TL;DRAbstract
Many applications e.g. in approximate reasoning, data summarisation, information retrieval etc. can profit from the use of fuzzy quantifiers like "almost all" or "many", which provide flexible means of information aggregation, and are capable of extracting meaningful linguistic summaries from large amounts of raw data. However, as will be shown by a number of counterexamples, existing approaches fail to provide a convincing interpretation of fuzzy quantifiers in the important case of two-place quantification (e.g. "about half of the blondes are tall"). The interpretation of fuzzy quantifiers should hence be based on a solid axiomatic foundation in order to guarantee predictable and linguistically wellmotivated results. In the report, an independent axiom system for "reasonable" approaches to fuzzy quantification is introduced, that are consistent with the use of quantifiers in NL. A number of linguistic adequacy cr
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Many applications e.g. in approximate reasoning, data summarisation, information retrieval etc. can profit from the use of fuzzy quantifiers like "almost all" or "many", which provide flexible means of information aggregation, and are capable of extracting meaningful linguistic summaries from large amounts of raw data. However, as will be shown by a number of counterexamples, existing approaches fail to provide a convincing interpretation of fuzzy quantifiers in the important case of two-place quantification (e.g. "about half of the blondes are tall"). The interpretation of fuzzy quantifiers should hence be based on a solid axiomatic foundation in order to guarantee predictable and linguistically wellmotivated results. In the report, an independent axiom system for "reasonable" approaches to fuzzy quantification is introduced, that are consistent with the use of quantifiers in NL. A number of linguistic adequacy cr
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