Logical Methods in Computer Science (Jan 2018)

A Real-Valued Modal Logic

  • Denisa Diaconescu,
  • George Metcalfe,
  • Laura Schnüriger

DOI
https://doi.org/10.23638/lmcs-14(1:10)2018
Journal volume & issue
Vol. Volume 14, Issue 1

Abstract

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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.

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