2000 character limit reached
Covariant-Contravariant Refinement Modal $μ$-calculus (2208.02989v1)
Published 5 Aug 2022 in cs.LO, cs.CL, and cs.FL
Abstract: The notion of covariant-contravariant refinement (CC-refinement, for short) is a generalization of the notions of bisimulation, simulation and refinement. This paper introduces CC-refinement modal $\mu$-calculus (CCRML${\mu}$) obtained from the modal $\mu$-calculus system K${\mu}$ by adding CC-refinement quantifiers, establishes an axiom system for CCRML${\mu}$ and explores the important properties: soundness, completeness and decidability of this axiom system. The language of CCRML${\mu}$ may be considered as a specification language for describing the properties of a system referring to reactive and generative actions. It may be used to formalize some interesting problems in the field of formal methods.