Proof Theory of Riesz Spaces and Modal Riesz Spaces

Christophe Lucas, Matteo Mio
2022 Logical Methods in Computer Science  
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.
doi:10.46298/lmcs-18(1:32)2022 fatcat:y5okiphl7zc3fc2iy3pwe76oqe