Archive for Mathematical Logic

, Volume 57, Issue 3–4, pp 361–380 | Cite as

Expressivity in chain-based modal logics

  • Michel Marti
  • George MetcalfeEmail author


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.


Modal logic Many-valued logic Bisimulation Modal equivalence Hennessy–Milner property 

Mathematics Subject Classification

03B45 03B50 03G10 


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Institute of Computer ScienceUniversity of BernBernSwitzerland
  2. 2.Mathematical InstituteUniversity of BernBernSwitzerland

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