# A Real-Valued Modal Logic

arXiv: https://arxiv.org/abs/1706.02854 · HTML: https://mlsanity.com/paper/1706.02854/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2017.

## Built on by (most cited first, 1 of 1)

- [Rotations of G"odel algebras with modal operators](https://mlsanity.com/paper/2405.19354/) (2024)

## Abstract (arXiv)

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.