On the Scope Interaction of Japanese Indefinites: An Epsilon Calculus Approach

On the Scope Interaction of Japanese Indefinites An Epsilon Calculus Approach ⋆ Masahiro Kobayashi a and Hiroaki Nakamura b aEducation Center, Tottori University, 4-101 Koyama-cho Minami, Tottori, 680-8550 Japan kobayashi@uec.tottori-u.ac.jp bDepartment of Liberal Arts, Japan Coast Guard Academy, 5-1 Wakaba-cho, Kure, Hiroshima, 737-8512 Japan nakamura@jcga.ac.jp Abstract. This study explores the scope properties of some indefinites in Japanese in terms of epsilon calculus. Different from ordinary noun phrases, quantificational noun phrases like indefinites are assigned higher-order categories and/or types in syntax, and taken to denote functions from sets to truth values in semantics, which results in great difficulty in deriv- ing proper interpretations of sentences with quantified expressions, given the tight syntax- semantics relation built into theories of grammar. We simply deal with all quantified expres- sions as terms of type e, and treat indefinites as choice functions, i.e., functions that apply to sets and arbitrarily select one of their members. Some indefinites can take arbitrarily wide scopes, depending on contextual information, whereas others have limitations on the freedom of scope taking. We adopt Dynamic Syntax to implement this idea, making it possible for the scope of indefinites to be left unspecified and fixed in a later stage of parsing. Keywords: indefinite expression, epsilon calculus, choice function, Skolemization, Dy- namic Syntax 1 Introduction In languages like English, the distinction between definite and indefinite NPs are explicitly indi- cated by syntactic devices such as determiners, demonstratives and articles, while such distinctions are blurred in languages like Japanese, with the exception of NPs containing demonstratives, and both of them simply occur as bare nominals (without determiners). English indefinites have been treated as existentially quantified expressions, but they are quite different from universally quan- tified ones like any N or all Ns in that the former often do not obey the island conditions and can take arbitrarily wide scopes and/or function as referential terms. As for the construal of in- definites, several different approaches have been proposed. The first one sticks to the parallel treatment of universal and existential quantifiers, both of which are treated as generalized quanti- fiers, and some new mechanism of assignments deals with peculiar properties of indefinites. The second approach posits two different categories for indefinites (referential nominal and existential quantifier), as proposed by Fodor and Sag (1982). The third one deals with indefinites as discourse referents, suggested by so-called Discourse Representation Theories (Kamp and Reyle, 1993), ar- guing that indefinites do not express existential force, but introduce new discourse referents to the contexts. The last one, which we will adopt in this paper, is to regard indefinites as choice func- tions. Among them, we will explore the use of epsilon terms as a syntactic counterpart of choice function, as proposed by Meyer Viol et al. (1999), Kempson et al. (2001), Cann et al. (2005), ⋆ We would like to thank anonymous reviewers for their comments. Copyright 2009 by Masahiro Kobayashi and Hiroaki Nakamura 269 23rd Pacific Asia Conference on Language, Information and Computation, pages 269–277 von Heusinger (2000), Peregrin …

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