The present project is concerned with the semantics of and, or and their counterparts in other languages. These two classes of coordinators (henceforth referred to as AND and OR) seem to have a central status in natural language grammars.

One traditional approach to and and or assigns them a so-called Boolean meaning, which is a generalization of the corresponding operations in classical logic. With the Boolean meaning, predicates applied to a coordinate structure always distribute down to the individual conjuncts. This allows us to derive reading (1-a) of the sentence in (1). However, it is well known that and-coordinations are compatible with non-distributive predicates (as in (1-b) and (2)), which suggests that a weaker, non-Boolean meaning for AND is available.

(1) Sue and Mary won 100 euros.

1. Sue won 100 euros and Mary won 100 euros.
2. Sue and Mary won 100 euros between them.

(2) Sue and Mary met.

Our project aims to investigate the hypothesis that the basic, lexical meaning of AND is non-Boolean cross-linguistically. If so, there is no systematic lexical ambiguity between Boolean and non-Boolean and. Boolean readings have to arise from the interaction of non-Boolean and with additional semantic operations that enforce distributivity.

In addition to the theoretical question how the non-Boolean meaning should be characterized, this approach raises interesting typological issues. For instance, it predicts that a cross-categorial non-Boolean meaning is available in a wide range of languages and language families. Further, it would be unexpected for a language to systematically use completely unrelated lexical items for Boolean and non-Boolean AND. So far, these predictions have not been tested systematically. Detailed semantic studies of non-Boolean conjunction only exist for a small number of mostly Indo-European languages.

In addition to extending and improving the existing semantic theories of non-Boolean AND, our project opens up two new avenues of research. First, we aim to provide semantically informative typological data that will allow us to test the typological predictions of our main hypothesis. The data will be collected using the SSWL database, a freely searchable online platform which allows linguists to add queries that are then answered by informants for a wide range of languages.

Second, on a more theoretical level, we attempt to bring together two conflicting research traditions in semantics. There is a large body of work on the enriched meaning of sentences containing coordinate structures which is based on the assumption that the scalar implicatures of such sentences are due to a contrast between Boolean AND and Boolean OR. We will explore the theoretical and empirical consequences of a non-Boolean theory of and for the contrast between AND and OR.