The Resolution Of Quantificational Ambiguity In The Tendum System

A method is described for handling the ambiguity and vagueness that is often found in quantifications the semantically complex relations between nominal and verbal constituents. In natural language certain aspects of quantification are often left open; it is argued that the analysis of quantification in a model-theoretic framework should use semantic representations in which this may also be done. This paper shows a form for such a representation and how "ambiguous" representations are used in an elegant and efficient procedure for semantic analysis, incorporated in the TENDUM dialogue system. The quantification ambi~uit[ explosion problem Quantification is a complex phenomenon that occurs whenever a nominal and a verbal constituent are combined in such a way that the denotation of the verbal constituent is predicated of arguments supplied by the (denotation of the) nominal constituent. This gives rise to a number of questions such as (i) What objects serve as predicate arguments? (2) Of how many objects is the predicate true? (3) How many objects are considered as potential arguments of the predicate? When we consider these questions for a sentence with a few noun phrases, we readily see that the sentence has a multitude of possible interpretations. Even a sentence with only one NP such as (I) Five boats were lifted has a variety of possible readings, depending on whether the boats were lifted individually, collectively, or in groups of five, and on whether the total number of boats involved is exactly five or at least five. For a sentence with two numerically quantified NPs, such as 'Three Russians visited five Frenchmen', Partee (1975) distinguished 8 readings depending on whether the Russians and the Frenchmen visited each other individually of collectively and on the relative scopes of the quantifiers. Partee's analysis is in fact still rather crude; a somewhat more refined analysis, which distinguishes group readings and readings with equally wide scope of the quantifiers, leads to 30 interpretations (Bunt, in press). This presents a problem for any attempt at a precise and systematic description of semantic structures in natural language. On the one hand an articulate analysis of quantification Js needed for obtaining the desired interpretations of every sentence, while on the other hand we do not want to end up with dozens of interpretations for every sentence. To some extent this "ambiguity explosion problem" is an artefact of the usual method of formal semantic analysis. In this method sentences are translated into formulae of a logical language, the truth conditions of which are determined by model-theoretic interpretation rules. Now one might want to consider a sentence like (i) not as ambiguous, but only as saying that five boats were lifted, w~thout specifying how they were lifted. But translation of the sentence into a logical representation forces one to be specific. That is, the logical representation language requires distinction between such interpretations as represented by (2) (individual reading) and (3) (group reading): (2) ~({x e BOATS: LIFTED(x)}) = 5 (3) 3 x E{ y C BOATS:~ (y) = 5} : LIFTED(x) In other words, the analysis framework forces us to make distinctions which we might not always want to make. To tackle this problem, I have devised a method of representing quantified expressions in a logical language with the possibility of leaving certain quantification aspects open. This method has been implemented in the TENDUM dialogue system, developed jointly at the Institute for Perception Research in Eindhoven and the Computational Linguistics Research Unit at Tilburg University, Department of Linguistics (Bunt, 1982; ~983; Bunt & thoe Schwartzenberg, 1982;). This method is not only of theoretical interest, but also provides a computationally efficient treatment of quantification. Ambiguity resolution In a semantic analysis system which translates natural language expressions into formal representations, all disambiguation takes place during this translation.