Even though Van der Sandt's presuppositions as anaphora approach is empirically successful, it fails to give a formal account of the interaction between world-knowledge and presuppositions. In this paper, an algorithm is sketched which is based on the idea of presuppositions as anaphora. It improves on this approach by employing a deductive system, Constructive Type Theory (CTT), to get a formal handle on the way world-knowledge influences presupposition projection. In CTT, proofs for expressions are explicitly represented as objects. These objects can be seen as a generalization of DRT's discourse markers. They are useful in dealing with presuppositional phenomena which require world-knowledge, such as Clark's bridging examples and Beaver's conditional presuppositions
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