The present dissertation aims to contribute to the investigation of the interaction between truth conditions and the asymmetries inherent in incremental interpretation, through the lens of the (a-)symmetries involved in presupposition ‘filtering’.Our argument is organised as follows: Chapter 1 sets the stage, introducing the problem of (a- )symmetries in natural language and setting out the particular questions involved in the (a-)symmetries of presupposition filtering. These questions are: 1) whether all connectives exhibit a common filter- ing profile with regards to (a-)symmetries; 2) to the extent that connectives differ in their filtering profiles, whether such differences are a matter of lexical stipulation or can be accounted for in a predictive way. 3) whether predictive theories of filtering in declaratives can be extended to ques- tions. 4) whether different approaches to deriving varying filtering profiles for each connective can be distinguished experimentally. The rest of the dissertation takes up each of these questions. Chapter 2 consists of an experimental investigation into the differences in filtering exhibited by conjunction vs disjunction. The results of the experiments argue for a difference in the filtering profile of the two connectives: conjunction shows a strong preference for asymmetric filtering, while disjunction a strong preference for symmetric filtering. Chapter 3 takes on the question whether such differences in filtering must be stipulated as part of the lexical entry of the meaning of connectives, or derived via the interaction of truth conditions with incremental interpretation. Three different systems are developed that opt for the latter route and predict asymmetric filtering for conjunction but symmetric filtering for disjunction. The different systems are contrasted on the basis of a ‘test suite’ of examples that have received attention in the presupposition literature, and differences in the predictions of the three systems are identified. Chapter 4 investigates the problem of accounting for filtering patterns in (coordinations) of polar questions. We argue that there are drawbacks to tackling this problem by making the resolution conditions for questions asymmetric, and extend one of the systems of chapter 3 to the questions data in a way that avoids this issue. Chapter 5 represents a first attempt to distinguish experimentally between the three systems de- veloped in chapter 3. It focuses on conjunctions whose first conjunct is negated and carries a presupposition. One of the systems developed in chapter 3 predicts the availability of symmetric filtering in this case, whereas the other two systems predict the opposite. While the results point to symmetric filtering being available in these conjunctions at least for some triggers, coming up with a design that was completely confound-free proved hard. As a result the results are somewhat inconclusive and the chapter ends by proposing modifications to our experimental designs that will hopefully provide a clearer picture in the future. Chapter 6 concludes, summarizing the main findings of the dissertation and setting out a future research agenda on the problem of presupposition and its (a-)symmetries.