How and why conventional implicatures project
Conventional Implicatures (CIs; in the sense of Potts 2005) are part of a larger class of projection phenomena. These phenomena also include presuppositions and anaphora, and can described as content that is not at-issue (cf. Simons, Tonhauser, Beaver & Roberts 2010). Despite the shared property of projection, CIs differ from other projection phenomena with respect to the information status of their contribution. Presuppositions, for instance, refer to established, or old information, whereas CIs contribute novel information to the discourse, like at-issue content. Here, we propose a unidimensional analysis of CIs and at-issue content, which highlights the similarity in projection behaviour of CIs, presuppositions, and anaphora. This analysis treats CIs as 'piggybacking' on their anchor; they introduce an anaphoric dependency on the interpretation site of their anchor, while at the same time requiring their anchor to refer to a specific referent in the discourse context. CIs are thus elaborations on the description of the referent referred to by their anchor. This analysis of CIs is formalized in Projective Discourse Representation Theory (PDRT; Venhuizen, Bos & Brouwer 2013), a representational framework in which the property of projection is accounted for by explicitly distinguishing between the introduction and interpretation site of semantic content. Our formal analysis explains the interpretational differences between CIs, presuppositions, anaphora, and at-issue content, without stipulating a fundamental distinction between them.