Connection Relations and Quantifier Scope

A formalism will be presented in this paper which makes it possible to realise the idea of assigning only one scope-ambiguous representation to a sentence that is ambiguous with regard to quantif ier scope. The scope de te rmina t ion resul ts in ex tending this representat ion with addit ional context and world knowledge conditions. If there is no scope determining information, the formalism can work further with this scope-ambiguous representation. Thus scope information does not have to be completely determined. 0. I N T R O D U C T I O N Many natural language sentences have more than one possible reading with regard to quantif ier scope. T h e most widely used methods for scope determination generate all possible readings of a sentence with regard to quantifier scope by applying all quantifiers which occur in the sentence in all combinatorically possible sequences. These methods do not make use of the inner structure and mean ing of a quantifier. At best, quant if iers are constra ined by external conditions in order to eliminate some scope relations. The best known methods are: determination of scope in LF in GB (May 1985), Cooper Storage (Cooper 1983, Keller 1988) and the a lgor i thm of Hobbs and Shieber (Hobbs/Shieber 1987). These methods assign, for instance, six possible readings to a sentence with three quantifiers. Using these methods, a sentence must be disambiguated in order to receive a semantic representation. This means that a scope-ambiguous sentence necessarily has several semantic representations, since the formalisms for the representation do not allow for scope-ambiguity. It is hard to imagine that human beings disambiguate scope-ambiguous sentences in the same way. The generat ion of all possible combinations of sequences of quantifiers and the assignment of these sequences to various readings seems to be cognitively inadequate. The problem becomes even more complicated when natural language quantifiers can be i n t e rp re t ed d i s t r i bu t ive ly as well as collectively, which can also lead to further readings. Let us take the following sentence from Kempson/Cormack (1981) as an example: Two examiners marked six scripts. The two quantifying noun phrases can in this case be interpreted either distributively or collectively. The quantifier two examiners can have wide scope over the quantifier six scripts, or vice versa, which all in all can lead to various readings. Kempson and Cormack assign four possible readings to this sentence,