This thesis develops the theory of dominance constraints, a family of logical languages that describe trees, and applies them as a formalism for the underspecified description of scope ambiguities in natural language. In underspecification approaches to ambiguity resolution, all readings of a sentence at once are
represented in an underspecified description, and are only enumerated by need.
On the one hand, dominance constraints allow us to model scope phenomena declaratively, within a logic formalism. On the other hand, we can view certain fragments of dominance constraints as graphs, which makes it possible to employ efficient graph algorithms to solve dominance constraints. All constraints that are used in scope underspecification seem to fall into these fragments.
In addition, we can use extra information such as anaphoric reference and world knowledge in order to restrict the set of readings described by a dominance constraint. The constraint is strengthened to exclude unintended readings without having to enumerate them.