 It makes a big difference whether L is a natural or an artificial language. Syntactic and semantic questions about a natural language are settled by and large through empirical investigation; syntactic and semantic questions about an artificial language are settled usually by checking what the appropriate stipulations are. Prima facie, natural languages might turn out not to be compositional, whereas many artificial languages were designed to meet such a requirement. (Compositionality is a bonus when it comes to proof-checking in computer languages, or inductive proofs in logical calculi.) Unless explicitly noted, talk of compositionality is to be taken as talk of compositionality of some particular natural language, or of natural languages in general.