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Alexander Koller Towards a Grand Unified Theory of UnderspecificationAbstractUnderspecification is an approach to dealing with scope ambiguities, a certain class of semantic ambiguities in natural language. The basic idea is to derive from a syntactic analysis of a sentence not all the (exponentially many) semantic representations, but one single compact description of all semantic representations. Then the actual semantic representations can be computed from the description by need. Underspecification has become the standard approach to dealing with scope in large-scale grammars. In my talk, I present one particular scope underspecification formalism, the language of dominance constraints. Dominance constraints have a particularly canonical definition (as a logic interpreted over trees), can be seen alternatively as a logic-based or a graph-based formalism, and very efficient solvers are available for them. Then I investigate the relationship between dominance constraints and two other popular underspecification formalisms: Hole Semantics and Minimal Recursion Semantics. While the formalisms all look superficially similar, it turns out that there are fundamental differences once we look more closely. However, I show that significant fragments of the three formalisms are indeed equivalent, and present empirical data that suggests that these fragments encompass all descriptions that are used by current grammars. These results bridge the gap between different underspecification formalisms for the first time, which makes resources such as grammars and solvers that were created for one formalism available to the others. On a more general level, they also clarify the expressive power that a formalism actually has to offer in the linguistic application. |