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The Monodic Fragment of Propositional Term Modal Logic

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Abstract

We study term modal logics, where modalities can be indexed by variables that can be quantified over. We suggest that these logics are appropriate for reasoning about systems of unboundedly many reasoners and define a notion of bisimulation which preserves propositional fragment of term modal logics. Also we show that the propositional fragment is already undecidable but that its monodic fragment (formulas using only one free variable in the scope of a modality) is decidable, and expressive enough to include interesting assertions.

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Acknowledgements

We thank the anonymous reviewers of this journal whose comments have greatly helped to improve the content as well as the presentation. We also thank the reviewers of \(LOFT\ 2016\), and M4M9 for their valuable comments. In an earlier version of this paper, we had erroneously claimed PTML to be decidable, and M4M9 reviewers pointed this out. We thank Varuni Prabhakar for help with the figures.

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  1. Institute of Mathematical Sciences (Homi Bhabha National Institute), Chennai, India

    Anantha Padmanabha & R. Ramanujam

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  1. Anantha Padmanabha
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  2. R. Ramanujam
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Correspondence to Anantha Padmanabha or R. Ramanujam.

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Padmanabha, A., Ramanujam, R. The Monodic Fragment of Propositional Term Modal Logic. Stud Logica 107, 533–557 (2019). https://doi.org/10.1007/s11225-018-9784-x

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