Resolution of Collective-Distributive Ambiguity Using Model-Based Reasoning

I present a semantic analysis of collective-distributive ambiguity, and resolution of such ambiguity by model-based reasoning. This approach goes beyond Scha and Stallard [17], whose reasoning capability was limited to checking semantic types. My semantic analysis is based on Link [14, 13] and Roberts [15], where distributivity comes uniformly from a quantificational operator, either explicit (e.g. each) or implicit (e.g. the D operator). I view the semantics module of the natural language system as a hypothesis generator and the reasoner in the pragmatics module as a hypothesis filter (cf. Simmons and Davis [18]). The reasoner utilizes a model consisting of domain-dependent constraints and domain-independent axioms for disambiguation. There are two kinds of constraints, type constraints and numerical constraints, and they are associated with predicates in the knowledge base. Whenever additional information is derived from the model, the Contradiction Checker is invoked to detect any contradiction in a hypothesis using simple mathematical knowledge. CDCL (Collective-Distributive Constraint Language) is used to represent hypotheses , constraints, and axioms in a way isomorphic to diagram representations of collective-distributive ambiguity. Collective-distributive ambiguity can be illustrated by the following sentence. (1) Two students moved a desk upstairs. (1) means either that two students TOGETHER moved one desk (a collective reading) or that each *The work described in this paper was done as a part of the author's doctoral dissertation at The University of Texas at Austin. of them moved a desk SEPARATELY (a distributive reading). Following Link [14, 13] and Roberts [15], distributivity comes from either an explicit quantifi-cational operator like each or an implicit distributive operator called the D operator. The D operator was motivated by the equivalence in the semantics of the following sentences. (2) a. Every student in this class lifted the piano. b. Students in this class each lifted the piano. c. Students in this class lifted the piano. (the distributive reading) Thus, the distributive readings of (1) and (2c) result from applying the D operator to the subjects. Now, look at another sentence "Five students ate four slices of pizza." It has 8 POSSIBLE readings because the D operator may apply to each of the two arguments of eat, and the two NPs can take scope over each other. Thus, 2x2x2 = 8. i j have extended Link's and Roberts's theories to quantify over events in Discourse Representation Theory (cf. Kamp [10], Heirn [9], Aone [2]) so that these readings can …