Klausur and Hausarbeit

Klausur There seems to be some confusion about the time and date of the Klausuren for this Module. Datum Di, 14. Jul Uhrzeit 12:00-13:00 Raum Marschnerstraße 29E, Haus 5, HS 015 Please email the Dozent in charge of the seminar you wish to take the Klausur in! (So, me if you want to take the Klausur in Semantics, Herr Heck, if you want to take the Klausur in Morphology, and Herr Müller if you want to take the Klausur in Syntax.

Generalized quantifiers and relations

Up until now, we have been restricting our attention to a simplified syntax for predicates, whereby they are uniformly boolean compounds of atomic one-place predicates - in plain English, we have been restricting our attention to intransitive verbs. A rationale for doing this is that very many interesting aspects of language can be studied with this restriction in place: we have discovered boolean algebras lurking everywhere language, allowing us to interpret boolean words uniformly across different denotational spaces; we have discovered universal properties of determiner denotations, and further sub-classified the space of determiners, observing that certain syntactic constructions seem to make reference to properly semantic properties of expressions; and we have seen that complicated inference patterns can be derived from monotonicity properties of lexical items.

Remarks on the Klausur

The following topics will figure prominently (exclusively) on the Klausur (should you decide to take it): Monotonicity especially determining the polarity of positions in sentences, the polarity properties of words, etc Properties of Determiners especially deciding whether determiners are e.g. intersective, what co-intersectivity means, etc Boolean connectives especially the inference patterns of boolean connectives, their pointwise definitions, etc

Monotonicity and reasoning with determiners

Last time we saw that natural language determiners can be classified according to the information they require to determine whether their noun argument is appropriately related to their predicate argument, and that this classification seemed to have some broader linguistic reality. This time, we will take a closer look at the partial order relation (\(\le\)) that is associated with any boolean domain. Recall that in the domain of truth values, the boolean order coincides with implication (with \(b \le c\) holding just in case \(b\) implies \(c\)), and that in the domain of sets, the boolean order coincides with the subset relation (with \(P \le Q\) holding just in case \(P\) is a subset of (or is equal to) \(Q\)).

Types of determiners

Last time we learned that, viewing determiners as relations between sets, they only take into account their first argument (\(A\)) and the intersection of their first and second arguments (\(A\cap B\)) into consideration. This empirical fact drastically reduces the possible determiners - it is a very powerful language universal. As it turns out, not all determiners even take this information into account. Here, I briefly introduce three (or six, depending on how you count) classes of determiners, which are individuated by the kind of information they make use of.