Abstract
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 (Martin-Löf [16]). We account for dependency relations in terms of dependent function types (\(\varPi \)-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.
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Notes
- 1.
An anaphor is subscripted by an index, while its antecedent is superscripted by the same index.
- 2.
This example is attributed to Lauri Karttunen in Hintikka and Carlson [10].
- 3.
There are important differences between Ranta’s [18] framework and that of DTS. First, while Ranta did not adopt the framework of compositional semantics, DTS provides a compositional derivation of the semantic representations involving anaphora. Another difference between Ranta’s and our analysis is that Ranta interprets common nouns as types, while DTS treats them as predicates. More discussion on these points can be found in Bekki and Mineshima [2].
- 4.
Some readers may think that proof terms have something in common with discourse referents in Discourse Representation Theory (Kamp and Reyle [12], Kamp et al. [11]) in that both objects are introduced by sentences and referred to afterward to resolve anaphora. There are at least two crucial differences. Firstly, as Ranta [18] discussed, while discourse referents are limited to individuals without any inner structure, proof terms can have any type. Secondly, together with the anaphora resolution mechanism provided in DTS, proof terms can contribute to logical inference, which yields a new proof term serving as an antecedent.
- 5.
In the case of every, we can provide its semantic representation in two ways: one possibility is to treat it simply as a \(\varPi \)-type as we have seen above; another possibility is to represent it in the same way as other generalized quantifiers such as most. Since these two formulas are mutually deducible, the account of generalized quantifiers presented here can be applied to the case of every as well.
- 6.
As \(\varPi \)-types correspond to the \(\forall \)–\(\exists \) reading (or distributive reading), the semantic representation of three provided by Tanaka [19] should correspond to the semantic representation of three...each. To obtain the semantic representation of three...each in a compositional way, we can integrate the existing analysis of plural objects into our framework (see Link [15] for the standard approach; for the treatment of plural objects in a dependently-typed setting, see Boldini [6] and Chatzikyriakidis and Luo [8]). A full discussion of this phenomenon is beyond the scope of this paper.
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Acknowledgments
This paper is a revised and expanded version of a paper presented at the Logic and Engineering of Natural Language Semantics 13 (LENLS13). We would like to thank Alastair Butler, Yusuke Kubota, Robert Levine, the audience of the workshop ‘New landscapes in theoretical computational linguistics,’ two anonymous reviewers, and the audience of LENLS13 for their valuable comments, suggestions, and discussions. We are also grateful to Robin Cooper for helpful discussions on an earlier version of this paper. The first author acknowledges the financial support from JSPS (Grant-in-Aid for JSPS Research Fellow; 15J11772).
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Tanaka, R., Mineshima, K., Bekki, D. (2017). On the Interpretation of Dependent Plural Anaphora in a Dependently-Typed Setting. In: Kurahashi, S., Ohta, Y., Arai, S., Satoh, K., Bekki, D. (eds) New Frontiers in Artificial Intelligence. JSAI-isAI 2016. Lecture Notes in Computer Science(), vol 10247. Springer, Cham. https://doi.org/10.1007/978-3-319-61572-1_9
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