Lindström (1966) introduced a very powerful notion of quantifiers, which permits multi-place quantification and the simultaneous binding of several variables. `Branching' quantifification was found to be useful by linguists e.g. 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 binary quantifiers Q1 and Q2, assuming crisp quantifiers and arguments. In the paper, I generalize his method to approximate quantifiers like "many" and fuzzy arguments like "young". A consistent interpretation is achieved by extending the DFS theory of fuzzy quantification (Glöckner 1997,2002), which rests on a system of formal adequacy criteria. The new analysis is important 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.
Fuzzy Quantifiers, Multiple Variable Binding and Branching Quantification
In: T. Bilgiç and B. De Baets and O. Kaynak (Eds.), Fuzzy Sets and Systems - IFSA 2003, LNAI 2715, Springer, 2003, pp. 135-142.
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