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B. van Tiel & B. Geurts Truth and typicality in the interpretation of quanti ers Proceedings of Sinn und Bedeutung 18 Edited by Urtzi Etxeberria, Anamaria al F aus, Aritz Irurtzun & Bryan Leferman453. example, Rosch (1975) found that participants consider sparrows to be more typical birds than penguins or chickens.
Negation with Multiple Quantifiers. We shall learn several basic proof techniques in Chapter 3.Some of them require negating a logical statement. Since many mathematical results are stated as quantified statements, it is necessary for us to learn how to negate a quantification.
Quantiers are well-suited for evaluating lan- guage model generalization because compared to other linguistics objects, their meanings are more abstract, and can be fully specied in theoretical terms that do not require grounding. Common examples of quantiers include some, all, a few, many, etc.
Previous studies of generalized quantiers have characterized various scope com-mutativity properties of quantiers in constructions with multiple quantication. No-tably, Westerstahl (1996) characterizes the class of self-commuting quantiers Πthose quantiers that satisfy the followingequivalence: (3) For all _u < ^: M _ s M_Mr \.
Generalized quantiers (e.g., few, most) are used to indicate the proportions predicates are satised (for example, some apples are red). One way to interpret quantier semantics is to explicitly bind these satisfactions with per-centage scopes (e.g., 30%-40% of apples are red). This approach can be helpful for tasks
existential quantiers (9), but laws may not (laws must be universal). H & O require all explanatory theories to be general (but not necessarily universal) and true. As we'll see, these assumptions have (by and large) remained in the contemporary literature on explanation. Scientic Explanation Seminar Background Notes (1/25/11) 10 ' & $ %
ture is closely similar to a more general genitive construction NP de NP (similar to the English NP of NP from which the English quantier construc-tion also originates), so that automatically (and even manually) sorting the relevant occurrences from the spurious ones poses a serious challenge. To cope with this difculty, I decided to be con-
