On the interpretation of dependent plural anaphora in a dependently-typed setting

Anaphora resolution is sensitive to dependency relations between objects. One example, which is well known in the plural anaphora literature, is the dependent interpretation of the pronoun it in the mini-discourse Every boy received a present. They each opened it. The standard account of the dependent interpretation records dependency relations using sets of assignment functions (van den Berg [4,5], Nouwen [17], Brasoveanu [7]). This approach, however, requires substantial changes to the central notion of context and gives special treatment to dependent interpretations. In this paper we provide an alternative account from the perspective of dependent type theory (MartinLöf [16]). We account for dependency relations in terms of dependent function types (Π-types), which are independently motivated objects within dependent type theory. We will adopt Dependent Type Semantics (Bekki [1], Bekki and Mineshima [2]) as a semantic framework and illustrate how dependent function types encode dependency relations and naturally provide a resource for dependent interpretations.