A many-valued modal logic is introduced that combines the usual Kripke frame semantics of the modal logic K with connectives interpreted locally at worlds by lattice and group operations over the real numbers. A labelled tableau system is provided and a coNEXPTIME upper bound obtained for checking validity in the logic. Focussing on the modal-multiplicative fragment, the labelled tableau system is then used to establish completeness for a sequent calculus that admits cut-elimination and an axiom system that extends the multiplicative fragment of Abelian logic.

@article{paperbot432,
  title = {A Real-Valued Modal Logic},
  author = {Denisa Diaconescu and George Metcalfe and Laura Schnüriger},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 14, Issue 1},
  year = {2018},
  doi = {10.23638/lmcs-14(1:10)2018}
}