Lindström 1966 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 1987 showed how to compute the three-place Lindström quantifier for "Q1 A's and Q2 B's R each other" from the two-place quantifiers Q1 and Q2, 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 quantifiers into the DFS theory of fuzzy quantification Glöckner 1997/2002, 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.
Branching of Fuzzy Quantifiers and Multiple Variable Binding: An Extension of DFS Theory
Technical Report TR2002-08, University of Bielefeld, Faculty of Technology, P.O.-Box 100131, 33501 Bielefeld, Germany, December 2002.
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