We present a general two-step algorithm which transforms a graph expressing the semantic dependencies between the words of an utterance into logic formulae representing the different semantic interpretations of the utterance. The algorithm focuses on the scopal elements of the utterance, i.e. quantifiers and scopal predicates. First, the scope of every scopal element is computed as a subgraph of the whole graph, given an order on these elements. Second, we use these scopes with their order to build a logic formula incrementally from the most internal to the most external scopal elements.