From Semantic Graphs to Logic Formulae

We present a general two-step algorithm which transforms a graph expressing the semantic dependencies between the words of an utterance into logic formulae repre- senting the different semantic interpreta- tions of the utterance. The algorithm focuses on the scopal ele- ments of the utterance, i.e. quantifiers and scopal predicates. First, the scope of ev- ery scopal element is computed as a sub- graph of the whole graph, given an order on these elements. Second, we use these scopes with their order to build a logic for- mula incrementally from the most internal to the most external scopal elements.