We propose a method to address the current lack of standards for both software product line variability modeling languages and their formal semantics. It allows specifying, in an agile, declarative, and solver-agnostic fashion the formal semantics of a domain-specific variability modeling language through a simple JSON based specification format. Our approach leverages the Common Logic Interchange Format (CLIF) standard for interoperability among logical inference engines. We demonstrate our approach with two concrete examples of Variability Models, and present the tooling and architecture that makes this possible.