Branching of Fuzzy Quantifiers and Multiple Variable Binding: An Extension of DFS Theory

Lindström [11] introduced a very powerful notion of quantifiers, which permits multi-place quantification and the simultaneous binding of several variables. A special case, 'branching' quantifiers, was found to be useful in linguistics, specifically for modelling reciprocal constructions like " Most men and most women admire each other ". Westerståhl [13] showed how to compute the three-place Lindström quantifier for " © ® each other " from the two-place quanti-fiers © b ª and ©  ¬ , assuming precise quantifiers and crisp arguments. In the report, I generalize Westerståhl's method to approximate quantifiers like " many " and fuzzy arguments like " young ". A consistent interpretation is achieved by incorporating Lindström quanti-fiers into the DFS theory of fuzzy quantification [5, 8], which rests on a system of formal adequacy criteria. The proposed analysis is of special importance to linguistic data summarization because the full meaning of reciprocal summarizers (e.g. describing factors which are " correlated " or " associated " with each other), can only be captured by branching quantification.