Representing Anaphora with Dependent Types

Discourse semantics based on dependent type theory, such as Ranta’s Type Theoretical Grammar, is expected to serve as a proof-theoretic alternative to standard, model-theoretic discourse semantics such as DRT and DPL. Its compositionality, however, with respect to anaphora and presupposition, has been left as an open problem, toward which several different approaches have been proposed. In this paper, I will point out that four problems still remain to be solved in the previous approaches, and present a compositional discourse theory that remedies this enterprise, by the combination of the following settings: 1) the context-passing mechanism, 2) @-operators for representing anaphora/presupposition triggers, 3) (bottom-up) semantic composition with raw terms, and 4) (top-down) anaphora resolution as type checking.

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