this paper, we propose a novel graph algorithm relying on graph connectivity, and inspired by [3]. It can enumerate all solved forms of a normal dominance constraint 2 ) per solved form, and thereby improves on the best previously known algorithm in e#ciency. # Humboldt Universitat zu Berlin, Germany + LORIA, Nancy, France # INRIA team Mostrare, Universite de Lille, France Universitat des Saarlandes, Germany Subquadratic running time can be achieved employing decremental graph biconnectivity algorithms

This paper presents a strategy that aims to efficiently avoid the generation of logically equivalent formulas that arise in scope processing applications. Constraint

This paper develops a framework for TAG (Tree Adjoining Grammar) semantics that brings together ideas from different recent approaches. Then, within this framework, an analysis of scope is proposed that accounts for the different scopal properties of quantifiers, adverbs, raising verbs and attitude verbs. Finally, including situation variables in the semantics, different situation binding possibilities are derived for different types of quantificational elements. 1

In this thesis, two requirements on Underspecified Representation Formalisms are investi-gated in detail in the context of underspecification of scope. The requirement on partial disambiguation, stating that partially disambiguated ambiguities need to be represented, does not carry much content unless it has become clear, exactly what those ambiguities are. In line with König and Reyle (1999), I argue that all theoretically possible patterns of ambiguity, i.e. subsets of readings, can occur in natural language and that therefore an underspecified representation formalism can only be regarded as expressively com-plete, if it provides representations for all of these subsets. This discussion is couched in a general formal setting, which facilitates clean definitions and allows for the derivation of formally precise results. With those formal definitions at hand, various underspeci-fied representation formalisms are evaluated. As it turns out, none of the investigated formalisms is expressively complete, which answers a corresponding question raised in (König and Reyle, 1999). These incompleteness results allow for a straightforward com-parison of the discussed approaches with respect to expressive power, which forms the

2.1 Overview of underspecification research................................. 4

We present a novel well-formedness condition for underspecified semantic representations which requires that every correct MRS representation must be a net. We apply this condition to identify a set of eleven rules in the English Resource Grammar (ERG) with bugs in their semantics component, and thus demonstrate that the net test is useful in grammar debugging. In addition, we show that a partly corrected ERG derives 3 % less non-nets on the Rondane treebank and we expect that after completing the correction of the ERG, only 5.5 % non-nets are derived, which we take as support for our initial hypothesis. 1

A translation from Quasi-Logical Forms (QLFs) to Hole Semantics (HS) is presented. The translation makes explicit the dominance constraints that are implicit in the QLFs. QLFs can then be used in the semantic composition stage only, and HS in the scope resolution stage only. Thus, each representation is used to accomplish the stage it is most suited for while avoiding its cumbersomeness in the other stage.

We define Canonical Form Minimal Recursion Semantics (CF-MRS) and prove that all the well-formed MRS structures generated by the MRS semantic composition algorithm are in this form. We prove that the qeq relationships are equivalent to outscoping relations when MRS structures are in this form. This result fills the gap between some underspecification formalisms and motivates defining a Canonical Form Underspecified Representation (CF-UR) which brings those underspecification formalisms together. Keywords UNDERSPECIFICATION,SEMANTIC FORMALISMS,MINIMAL RE-CURSION SEMANTICS

Abstract not found

Abstract. We give polynomial-time algorithms for satisfiability and enumeration of underspecified semantic representations in a canonical form. This canonical form brings several underspecification formalisms together into a uniform framework (Manshadi et al., 2008), so the algorithms can be applied to any underspecified representation that can be converted to this form. In particular, our algorithm can be applied to Canonical Form Minimal Recursion Semantics (CF-MRS). An efficient satisfiability and enumeration algorithm has been found for a subset of MRS (Niehren and Thater, 2003). This subset, however, is not broad enough to cover all the meaningful MRS structures occurring in practice. CF-MRS, on the other hand, provably covers all MRS structures generated by the MRS semantic composition process.