On Presupposition Projection with Trivalent Connectives

A basic puzzle about presuppositions concerns their projection from
propositional constructions. This problem has regained much attention in the last
decade since many of its prominent accounts, including variants of the trivalent
Strong Kleene connectives, suffer from the so-called proviso problem. This paper argues that basic insights of the Strong Kleene system can be used without
invoking the proviso problem. It is shown that the notion of determinant value
that underlies the definition of the Strong Kleene connectives leads to a natural
generalization of the filtering conditions proposed in Karttunen’s article “Presuppositions of compound sentences” (LI, 1973). Incorporating this generalized condition into an incremental projection algorithm avoids the proviso problem as well as the derivation of conditional presuppositions. It is argued that the same effects that were previously modelled using conditional presuppositions may be viewed as effects of presupposition suspension and contextual inference on presupposition projection.