Proof Theory of Riesz Spaces and Modal Riesz Spaces [article]

Christophe Lucas, Matteo Mio
2022 arXiv   pre-print
We design hypersequent calculus proof systems for the theories of Riesz spaces and modal Riesz spaces and prove the key theorems: soundness, completeness and cut elimination. These are then used to obtain completely syntactic proofs of some interesting results concerning the two theories. Most notably, we prove a novel result: the theory of modal Riesz spaces is decidable. This work has applications in the field of logics of probabilistic programs since modal Riesz spaces provide the algebraic
more » ... emantics of the Riesz modal logic underlying the probabilistic mu-calculus.
arXiv:2004.11185v9 fatcat:oiwnu2hf5vfqne6sd5pu52qdpy