Resolution of collective-distributive ambiguity using model-based reasoning

Abstract

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.