Limited Symmetry

This paper aims to tackle some of the basic (a-)symmetries of presupposition projection in a pragmatic, bivalent, and incrementally-oriented framework. The main data point that we are trying to capture is that projection from the first conjunct of a conjunction is asymmetric, while projection from the first disjunct of a disjunction can be symmetric. We argue that a solution where there are effectively two filtering mechanisms, one symmetric and one asymmetric, [11], is not tenable given recent experimental evidence, [4, 7]. Instead, we propose a bivalent system, where at each point during the incremental interpretation of a sentence S, the comprehender is trying to compute the sets of worlds in the context where the truth value of S has already been determined. This computation plays out differently in the case of conjunction vs the case of disjunction, and coupled with appropriate definitions of the incremental interpretation process and of what it means for a presupposition to project in the current system, it leads to asymmetric conjunction, but symmetric disjunction.