{ "paper_id": "Y09-1029", "header": { "generated_with": "S2ORC 1.0.0", "date_generated": "2023-01-19T13:43:25.577956Z" }, "title": "On the Scope Interaction of Japanese Indefinites An Epsilon Calculus Approach", "authors": [ { "first": "Masahiro", "middle": [], "last": "Kobayashi", "suffix": "", "affiliation": { "laboratory": "", "institution": "Tottori University", "location": { "addrLine": "4-101 Koyama-cho Minami", "postCode": "680-8550", "settlement": "Tottori", "country": "Japan" } }, "email": "kobayashi@uec.tottori-u.ac.jp" }, { "first": "Hiroaki", "middle": [], "last": "Nakamura", "suffix": "", "affiliation": {}, "email": "nakamura@jcga.ac.jp" } ], "year": "", "venue": null, "identifiers": {}, "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 deriving proper interpretations of sentences with quantified expressions, given the tight syntaxsemantics relation built into theories of grammar. We simply deal with all quantified expressions 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.", "pdf_parse": { "paper_id": "Y09-1029", "_pdf_hash": "", "abstract": [ { "text": "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 deriving proper interpretations of sentences with quantified expressions, given the tight syntaxsemantics relation built into theories of grammar. We simply deal with all quantified expressions 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.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Abstract", "sec_num": null } ], "body_text": [ { "text": "In languages like English, the distinction between definite and indefinite NPs are explicitly indicated 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 quantified 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 indefinites, 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 quantifiers, 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) , arguing 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 functions. 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) ,", "cite_spans": [ { "start": 1105, "end": 1125, "text": "Fodor and Sag (1982)", "ref_id": "BIBREF3" }, { "start": 1246, "end": 1268, "text": "(Kamp and Reyle, 1993)", "ref_id": "BIBREF4" }, { "start": 1595, "end": 1619, "text": "Meyer Viol et al. (1999)", "ref_id": "BIBREF7" }, { "start": 1622, "end": 1643, "text": "Kempson et al. (2001)", "ref_id": "BIBREF5" }, { "start": 1646, "end": 1664, "text": "Cann et al. (2005)", "ref_id": "BIBREF1" } ], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1" }, { "text": "We would like to thank anonymous reviewers for their comments.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1" }, { "text": "von Heusinger (2000) , Peregrin and von Heusinger (2004) , among others. We will argue that the use of -operator allows a flexible treatment of indefinites to account for their divergent behaviors concerning scope choice, and give a unified account of surprisingly different interpretations of indefinites with respect to scope taking.", "cite_spans": [ { "start": 4, "end": 20, "text": "Heusinger (2000)", "ref_id": "BIBREF10" }, { "start": 23, "end": 56, "text": "Peregrin and von Heusinger (2004)", "ref_id": "BIBREF8" } ], "ref_spans": [], "eq_spans": [], "section": "Copyright 2009 by Masahiro Kobayashi and Hiroaki Nakamura", "sec_num": null }, { "text": "(1) a. Every boy loves a girl. (\u2200 > \u2203, \u2203 > \u2200) b. Every boy loves a certain girl. ( * \u2200 > \u2203, \u2203 > \u2200) c. Every building has a guard standing in front of it. (\u2200 > \u2203, * \u2203 > \u2200)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Copyright 2009 by Masahiro Kobayashi and Hiroaki Nakamura", "sec_num": null }, { "text": "The three underscored objects in (1) show different scopal properties, as the scope preferences in parenthesis show. Though linear interpretation is overwhelmingly preferred in (1a), the indefinite object a girl can take scope over the subject if some appropriate situation is given. \"A certain + N\" forms as in (1b) usually do not get narrow scope interpretations, but still it is possible to receive intermediate interpretations depending on context. We will show this scope interaction on the basis of Dynamic Syntax (Kempson et al., 2001; Cann et al., 2005) . Relational nouns like guard in (1c) almost always require dependent scope relations irrespective of the positions they appear in sentences. We will try to give a unified explanation of these three kinds of noun phrases in terms of choice function and a scope-choice device in this paper.", "cite_spans": [ { "start": 520, "end": 542, "text": "(Kempson et al., 2001;", "ref_id": "BIBREF5" }, { "start": 543, "end": 561, "text": "Cann et al., 2005)", "ref_id": "BIBREF1" } ], "ref_spans": [], "eq_spans": [], "section": "Copyright 2009 by Masahiro Kobayashi and Hiroaki Nakamura", "sec_num": null }, { "text": "First, we give an outline of our choice function approach to the scope of indefinites, and introduce some assumptions necessary to account for their peculiarities regarding scope taking. It is assumed that sentence (1a) has two interpretations, represented in (2a) and (2b):(", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Scope Independence and Skolemization", "sec_num": "2" }, { "text": "2) a. \u2200x[Bx \u2192 \u2203y[Gy & Lxy] b. \u2203y[Gy \u2227 \u2200y[Bx \u2192 Lxy]]", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Scope Independence and Skolemization", "sec_num": "2" }, { "text": "Fodor and Sag (1982) attempted to explain arbitrarily wide scope phenomena of indefinites and island insensitivity, classifying them into the two groups, quantificational indefinites, as illustrated in (2a) and referential indefinites, as in (2b). This dichotomy of indefinites was refuted by many researchers who cite a sentence like (3) as a counter example.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Scope Independence and Skolemization", "sec_num": "2" }, { "text": "(3) Every professor rewarded every student that read some book on his reading list. (Abusch, 1993) Sentence (3) allows the intermediate scope reading, meaning that, for every professor x, there is a certain book y such that for every student z, x rewarded z who read y on x's reading list, in which some book takes scope over the preceding universally quantified expression every student in the matrix clause but still co-varies along with the choice of professor. Recently, a new approach has been proposed to deal with the (unboundedly) wide scope phenomena of indefinites by Kratzer (1998) , Reinhart (1997) , Winter (1997) , Chierchia (2001) , among others. The object girl in (1a) can be taken to be a choice function, which picks out a witness to the existential quantifier which satisfies the formula. Following Meyer Viol et al. (1999) , Kempson et al. (2001) , Cann et al. (2005 ), von Heusinger (2000 , Peregrin and von Heusinger (2004) , we adopt the -notation as its syntactic counterpart, originally proposed by David Hilbert in the early 20th century. Different from the existential quantifier which denotes a function from sets (or relations) to truth values, the epsilon operator is a term constructor. Since the epsilon operator is interpreted by a choice function, it assigns one of its elements to a non-empty set s. Observe (4) as an example. (4) is true if and only if there is at least one entity belonging to the set of horses, and it is eating grass. U ma in (4) can be expressed as an -term as x(Horse(x) & Eat(grass)(x)). The predicate logic with the epsilon calculus allows the conversion as seen in (5). In addition to this version of the choice function theory, we appeal to the concept of Skolemization here. Suppose that we have the prenex normal form (6a) and (6b) from interpretation (2a) and (2b), respectively.", "cite_spans": [ { "start": 84, "end": 98, "text": "(Abusch, 1993)", "ref_id": "BIBREF0" }, { "start": 578, "end": 592, "text": "Kratzer (1998)", "ref_id": "BIBREF6" }, { "start": 595, "end": 610, "text": "Reinhart (1997)", "ref_id": "BIBREF9" }, { "start": 613, "end": 626, "text": "Winter (1997)", "ref_id": "BIBREF11" }, { "start": 629, "end": 645, "text": "Chierchia (2001)", "ref_id": "BIBREF2" }, { "start": 825, "end": 843, "text": "Viol et al. (1999)", "ref_id": "BIBREF7" }, { "start": 846, "end": 867, "text": "Kempson et al. (2001)", "ref_id": "BIBREF5" }, { "start": 870, "end": 887, "text": "Cann et al. (2005", "ref_id": "BIBREF1" }, { "start": 888, "end": 910, "text": "), von Heusinger (2000", "ref_id": "BIBREF10" }, { "start": 913, "end": 946, "text": "Peregrin and von Heusinger (2004)", "ref_id": "BIBREF8" } ], "ref_spans": [], "eq_spans": [], "section": "Scope Independence and Skolemization", "sec_num": "2" }, { "text": "(6) a. \u2200x\u2203y[(Bx \u2227 Gy \u2227 Lxy) \u2228 (\u00acBx \u2227 Gy \u2227 Lxy) . . . \u2228 (\u00acBx \u2227 \u00acGy \u2227 \u00acLxy)] b. \u2203x\u2200y[(Bx \u2227 Gy \u2227 Lxy) \u2228 (\u00acBx \u2227 Gy \u2227 Lxy) . . . \u2228 (\u00acBx \u2227 \u00acGy \u2227 \u00acLxy)]", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Scope Independence and Skolemization", "sec_num": "2" }, { "text": "We can eliminate the existential quantifier from the formulae in (6) via replacing the variables bound by the existential quantifier with a new function symbol f in (6a) or with a Skolem constant in (6b). The Skolemized formulae obtained from (6a) and (6b) are (7a) and (7b), respectively:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Scope Independence and Skolemization", "sec_num": "2" }, { "text": "(7) a. \u2200x[Bx \u2227 G(f x) \u2227 L(x,f x)) \u2228 (\u00acBx \u2227 G(f x) \u2227 Lx(x,f x)) . . . (\u00acBx \u2227 \u00acG(f x) \u2227 \u00acLx(x,f x))] b. \u2200x[Bx \u2227 G(a) \u2227 L(x,a)) \u2228 (\u00acBx \u2227 G(a) \u2227 Lx(x,a)) \u2228 (\u00acBx \u2227 \u00acG(a) \u2227 \u00acLx(x,a))]", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Scope Independence and Skolemization", "sec_num": "2" }, { "text": "Then, in the Skolemized formula in (7a), the variables bound by the existential quantifier in (6a) get dependent on those bound by the universal quantifier (i.e., Skolemized functions), while the variables bound by the existential quantifier in (6b) are interpreted as a (Skolem) constant, denoting some unique individual satisfying the whole formula. Now, we are ready to give a unified account for Japanese indefinites, with the notion of \"Skolemized choice function\" in the sense of Chierchia (2001) .", "cite_spans": [ { "start": 486, "end": 502, "text": "Chierchia (2001)", "ref_id": "BIBREF2" } ], "ref_spans": [], "eq_spans": [], "section": "Scope Independence and Skolemization", "sec_num": "2" }, { "text": "The Japanese data we will examine here are illustrated as in 8 PAST \"Every resident took his or her child to the festival.\" (8a) is ambiguous between subject and object wide scope readings (though the preferred interpretation is that every pupil has scope over a dog, it is possible to imagine a situation something like pupils keeping and taking care of one dog at school etc.). In (8b), a certain must take a wide scope with respect to every student, but its value can still co-vary with the choice of prof essor. The choice of the referent of child in (8c) must be dependent on the particular choice of a referent of resident and the inverse scope interpretation is impossible.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Indefinite with Underspecifie Scope", "sec_num": "3" }, { "text": "One of advantages of using -terms is that quantified terms can be dealt with as individual denoting expressions, not as generalized quantifiers, and that we can eliminate existential quantifiers from formulae. Suppose that we want to derive the two different interpretations for sentence (1a) or (8a) from a single formula with the -term. Kempson et al./Cann et al./von Heusinger propose to remove a predicate corresponding to a nuclear scope from a -term, and let it denote a choice function picking out a witness from the denotation of the restrictor (referred to by the common noun), and the scope determination can be delayed to allow for scope inversion. So, if our initial -term translation for (8a) is something like y(P upil(y)), formula (9) is obtained:", "cite_spans": [ { "start": 339, "end": 387, "text": "Kempson et al./Cann et al./von Heusinger propose", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Indefinite with Underspecifie Scope", "sec_num": "3" }, { "text": "(9) \u2200x[P upil(x) \u2192 T ake-care(x, y(Dog(y)))]", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Indefinite with Underspecifie Scope", "sec_num": "3" }, { "text": "Notice that the -term in (9) is underspecified with respect to scope choice because scope is finally determined pragmatically. Following Kempson et al. (2001) and Cann et al. (2005) , we assume that final scope determination requires two elements: formulae with epsilon terms like (9) and scope statements in the form of Scope(S\u2203, * \u2203 > \u2200)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Relational Nouns", "sec_num": "4.2" }, { "text": "b. Every building has a guard standing in front of it. (\u2200 > \u2203, * \u2203 > \u2200) (Winter 2001) Due to the conflict in scope choice, relational nouns do not comfortably co-occur with a certain, as in * ?A certain guard is standing in f ront of every building. / ? * Every building has a certain guard in f ront of it. We have to reflect this property scope dependency in the lexical definition of -terms for relational nouns. A proper form of an -term for child should be something like (23), which requires the -term to be an inherent Skolem function.", "cite_spans": [ { "start": 72, "end": 85, "text": "(Winter 2001)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Relational Nouns", "sec_num": "4.2" }, { "text": "(23) Scope( S < y < . . . < x) : x(Child-of (x)(y))", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Relational Nouns", "sec_num": "4.2" }, { "text": "It should be noted in (23) that the free variable y is introduced into the -term, which needs to get bound somewhere in the course of derivation, and the scope statement requires its scope to be (most) locally defined. The logical form for (8c) is shown in (24a), which must be converted to the Skolem normal form in (24b):", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Relational Nouns", "sec_num": "4.2" }, { "text": "(24) a. Scope(S