Polarity in the Semantics of Natural Language

This paper provides an overview of polarity phenomena in human languages. There are three prominent paradigms of polarity items: negative polarity items (NPIs), positive polarity items (PPIs), and free choice items (FCIs). What they all have in common is that they have limited distribution: they cannot occur just anywhere, but only inside the scope of licenser, which is negation and more broadly a nonveridical licenser, PPIs, conversely, must appear outside the scope of negation. The need to be in the scope of a licenser creates a semantic and syntactic dependency, as the polarity item must be c-commanded by the licenser at some syntactic level. Polarity, therefore, is a true interface phenomenon and raises the question of well-formedness that depends on both semantics and syntax. Nonveridical polarity contexts can be negative, but also non-monotonic such as modal contexts, questions, other non-assertive contexts (imperatives, subjunctives), generic and habitual sentences, and disjunction. Some NPIs and FCIs appear freely in these contexts in many languages, and some NPIs prefer negative contexts. Within negative licensers, we make a distinction between classically and minimally negative contexts. There are no NPIs that appear only in minimally negative contexts. The distributions of NPIs and FCIs crosslinguistically can be understood in terms of general patterns, and there are individual differences due largely to the lexical semantic content of the polarity item paradigms. Three general patterns can be identified as possible lexical sources of polarity. The first is the presence of a dependent variable in the polarity item—a property characterizing NPIs and FCIs in many languages, including Greek, Mandarin, and Korean. Secondly, the polarity item may be scalar: English any and FCIs can be scalar, but Greek, Korean, and Mandarin NPIs are not. Finally, it has been proposed that NPIs can be exhaustive, but exhaustivity is hard to precisely identify in a non-stipulative way, and does not characterize all NPIs. NPIs that are not exhaustive tend to be referentially vague, which means that the speaker uses them only if she is unable to identify a specific referent for them.

The semantics of Scandinavian ‘when’-clauses

The system of temporal connectives in Scandinavian exhibits an interesting variation in that Danish, like e.g. German, is a two-‘when’ language, i.e. it has two temporal connectives that have divided between them the semantic area covered in English by the single connective when. One of the two Danish connectives (da) is restricted to past episodic clauses, while the other one (når) may be used in past and present habitual clauses and in future clauses. Swedish, on the other hand, like e.g. English, is a one-‘when’ language: it has only one temporal connective corresponding to the two Danish ones, whereas Norwegian presents an intermediate situation, possibly a stage in the development from a two-‘when’ to a one-‘when’ system. This paper proposes a semantic analysis of the two ‘when’s in Danish: On the one hand, the semantics of da-clauses is similar to the semantics of definite DPs in that a da-clause presupposes that, in the current discourse situation, there is one and only one eventuality corresponding to the description it conveys. This makes it possible for a da-clause to have a reference-setting function with respect to its superordinate clause. On the other hand, når-clauses are similar to indefinite DPs in that they contribute propositions with an unbound eventuality argument, and therefore they yield descriptions of eventualities that never get referentially bound, but always occur in the scope of a non-existential quantifier. This restricts the use of når-clauses to habitual sentences and future sentences. This analysis involves the elaboration of a novel and more adequate formal semantic description of habitual sentences.