A Type-theoretic Approach to Double Negation Elimination in Anaphora ⋆ Daisuke Bekki 1,2 1 Ochanomizu University ⋆⋆ 2 National Institute of Informatics bekki α is.ocha.ac.jp Abstract. This paper proposes a proof-theoretic, compositional dis- course semantics of natural language, which we call Dependent Type Semantics (DTS). The formalization of DTS is based on polymorphic dependent type theory, instead of standard Montagovian or dynamic frameworks. We show that DTS provides a solution to the cases of dy- namic binding where double negation elimination is involved in order to establish a dynamic link, which has long been problematic to most dy- namic semantics. A comparison is made with the previous work including Double Negation DRT. 1 Dependent Type Semantics This paper proposes a proof-theoretic, compositional discourse semantics of nat- ural language that we call Dependent Type Semantics (henceforth DTS). The formalization of DTS is based on polymorphic dependent type theory (PDTT) instead of standard Montagovian or dynamic frameworks. The first use of de- pendent type theory for natural language semantics is attributed to Sundholm [16], in which sentence (1a), for instance, is assigned a semantic representation (SR) (1b) (slightly adapted for the purpose of our analysis). (1) a. Every farmer who owns a donkey beats it. b. (Πu:(Σx:Entity)(Farmer(x) ∧(Σy:Entity)(Donkey(y) ∧ Own(x, y))))Beat(π 1 (u),π 1 π 2 π 2 (u)) One of the advantages of Sundholmian representation is that empirically correct inferences such as (2), including dynamic binding, can be proven using the natural deduction-style proof system, without recourse to a model theory. ⋆ My sincere thanks to the anonymous reviewers of LENLS10 who gave me insightful comments. I also thank Rick Nouwen and Ben Rodenhaeuser for discussing the issue of doulbe negation elimination in October 2012. Daisuke Bekki is partially supported by a Grant-in-Aid for Young Scientists (A) (No. 22680013) from the Ministry of Education, Science, Sports and Culture . ⋆⋆ Graduate School of Humanities and Sciences, Faculty of Science, 2-1-1 Ohtsuka, Bunkyo-ku, Tokyo 112-8610, Japan.