Title: A Real-Valued Modal Logic,
Abstract: 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.