Parsimonious Semantic Representations with Projection Pointers

The influential idea by van der Sandt (1992) to treat presuppositions as anaphora in the framework of Discourse Representation Theory (DRT, Kamp and Reyle, 1993) has inspired a lot of debate as well as elaborations of his account. In this paper, we propose an extension of DRT, called Projective DRT, which adds pointers to all DRT referents and conditions, indicating their projection site. This means that projected content need not be moved from the context in which it is introduced, while it remains clearly discernible from asserted content. This approach inherits the attractive properties from van der Sandt’s approach to presupposition, but precludes a two-step resolution algorithm by treating projection as variable binding, which increases compositionality and computational efficiency. The result is a flexible representational framework for a descriptive theory of projection phenomena.

Discourse semantics with information structure

The property of projection poses a challenge to formal semantic theories, due to its apparent non-compositional nature. Projected content is therefore typically analyzed as being different from and independent of asserted content. Recent evidence, however, suggests that these types of content in fact closely interact, thereby calling for a more integrated analysis that captures their similarities, while respecting their differences. Here, we propose such a unified, compositional semantic analysis of asserted and projected content. Our analysis captures the similarities and differences between presuppositions, anaphora, conventional implicatures and assertions on the basis of their information structure, that is, on basis of how their content is contributed to the unfolding discourse context. We formalize our analysis in an extension of the dynamic semantic framework of Discourse Representation Theory (DRT)—called Projective DRT (PDRT)—that employs projection variables to capture the information-structural aspects of semantic content; different constellations of such variables capture the differences between the different types of projected and asserted content within a single dimension of meaning. We formally derive the structural and compositional properties of PDRT, as well as its semantic interpretation. By instantiating PDRT as a mature semantic formalism, we argue that it paves way for a more focused investigation of the information-structural aspects of meaning

PDRT-SANDBOX:An implementation of Projective Discourse Representation Theory

We introduce PDRT-SANDBOX, a Haskell library that implements Projective Dis- course Representation Theory (PDRT) (Venhuizen et al., 2013), an extension of Discourse Representation Theory (DRT) (Kamp, 1981; Kamp and Reyle, 1993). The implementation includes a translation from PDRT to DRT and first-order logic, composition via different types of merge, and unresolved structures based on Mon- tague Semantics (Muskens, 1996), defined as Haskell functions