Witness-based quantification
Robin Cooper · 2023
Abstract This chapter looks at generalized quantifiers from the perspective of dialogic interaction. Traditionally generalized quantifiers are treated as sets of sets or sets of properties. Barwise and Cooper also introduced the auxiliary notion of witness set for quantifiers under the heading “Processing quantified statements”. This chapter turns things around and make the characterization of witness sets the primary notion in defining quantifiers. This makes it more straightforward to account for the anaphoric possibilities relating to quantified expressions in dialogue. We often use quantified statements in dialogue when we have inadequate information to determine their truth. This is particularly true of determiners like every and most when talking about large sets. We suggest that this phenomenon can be analyzed by estimating a probability based on the evidence presented in our cognitive resources (long-term memory or beliefs as discussed in Chapters 4 and 6).