The set ∆ can then be derived from Γ using the following natural deduction rules: 4 • Initialize ∆ with lambda terms (sets) that have no outscoped sets in Γ: • Add constraints to appropriate sets in ∆: • Add constraints of supersets as constraints on subsets in ∆: For example, the graph in Figure 2 can be translated into the following lambda calculus expression (including quantifiers over eventualities in the source graph, to eliminate unbound variables): The semantic dependency representation defined in this paper assumes semantic dependencies other than those representing continuations are derived compositionally by a categorial grammar.
this definition assumes a Generalized Categorial Grammar (GCG) (Bach, 1981;Oehrle, 1994), because it can be used to distinguish argument and modifier compositions (from which restrictor and nuclear scope sets are derived in a treestructured continuation graph), and because large GCG-annotated corpora defined with this distinction are readily available (Nguyen et al., 2012).