Bare numerals present an interesting challenge to formal semantics and pragmatics: they seem to be compatible between various readings (‘at least’, ‘exactly’, and ‘at most’ readings), and the choice of a particular reading seems to depend on complex interactions between contextual factors and linguistic structure. The goal of this article is to present and discuss some of the current approaches to the interpretation of bare numerals in formal semantics and pragmatics. It discusses four approaches to the interpretation of bare numerals, which can be summarized as follows:

1. In the neo-Gricean view, the basic, literal meaning of numerals amounts to an ‘at least interpretation’, and the ‘exactly n’ reading results from a pragmatic enrichment of the literal reading, i.e. it is accounted for in terms of scalar implicatures.
2. In the underspecification view, the interpretation of numerals is ‘underspecified’, with the result that they can freely receive the ‘at least’, ‘exactly’, or ‘at most’ reading, depending on which of these three construals is contextually the most relevant.
3. In the ‘exactly’-only view, the numerals' basic, literal meaning corresponds to the ‘exactly’ reading, and the ‘at least’ and ‘fewer than n’ readings result from the interaction of this literal meaning with background, non-linguistic knowledge.
4. In the ambiguity view, numerals are ambiguous between two readings, the ‘at least’ and ‘exactly’ readings.

The article argues that in order to account for all the relevant data, one needs to adopt a certain version of the ambiguity view. But it suggests that numerals should not necessarily be thought of as being lexically ambiguous, but rather as giving rise to ambiguities through their interactions with so-called exhaustivity operators. According to such a view, the ambiguities triggered by numerals are to be explained in terms of a non-Gricean theory of scalar implicatures.

Part 1 of Tense in Adjuncts presents a compositional analysis of tense in relative clauses (RCs). The languages under investigation are English, Russian, and Japanese. We introduce the syntax and semantics of tense and the theory of feature transmission under variable binding, which mediates between syntax/semantics and morphology. In sequence of tense languages such as English, the morphology of the tense in a RC will be licensed by a non-local tense if the RC is embedded under will. In other constructions, the RC tense is licensed by a local tense. In non-sequence of tense languages, the tense in the RC is also determined by a local tense. The paper says which factors are responsible for the tense distribution in the different languages under consideration.

Part 1 of this article treats tense in relative clauses in English, Russian and Japanese. The temporal center in relative clauses can always be anaphoric, and sometimes it has to be the anaphoric Tpro. In Part 2, we investigate tense in temporal adverbial clauses (TACs) headed by ‘after’, ‘before’ and ‘when’. We argue for the following points: 1. English TAC Tense is bound in Present adjuncts under matrix ‘will’, in other constructions the TAC Tense is deictic. Tense licensing is non-local in bound constructions, while in deictic constructions it is local. 2. Russian TAC Tense is deictic, and the tense licensing is local. 3. Japanese TAC Tense is bound. We have a ‘tenseless’ construction in the adjunct, and tense licensing is local.