Christophe Lucas ; Matteo Mio - Proof Theory of Riesz Spaces and Modal Riesz Spaces

lmcs:6428 - Logical Methods in Computer Science, February 17, 2022, Volume 18, Issue 1 -
Proof Theory of Riesz Spaces and Modal Riesz SpacesArticle

Authors: Christophe Lucas ; Matteo Mio

    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 semantics of the Riesz modal logic underlying the probabilistic mu-calculus.

    Volume: Volume 18, Issue 1
    Published on: February 17, 2022
    Accepted on: November 24, 2021
    Submitted on: April 24, 2020
    Keywords: Computer Science - Logic in Computer Science
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