Model checking is a widely used technique for verifying complex concurrent systems. The models used in classical model checking methods are assumed to be complete and consistent. However, a recent body of work has shown that this is not always the case, and multi-valued logics have been proposed to represent such models, spawning an extension of classical model checking, known as, multi-valued model checking. In this paper, we define a multi-valued set based semantics for the multi-valued modal μ-calculus and present a novel interpretation of logic programs to support multi-valued sets as first-class entities, that can be used as a practical deductive multi-valued model checking framework. This framework provides a semantics preserving encoding of multi-valued transition systems, and allows verification of arbitrary multi-valued modal μ-calculus properties. A prototype implementation of this framework has also been realized.