M.Sc Thesis

M.Sc StudentAltman Alon
SubjectComputation and Specification of Scope Dominance with
Monotone Quantifiers in Natural Language
DepartmentDepartment of Computer Science
Supervisor MR Yoad Winter


Scope ambiguity is a prevalent phenomenon in natural language, which has been studied extensively in theoretical and computational linguistics. However, one problem that has only partly been addressed in the literature is the formal characterization of entailment relations between different readings of scopally ambiguous sentences, and the way to compute such relations effectively. It is occasionally observed that the two readings of simple transitive sentences such as a referee read every abstract (or every referee read an abstract) are logically dependent. However, the general conditions under which such entailments ensue have not been systematically studied. The characterization of these conditions is not only of intrinsic logical interest but is also significant for theoretical and computational semantics.

This thesis first employs generalized quantifier theory in order to characterize the conditions under which two upward monotone quantifiers  Q_{1}  and  Q_{2}  display what we call scope dominance. This is a situation where any binary relation  R  supports an entailment relation between the two propositions it forms with  Q_{1}  and  Q_{2} :  Q_{1}x\; Q_{2}y\; R(x,y)  and  Q_{2}y\; Q_{1}x\; R(x,y) . This characterization, which was originally proved for a limited class of natural language quantifiers (the ones that are formed by the so-called finitely based determiners), has been later extended by Altman et al. (2002) to arbitrary upward monotone quantifiers over countable domains. This theorem enables us to specify, once the denotations of NPs in a natural language sentence are determined, whether there is a logical dependency between its different scope construals. This formal result is the core ingredient in an algorithm that is developed for computing scope dominance in a fragment of natural language. The algorithm addresses three inter-related problems in the application of this result. First, it computes the relevant semantic properties of NP coordinations recursively from the lexical properties of their constituents. Second, the algorithm deals with lexical "super-concept" relations between nominals (like, for instance, the super-concept relation between the noun animal and the noun dog). Third, the algorithm takes into account cardinality presuppositions that are triggered by noun phrases such as the three people, which affect scope dominance relations. The main procedure within the algorithm assigns sets to lexical nominals in the sentence according to lexical information about determiners they combine with. It is then proved that the sets that are assigned by this procedure, which represent one model for interpreting the sentence, are indicative (under certain limitations) of scope dominance across infinitely many models. This occurs thanks to familiar constraints on natural language determiners. The algorithm is implemented as a working demo application in SML, which also includes a heuristics for overcoming some of the limitations of the set assignment procedure.