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Feature Diagrams (FDs) are a family of popular modelling languages used to address the feature interaction problem, particularly in software product lines, FDs were first introduced by Kang as part of the FODA (Feature-Oriented Domain Analysis) method back in 1990. Afterwards, various extensions of FODA FDs were introduced to compensate for a purported ambiguity and lack of precision and expressiveness. However, they never received a formal semantics, which is the hallmark of precision and unambiguity and a prerequisite for efficient and safe tool automation. The reported work is intended to contribute a more rigorous approach to the definition, understanding, evaluation, selection and implementation of FD languages. First, we provide a survey of FD variants. Then, we give them a formal semantics, thanks to a generic construction that we call Free Feature Diagrams (FFDs). This demonstrates that FDs …