In this paper, we present a system for generating semantic representations from Universal Dependencies syntactic parses. The foundation of our pipeline is a rule-based interpretation system, designed to be as universal as possible, which produces the correct semantic structure; the content of this structure can then be filled in by additional (sometimes language-specific) post-processing. The rules which generate semantic resources rely as far as possible on the UD parse alone, so that they can apply to any language for which such a parse can be given (a much larger number than the number of languages for which detailed semantically annotated corpora are available). We discuss our general approach, and highlight areas where the UD annotation scheme makes semantic interpretation less straightforward. We compare our results with the Parallel Meaning Bank, and show that when it comes to modelling semantic structure, our approach shows potential, but also discuss some areas for expansion.