Abstract
This paper proposes an extension of Dependency Tree Semantics (DTS), an underspecified formalism originally proposed in Robaldo (2007). The crucial advantage of DTS as compared to other contemporary proposals is its ability to represent Independent Set (IS) readings (a.k.a. scopeless readings), e.g. cumulative and collective readings. DTS achieves the expressivity needed to represent IS readings because it underspecifies Skolem-like functional dependencies. This paper extends DTS by introducing additional meta-constraints in First-Order Logic dedicated to disambiguating underspecified structures. However, it is worth noting that the meta-constraints are independent from DTS, and could be easily re-implemented in any underspecified theory. The meta-constraints achieve flexible disambiguation, in the sense that they allow ambiguous structures to be specified independently of the linguistic (rather than logical) knowledge used. Secondly, DTS, equipped with the meta-constraints, becomes an expressively complete formalism in the sense of Ebert (2005). Expressive completeness is a desirable property for an underspecified formalism, because it allows a representation for each possible subset of available readings.
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