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Expressivity in chain-based modal logics

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Abstract

We investigate the expressivity of many-valued modal logics based on an algebraic structure with a complete linearly ordered lattice reduct. Necessary and sufficient algebraic conditions for admitting a suitable Hennessy–Milner property are established for classes of image-finite and (appropriately defined) modally saturated models. Full characterizations are obtained for many-valued modal logics based on complete BL-chains that are finite or have the real unit interval [0, 1] as a lattice reduct, including Łukasiewicz, Gödel, and product modal logics.

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Authors and Affiliations

  1. Institute of Computer Science, University of Bern, Neubrückstrasse 10, 3012, Bern, Switzerland

    Michel Marti

  2. Mathematical Institute, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland

    George Metcalfe

Authors
  1. Michel Marti
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  2. George Metcalfe
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Correspondence to George Metcalfe.

Additional information

Preliminary results from this work were reported in the proceedings of AiML 2014 [21].

Supported by Swiss National Science Foundation Grant 200021_165850.

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Marti, M., Metcalfe, G. Expressivity in chain-based modal logics. Arch. Math. Logic 57, 361–380 (2018). https://doi.org/10.1007/s00153-017-0573-4

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  • DOI: https://doi.org/10.1007/s00153-017-0573-4

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