Proof Theory of Riesz Spaces and Modal Riesz Spaces
-
Published:2022-02-17
Issue:
Volume:Volume 18, Issue 1
Page:
-
ISSN:1860-5974
-
Container-title:Logical Methods in Computer Science
-
language:en
-
Short-container-title:
Author:
Lucas Christophe,Mio Matteo
Abstract
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.
Funder
French National Research Agency
European Commission
Publisher
Centre pour la Communication Scientifique Directe (CCSD)
Subject
General Computer Science,Theoretical Computer Science