We propose a novel account of presupposition projection that derives the
fact that filtering behaves asymmetrically for conjunction but
symmetrically for disjunction. Our account is rooted in parsing, but
manages to derive the relevant (a-)symmetries through a single underlying
mechanism (contra accounts employing distinct symmetric vs asymmetric
filtering mechanisms, cf. Schlenker 2009). Apart from handling the contrast
between conjunction and disjunction, our account makes interesting
predictions in the case of conditionals, where it manages to capture
certain cases of symmetric behavior.