Covariant-Contravariant Refinement Modal μ-calculus

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 μ-calculus (CCRMLμ) obtained from the modal μ-calculus system Kμ by adding CC-refinement quantifiers, establishes an axiom system for CCRMLμ and explores the important properties: soundness, completeness and decidability of this axiom system. The language of CCRMLμ 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.