{
    "paper_id": "P02-1010",
    "header": {
        "generated_with": "S2ORC 1.0.0",
        "date_generated": "2023-01-19T09:30:39.036658Z"
    },
    "title": "Ellipsis Resolution with Underspecified Scope",
    "authors": [
        {
            "first": "Michael",
            "middle": [],
            "last": "Schiehlen",
            "suffix": "",
            "affiliation": {},
            "email": "mike@ims.uni-stuttgart.de"
        }
    ],
    "year": "",
    "venue": null,
    "identifiers": {},
    "abstract": "The paper presents an approach to ellipsis resolution in a framework of scope underspecification (Underspecified Discourse Representation Theory). It is argued that the approach improves on previous proposals to integrate ellipsis resolution and scope underspecification (Crouch, 1995; Egg et al., 2001) in that application processes like anaphora resolution do not require full disambiguation but can work directly on the underspecified representation. Furthermore it is shown that the approach presented can cope with the examples discussed by Dalrymple et al. (1991) as well as a problem noted recently by Erk and Koller (2001).",
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        "abstract": [
            {
                "text": "The paper presents an approach to ellipsis resolution in a framework of scope underspecification (Underspecified Discourse Representation Theory). It is argued that the approach improves on previous proposals to integrate ellipsis resolution and scope underspecification (Crouch, 1995; Egg et al., 2001) in that application processes like anaphora resolution do not require full disambiguation but can work directly on the underspecified representation. Furthermore it is shown that the approach presented can cope with the examples discussed by Dalrymple et al. (1991) as well as a problem noted recently by Erk and Koller (2001).",
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                "section": "Abstract",
                "sec_num": null
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            {
                "text": "Explicit computation of all scope configurations is apt to slow down an NLP system considerably. Therefore, underspecification of scope ambiguities is an important prerequisite for efficient processing. Many tasks, like ellipsis resolution or anaphora resolution, are arguably best performed on a representation with fixed scope order. An underspecification formalism should support execution of these tasks. This paper aims to upgrade an existing underspecification formalism for scope ambiguities, Underspecified Discourse Representation Theory (UDRT) (Reyle, 1993) , so that both ellipsis and anaphora resolution can work on the underspecified structures. Several proposals have been made in the literature on how to integrate scope underspecification and ellipsis resolution in a single formalism, e.g. Quasi-Logical Forms (QLF) (Crouch, 1995) and the Constraint Language for Lambda Structures (CLLS) (Egg et al., 2001) . That work has primarily aimed at devising methods to untangle quantifier scoping and ellipsis resolution which often interact closely (see Section 6). To this end, description languages have been modelled in which the disambiguation steps of a derivation need not be executed but rather can be explicitly recorded as constraints on the final structure. Constraints are only evaluated when the underspecified representation is finally interpreted. In contrast, UDRT aims at providing a representation formalism that supports interpretation processes such as theorem proving and anaphora resolution. Understood in this sense, underspecification often obviates the need for complete disambiguation. Another consequence is, however, that the strategy of postponing disambiguation steps is in some cases insufficient. A case in point is the phenomenon dubbed Missing Antecedents by Grinder and Postal (1971) , illustrated in sentence (1): One of the pronoun's antecedents is overt, the other is supplied by ellipsis resolution.",
                "cite_spans": [
                    {
                        "start": 554,
                        "end": 567,
                        "text": "(Reyle, 1993)",
                        "ref_id": "BIBREF12"
                    },
                    {
                        "start": 833,
                        "end": 847,
                        "text": "(Crouch, 1995)",
                        "ref_id": "BIBREF2"
                    },
                    {
                        "start": 905,
                        "end": 923,
                        "text": "(Egg et al., 2001)",
                        "ref_id": "BIBREF4"
                    },
                    {
                        "start": 1803,
                        "end": 1828,
                        "text": "Grinder and Postal (1971)",
                        "ref_id": "BIBREF8"
                    }
                ],
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                "eq_spans": [],
                "section": "Introduction",
                "sec_num": "1"
            },
            {
                "text": "(1) Harry sank a destroyer\u00a2 and so did Bill and they\u00a2",
                "cite_spans": [],
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                "eq_spans": [],
                "section": "Introduction",
                "sec_num": "1"
            },
            {
                "text": "both went down with all hands. (Grinder and Postal, 1971, 279) Most approaches to ellipsis and anaphora resolution, e.g. (Asher, 1993; Crouch, 1995; Egg et al., 2001) , can readily derive the reading. But consider:",
                "cite_spans": [
                    {
                        "start": 31,
                        "end": 62,
                        "text": "(Grinder and Postal, 1971, 279)",
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                    {
                        "start": 121,
                        "end": 134,
                        "text": "(Asher, 1993;",
                        "ref_id": "BIBREF1"
                    },
                    {
                        "start": 135,
                        "end": 148,
                        "text": "Crouch, 1995;",
                        "ref_id": "BIBREF2"
                    },
                    {
                        "start": 149,
                        "end": 166,
                        "text": "Egg et al., 2001)",
                        "ref_id": "BIBREF4"
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                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "\u00a4 \u00a3\u00a5",
                "sec_num": null
            },
            {
                "text": "(2) Harry sometimes reads a book about a seabattle and so does Bill. They borrow those books from the library.",
                "cite_spans": [],
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                "section": "\u00a4 \u00a3\u00a5",
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                "text": "Example (2) still retains five readings (Are there two or even more books? are there one, two, or more than two sea-battles?). An underspecified representation should not be committed to any of these readings, but it should specify that \"a book\" has narrow scope with respect to the conjunction. Furthermore, an approach to underspecification and ellipsis resolution should make clear why this representation is to be constructed for the discourse (2). While QLF fails the first requirement (a single representation), CLLS fails the second (triggers for construction).",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "\u00a4 \u00a3\u00a5",
                "sec_num": null
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            {
                "text": "(3) * A destroyer\u00a2 went down in some battle and a cruiser did too. Harry sank both destroyers\u00a2",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "\u00a4 \u00a3\u00a5",
                "sec_num": null
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            {
                "text": "\u00a4 \u00a3\u00a5 .",
                "cite_spans": [],
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                "section": "\u00a4 \u00a3\u00a5",
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                "text": "The discourse in (3) is not well-formed. But none of the approaches mentioned can ascertain this fact without complete scope resolution (or ad-hoc restrictions). The paper is organized as follows. Section 2 gives a short introduction to UDRT. Section 3 formulates the general setup of ellipsis resolution assumed in the rest of the paper. Section 4 presents a proposal to deal with scope parallelism in an underspecified representation. Section 5 shows how ellipsis can be treated if it is contained in its antecedent. Section 6 describes a way to model the interaction of ellipsis resolution and scope resolution in an underspecified structure. In section 7 strict and sloppy identity is discussed. Section 8 concludes.",
                "cite_spans": [],
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                "section": "\u00a4 \u00a3\u00a5",
                "sec_num": null
            },
            {
                "text": "Representation Structures Reyle (1993) proposes a formalism for underspecification of scope ambiguity. The underspecified representations are called Underspecified Discourse Representation Structures (UDRSs). Completely specified UDRSs correspond to the Discourse Representation Structures (DRSs) of Kamp and Reyle (1993) . A UDRS is a triple consisting of a top label, a set of labelled conditions or discourse referents, and a set of subordination constraints. A UDRS is (partially) disambiguated by adding subordination constraints. A UDRS must, however, always comply with the following wellformedness conditions: (1) It does not contain cycles (subordination is a partial order). (2) No label is subordinated to two labels which are siblings, i.e. part of the same complex condition (subordination is a tree order). Figure 1 shows the UDRS for sentence 4 in formal and graph representation.",
                "cite_spans": [
                    {
                        "start": 26,
                        "end": 38,
                        "text": "Reyle (1993)",
                        "ref_id": "BIBREF12"
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                    {
                        "start": 300,
                        "end": 321,
                        "text": "Kamp and Reyle (1993)",
                        "ref_id": "BIBREF9"
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                "ref_spans": [
                    {
                        "start": 821,
                        "end": 829,
                        "text": "Figure 1",
                        "ref_id": null
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                "section": "Underspecified Discourse",
                "sec_num": "2"
            },
            {
                "text": "(4) Every professor found most solutions. x l6: most( y, l3: ,l4: ) y",
                "cite_spans": [],
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                "eq_spans": [],
                "section": "Underspecified Discourse",
                "sec_num": "2"
            },
            {
                "text": "\u00a1 \u00a3 \u00a2 , { \u00a1 \u00a5 \u00a4 \u00a7 \u00a6 every\u00a9 \u00a1 \u00a1 , { \u00a1 \u00a4 \u00a7 \u00a1 \u00a2 , \u00a1 \u00a6 \u00a9 \u00a1 \u00a3 ! \" \u00a6 professor\u00a9 , \u00a1 \u00a5 ! \" \u00a1 , \u00a1 \u00a3 # \" \u00a6 most\u00a9 \u00a1 \u00a3 $ \u00a1 \u00a3 % & , \u00a1 \u00a5 # \" \u00a1 \u00a2 , \u00a1 $ \u00a6 ( ' , \u00a1 \u00a3 ) \" \u00a6 solution\u00a8' 0 , \u00a1 \u00a5 ) \" \u00a1 \u00a5 $ , \u00a1 \u00a5 1 \u00a7 \u00a6 find\u00a9 ' 0 }, \u00a1 1 \u00a7 \u00a1 , \u00a1 1 \u00a7 \u00a1 % }2",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Underspecified Discourse",
                "sec_num": "2"
            },
            {
                "text": "Figure 1: UDRS for sentence 4For pronouns and definite descriptions another type of constraint is introduced, accessibility constraints.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Underspecified Discourse",
                "sec_num": "2"
            },
            {
                "text": "is accessible from in a condition expressing material implication or a generalized quantifier (Kamp and Reyle, 1993) . An accessibility constraint",
                "cite_spans": [
                    {
                        "start": 94,
                        "end": 116,
                        "text": "(Kamp and Reyle, 1993)",
                        "ref_id": "BIBREF9"
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                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "5 4",
                "sec_num": "3"
            },
            {
                "text": "3 Q 6 acc 3 5 4",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "5 4",
                "sec_num": "3"
            },
            {
                "text": "indicates that 3 5 4 is an anaphoric element or a presupposition; it thus can be used as a trigger for anaphora resolution and presupposition binding (van der Sandt, 1992 ) and an equality constraint between two discourse referents are introduced. Binding constraints are interpreted as equality in the subordination order. Any unbound presuppositions remaining after anaphora resolution (corresponding to accessibility constraints without binding constraints) are accommodated, i.e. they end up in an accessible scope position which is as near to the top as possible. Figure 2 shows the UDRS for sentence (5). Accessibility constraints are marked by broken lines, binding constraints are shown as squiggles.",
                "cite_spans": [
                    {
                        "start": 150,
                        "end": 170,
                        "text": "(van der Sandt, 1992",
                        "ref_id": "BIBREF14"
                    }
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                "ref_spans": [
                    {
                        "start": 569,
                        "end": 577,
                        "text": "Figure 2",
                        "ref_id": null
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                "eq_spans": [],
                "section": "5 4",
                "sec_num": "3"
            },
            {
                "text": "(5) John revised his paper. l7: revise( x, y ) l4: paper( y ) of( y, z )",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "5 4",
                "sec_num": "3"
            },
            {
                "text": "l6: z = x l5: z l1: x l2: John( x ) l3: y l0 \u00a1 \u00a2 , { \u00a1 \u00a6 \u00a9 , { \u00a1 \u00a5 1 acc \u00a1 , \u00a1 \u00a7 \u00a6 John\u00a9 , \u00a1 \u00a5 \u00a7 \u00a1 , \u00a1 $ \u00a6 ' , \u00a1 \u00a5 1 acc \u00a1 $ , \u00a1 % \u00a6 paper\u00a8' , \u00a1 % \u00a1 $ , \u00a1 \u00a5 % \" \u00a6 of\u00a8' \u00a1 , \u00a1 \u00a4 \u00a6 \u00a1 , \u00a1 % acc \u00a1 \u00a4 , \u00a1 \u00a5 # \" \u00a6 gender\u00a8\u00a1 \u00a3 \u00a2 masc, \u00a1 \u00a5 # \" \u00a1 \u00a5 \u00a4 , \u00a1 # \u00a6 \u00a1 \u00a2 \u00a9 , \u00a1 # \u00a5 \u00a4 \u00a6 \u00a1 , \u00a1 1 \u00a7 \u00a6 revise\u00a9 ' 0 }, \u00a1 1 \u00a7 \u00a1 \u00a3 \u00a2 }2",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "5 4",
                "sec_num": "3"
            },
            {
                "text": "Figure 2: UDRS for sentence 53 Ellipsis Resolution Sag (1976) and Williams (1977) have argued convincingly that VP ellipsis should be resolved on a level where scope is fixed. Dalrymple et al. (1991) distinguish two tasks in ellipsis resolution: ",
                "cite_spans": [
                    {
                        "start": 51,
                        "end": 61,
                        "text": "Sag (1976)",
                        "ref_id": "BIBREF13"
                    },
                    {
                        "start": 66,
                        "end": 81,
                        "text": "Williams (1977)",
                        "ref_id": "BIBREF15"
                    },
                    {
                        "start": 176,
                        "end": 199,
                        "text": "Dalrymple et al. (1991)",
                        "ref_id": "BIBREF3"
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "5 4",
                "sec_num": "3"
            },
            {
                "text": "\u00a7 \u00a9 6 \u00a9 \u00a9 6 ! \u00a9 \" .",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "5 4",
                "sec_num": "3"
            },
            {
                "text": "The paper does not have much to say about task 1. Rather, some \"parallelism\" module is assumed to take care of task 1. This module determines the UDRS representations of the source clause and of the source and target parallel elements. It also provides a bijective function # associating the parallel labels and discourse referents in source and target.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "5 4",
                "sec_num": "3"
            },
            {
                "text": "For task 2 we adopt the substitutional approach advocated by Crouch (1995) : The semantic representation of the target \u00a7 is a copy of the source \u00a7 where target parallel elements have been substituted for source parallel elements (",
                "cite_spans": [
                    {
                        "start": 61,
                        "end": 74,
                        "text": "Crouch (1995)",
                        "ref_id": "BIBREF2"
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "5 4",
                "sec_num": "3"
            },
            {
                "text": "\u00a7 % $ \u00a7 & \u00a9 6 ( ' \u00a9 6 ) \u00a9 ' \u00a9 1 0",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "5 4",
                "sec_num": "3"
            },
            {
                "text": ") . In contrast to Higher-Order Unification (HOU) (Dalrymple et al., 1991) substitution is deterministic: Ambiguities somehow cropping up in the interpretation process (i.e. the strict/sloppy distinction) require a separate explanation.",
                "cite_spans": [
                    {
                        "start": 50,
                        "end": 74,
                        "text": "(Dalrymple et al., 1991)",
                        "ref_id": "BIBREF3"
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "5 4",
                "sec_num": "3"
            },
            {
                "text": "It has frequently been observed that structural ambiguity does not multiply in contexts involving ellipsis: A scope ambiguity associated with the source must be resolved in the same way in source and target. Sentence (6) e.g. has no reading where all professors found the same solution but the students who found a solution each found a different one.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Scope Parallelism",
                "sec_num": "4"
            },
            {
                "text": "(6) Every professor found a solution, and most students did, too.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Scope Parallelism",
                "sec_num": "4"
            },
            {
                "text": "Scope parallelism seems to be somewhat at odds with the idea of resolving ellipses on scopally underspecified representations. If the decisions on scope order have not yet been taken, how can they be guaranteed to be the same in source and target? The QLF approach (Crouch, 1995) gives an interesting answer to this question: It uses re-entrancy to propagate scope decisions among parallel structures. In sentence (6), we see that a scope decision can resolve more than one ambiguity. In UDRT, scope decisions are modelled as subordination constraints. Consequently, sentence (6) shows that subordination constraints may affect more than one pair of labels. Remember that in each process of ellipsis resolution 2 the parallelism module returns a bijective function # \u00a2 which expresses the parallelism between labels and discourse referents in source and target. As sentence (6) shows, a subordination constraint that links two source labels ",
                "cite_spans": [
                    {
                        "start": 265,
                        "end": 279,
                        "text": "(Crouch, 1995)",
                        "ref_id": "BIBREF2"
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Scope Parallelism",
                "sec_num": "4"
            },
            {
                "text": ". Thus the subordination constraint does not distinguish between source label and parallel labels. Formally, we define two labels are the source labels, it does not make sense, and actually will often lead to a structure violating the wellformedness conditions, to connect e.g. the source label",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "2",
                "sec_num": null
            },
            {
                "text": "3 6",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "2",
                "sec_num": null
            },
            {
                "text": "with some target label # \u00a2 334 5",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "2",
                "sec_num": null
            },
            {
                "text": ". Thus we still need a proviso that only such labels can be linked that were determined to be parallel to the source label in the same sequence of ellipsis resolutions. We talk about a sequence here, because, as sentence 7shows, ellipses may be nested. 7John arrived before the teacher did (1 arrive),",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "2",
                "sec_num": null
            },
            {
                "text": "and Bill did too (2 arrive before the teacher did (1 arrive)).",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "2",
                "sec_num": null
            },
            {
                "text": "For the implementation of classes, we take our cues from Prolog (Erbach, 1995; Mellish, 1988) . In Prolog, class membership is most efficiently tested via unification. For unification to work, the class members must be represented as instances of the representation of the class. If class members are mutually exclusive, their representations must have different constants at some argument position. In this vein, we can think of a label as a Prolog term whose functor denotes the equivalence class and whose argument describes the sequence of ellipsis resolutions that generated the label. Such a sequence can be modelled as a list of numbers which denote resolutions of particular ellipses. An empty list indicates that the label was generated directly by semantic construction. We will call the list of resolution numbers associated with a label the label's context. For reasons that will become clear only in section 7 discourse referents also have contexts. Although subordination constraints connect classes of labels, they are always evaluated in a particular context. Thus",
                "cite_spans": [
                    {
                        "start": 64,
                        "end": 78,
                        "text": "(Erbach, 1995;",
                        "ref_id": "BIBREF5"
                    },
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                        "start": 79,
                        "end": 93,
                        "text": "Mellish, 1988)",
                        "ref_id": "BIBREF11"
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                "section": "2",
                "sec_num": null
            },
            {
                "text": "3 7 6 @ 3 \u00a1 (or, more explicitly, \u00a2 \u00a4 \u00a3 E 3 8 6 &\u00a3 0 @ 3 \u00a1 &\u00a3 0",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "2",
                "sec_num": null
            },
            {
                "text": ") can be spelled out as",
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                "sec_num": null
            },
            {
                "text": "3 7 6 & 0 @ 3 \u00a1 & 0 or 3 6 & \u00a6 \u00a5 0 @ 3 & \u00a6 \u00a5 0 , but never 3 6 & 0 @ 3 & \u00a6 \u00a5 0",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "2",
                "sec_num": null
            },
            {
                "text": "because in this case context changes.",
                "cite_spans": [],
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                "eq_spans": [],
                "section": "2",
                "sec_num": null
            },
            {
                "text": "While scope resolution is subject to parallelism and binding is too (see Section 7), examples like (9) suggest that accommodation sites need not be parallel 1 . (\"The jeweler\" is accommodated with wide 1 Asher et al. (2001) use parallelism between subordination and accommodation to explain the \"wide-scope puzzle\" observed by Sag (1976) . Sentence (8) has only one reading: A specific nurse saw all patients.",
                "cite_spans": [
                    {
                        "start": 202,
                        "end": 223,
                        "text": "1 Asher et al. (2001)",
                        "ref_id": null
                    },
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                        "start": 327,
                        "end": 337,
                        "text": "Sag (1976)",
                        "ref_id": "BIBREF13"
                    }
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                "eq_spans": [],
                "section": "2",
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            },
            {
                "text": "(8) A nurse saw every patient. Dr. Smith did too. scope, but \"his wife\" is not.) (9) If Peter is married, his wife is lucky and the jeweler is too.",
                "cite_spans": [],
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                "eq_spans": [],
                "section": "2",
                "sec_num": null
            },
            {
                "text": "Ellipsis resolution works as follows. In semantic construction, all occurrences of labels and discourse referents (except those in subordination constraints) are assigned the empty context ( & 0 ), if any, are added to the semantic representation of the target. Figure 3 shows the UDRS for sentence (6) after ellipsis resolution. Erk and Koller (2001) discuss sentence (10) which has a reading in which each student went to the station on a different bike. The example is problematic for all approaches which assume source and target scope order to be identical (HOU, QLF, CLLS).",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 262,
                        "end": 270,
                        "text": "Figure 3",
                        "ref_id": "FIGREF6"
                    }
                ],
                "eq_spans": [],
                "section": "2",
                "sec_num": null
            },
            {
                "text": "\u00a1 \u00a2 \u00a9 , { \u00a1 \u00a9 \u00a6 every\u00a9 \u00a9 \u00a1 \u00a9 \u00a1 $ \u00a9 , { \u00a1 \u00a1 ) , \u00a1 \u00a9 \u00a6 \u00a9 \u00a9 , \u00a1 % \u00a9 \u00a6 professor\u00a9 \u00a9 , \u00a1 % \u00a1 , \u00a1 \u00a4 \u00a9 \u00a6 ' \u00a9 , \u00a1 \u00a4 \u00a1 ) , \u00a1 \u00a5 # \u00a9 \u00a6 solution\u00a8' \u00a9 , \u00a1 \u00a5 # \u00a7 \u00a1 \u00a4 , \u00a1 1 \u00a9 \u00a6 find\u00a9 \u00a9 ' \u00a9 , \u00a1 \u00a5 1 \u00a1 $ , \u00a1 1 \u00a1 \u00a4 \u00a1 \u00a5 ! \u00a9 \u00a6 and\u00a8\u00a1 ) \u00a9 \u00a1 ) \u00a9 , \u00a1 \u00a3 ! \u00a7 \u00a1 \u00a5 \u00a2 }2 },",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "2",
                "sec_num": null
            },
            {
                "text": "(10) John went to the station, and every student did too, on a bike. Erk and Koller (2001) go on to propose an extension of CLLS that permits the reading. In the approach proposed here no special adjustments are needed: The indefinite NP is designated by labels that do not have counterparts in the source. The subordination order is still the same in source and target.",
                "cite_spans": [
                    {
                        "start": 69,
                        "end": 90,
                        "text": "Erk and Koller (2001)",
                        "ref_id": "BIBREF6"
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "2",
                "sec_num": null
            },
            {
                "text": "The elliptical clause can also be contained in the source, cf. example (11).",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Antecedent-Contained Ellipsis",
                "sec_num": "5"
            },
            {
                "text": "(11) John greeted every person that Bill did.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Antecedent-Contained Ellipsis",
                "sec_num": "5"
            },
            {
                "text": "In this case the quantifier embedding the elliptical clause necessarily takes scope over the source. The treatment of this phenomenon in QLF and CLLS, which consists in checking for cyclic formulae after scope resolution, cannot be transferred to UDRT, since it presupposes resolved scope. Rather we make a distinction between proposed source and actual source. If the target is not contained in the (proposed) source, the actual source is the proposed source. Otherwise, the actual source is defined to be that part of the proposed source which is potentially subordinated 2 by the nuclear scope of the quantifier whose restriction contains the target.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Antecedent-Contained Ellipsis",
                "sec_num": "5"
            },
            {
                "text": "Sentence (6) has a third reading in which the indefinite NP \"a solution\" is raised out of the source clause and gets wide scope over the conjunction. In this case, the quantifier itself is not copied, only the bound variables which remain in the source. Generally, a quantifier that may or may not be raised out of the source is only copied if it gets scope inside the source. Thus the exact determination of the semantic material to be copied (i.e. of the source) is dependent on scope decisions. Consequently, in an approach working on fully specified representations (Dalrymple et al., 1991) scope resolution cannot simply precede ellipsis resolution but rather is interleaved with it. Crouch (1995) considers ordersensitivity of interpretation a serious drawback. In his approach, underspecified formulae are copied in ellipsis resolution. In such formulae, quantifiers are not expressed directly but rather stored in \"q-terms\". Q-terms are interpreted as bound variables. Quantifiers are introduced into interpreted structure only when their scope is resolved. Since scope resolution is seen as constraining the structure rather than as an operation of its own, the QLF approach manages to untangle scope resolution and ellipsis resolution. In CLLS (Egg et al., 2001 ) no copy is made in the underspecified representation. In both approaches, the quantifier is not copied until scope resolution.",
                "cite_spans": [
                    {
                        "start": 570,
                        "end": 594,
                        "text": "(Dalrymple et al., 1991)",
                        "ref_id": "BIBREF3"
                    },
                    {
                        "start": 689,
                        "end": 702,
                        "text": "Crouch (1995)",
                        "ref_id": "BIBREF2"
                    },
                    {
                        "start": 1254,
                        "end": 1271,
                        "text": "(Egg et al., 2001",
                        "ref_id": "BIBREF4"
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Interaction of Ellipsis Resolution and Quantifier Scoping",
                "sec_num": "6"
            },
            {
                "text": "But the Missing Antecedents phenomenon (1) shows that a copy of the quantifier must be available even before scope resolution so that it can serve as antecedent. But this copy may evaporate later on when more is known about the scope configuration. We will call conditions that possibly evaporate phantom conditions. For their implementation we make use of the fact that a UDRS collects labelled conditions and subordination constraints in sets. In sets, identical elements collapse. Thus, a condition that is completely identical to another condition will vanish in a UDRS. Phantom conditions only arise by parallelism; hence they are identical to their originals but for the context of their labels and discourse referents. To capture the effect of possible evaporation, it suffices to make the update of context in a phantom condition dependent on the relevant scope decision. To implement phantom conditions in a Prolog-style environment, we insert a meta-variable in place of the context and control its instantiation by a special constraint expressing the dependence on the pertinent subordination constraint (a conditional constraint). Conditional constraints have the form $ 33",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Interaction of Ellipsis Resolution and Quantifier Scoping",
                "sec_num": "6"
            },
            {
                "text": "6 @ 3 4 \u00a2 \u00a1 & 2 \u00a4 \u00a3 K 0 E K5",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Interaction of Ellipsis Resolution and Quantifier Scoping",
                "sec_num": "6"
            },
            {
                "text": "where is the context variable, 2 is a resolution number, and K is some context. is added. If the subsequent discourse contains a singular anaphoric NP \"the solution\", anaphora resolution introduces the converse subordination constraint is the top label of the source. Consider the UDRS for sentence (12) in Figure 5 with three conditional constraints: ).",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 307,
                        "end": 315,
                        "text": "Figure 5",
                        "ref_id": null
                    }
                ],
                "eq_spans": [],
                "section": "Interaction of Ellipsis Resolution and Quantifier Scoping",
                "sec_num": "6"
            },
            {
                "text": "EQUATION",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [
                    {
                        "start": 0,
                        "end": 8,
                        "text": "EQUATION",
                        "ref_id": "EQREF",
                        "raw_str": "\u00a1 \u00a3 \u00a2 \u00a9 , { \u00a1 \u00a9 \u00a6 every\u00a9 \u00a9 \u00a1 \u00a9 \u00a1 \u00a5 $ \u00a9 , { \u00a1 \u00a1 \u00a5 ) , \u00a1 \u00a9 \u00a6 \u00a9 \u00a9 , \u00a1 \u00a3 % \u00a9 \u00a6 professor\u00a9 \u00a9 , \u00a1 \u00a5 % \" \u00a1 , \u00a1 \u00a4 \u00a9 \u00a6 ( ' \u00a9 , \u00a1 \u00a4 \u00a1 \u00a5 \u00a2 , \u00a1 # \u00a9 \u00a6 solution\u00a8' \u00a9 , \u00a1 # \u00a1 \u00a4 , \u00a1 1 \u00a9 \u00a6 find\u00a9 \u00a9 ' \u00a9 , \u00a1 1 \u00a1 \u00a5 $ , \u00a1 1 \u00a7 \u00a1 \u00a4 \u00a1 ! \u00a9 \u00a6 and\u00a8\u00a1 \u00a5 ) \u00a9 \u00a1 \u00a5 ) \u00a9 , \u00a1 ! \u00a1 \u00a2 , \u00a1 \u00a9 \u00a6 most\u00a9 \u00a9 \u00a1 \u00a9 \u00a1 $ \u00a9 , \u00a1 \u00a9 \u00a6 \u00a9 \u00a9 , \u00a1 \u00a3 % \u00a9 \u00a6 student\u00a9 \u00a9 , \u00a1 \u00a4 \u00a6 \u00a5 \u00a6 ( ' \u00a6 \u00a5 , \u00a1 \u00a3 # \u00a6 \u00a5 \u00a6 solution\u00a8'\u00a6\u00a5 8 , \u00a1 \u00a5 1 \u00a9 \u00a6 find\u00a9 \u00a9 ' \u00a6 \u00a5 8 }, \u00a5",
                        "eq_num": "\u00a2\u00a1\u00a4 \u00a1"
                    }
                ],
                "section": "Interaction of Ellipsis Resolution and Quantifier Scoping",
                "sec_num": "6"
            },
            {
                "text": "EQUATION",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [
                    {
                        "start": 0,
                        "end": 8,
                        "text": "EQUATION",
                        "ref_id": "EQREF",
                        "raw_str": "$ 33\u00a1 @ 3 \u00a1 \u00a1 & \u00a6 \u00a5 0 E & 05 , \u00a5",
                        "eq_num": "$ 33\u00a1"
                    }
                ],
                "section": "Interaction of Ellipsis Resolution and Quantifier Scoping",
                "sec_num": "6"
            },
            {
                "text": "In the treatment of strict/sloppy ambiguity, we follow the approach of Kehler (1995) which predicts five readings for the notorious example (13) from Gawron and Peters (1990).",
                "cite_spans": [
                    {
                        "start": 71,
                        "end": 84,
                        "text": "Kehler (1995)",
                        "ref_id": "BIBREF10"
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Strict and Sloppy Identity",
                "sec_num": "7"
            },
            {
                "text": "(13) John revised his paper before the teacher did, and Bill did too.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Strict and Sloppy Identity",
                "sec_num": "7"
            },
            {
                "text": "In Kehler's (1995) approach, strict/sloppy ambiguity results from a bifurcation in the process of ellipsis resolution: There are two ways to copy the binding constraint linking an anaphor with its antecedent if the antecedent is in the source 3 . Let",
                "cite_spans": [
                    {
                        "start": 3,
                        "end": 18,
                        "text": "Kehler's (1995)",
                        "ref_id": "BIBREF10"
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Strict and Sloppy Identity",
                "sec_num": "7"
            },
            {
                "text": "3 8 6 3 K 5 E \u00a7 3 K 5 $ 3 J 5 , 3 9 6 3 K 5 RT 3 5 4 1 3 J 5",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Strict and Sloppy Identity",
                "sec_num": "7"
            },
            {
                "text": "be a binding constraint as introduced by anaphora resolution. The sloppy way to copy the constraint is the usual one, i.e. updating the contexts with the new resolution number. Figure 6 : UDRS for a reading of sentence (13)",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 177,
                        "end": 185,
                        "text": "Figure 6",
                        "ref_id": null
                    }
                ],
                "eq_spans": [],
                "section": "Strict and Sloppy Identity",
                "sec_num": "7"
            },
            {
                "text": "sloppy 3 6 & 2 \u00a3 K 0 E \u00a7 & 2 \u00a4 \u00a3 K 0 $ & 2 \u00a4 \u00a3 J 0 , 3 6 & 2 \u00a4 \u00a3 K 0 RT 3 4 & 2 \u00a4 \u00a3 J 0",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Strict and Sloppy Identity",
                "sec_num": "7"
            },
            {
                "text": "The strict way is to bind the variable of the copied pronoun to the variable of the source pronoun. Figure 6 shows the UDRS for a particular reading of sentence (13): John and Bill revised their own papers before the teacher revised John's paper. The pronoun is first copied strict (",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 100,
                        "end": 108,
                        "text": "Figure 6",
                        "ref_id": null
                    }
                ],
                "eq_spans": [],
                "section": "Strict and Sloppy Identity",
                "sec_num": "7"
            },
            {
                "text": "strict 3 9 6 & 2 \u00a4 \u00a3 K 0 E \u00a7 & 2 \u00a4 \u00a3 K 0 $ \u00a7 3 K 5 , 3 9 6 & 2 \u00a4 \u00a3 K 0 RT 3 8 6 3 K 5",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Strict and Sloppy Identity",
                "sec_num": "7"
            },
            {
                "text": "& \u00a6 \u00a5 0 $ & 0 3 $ \u00a7 & 05 ), then sloppy ( & \u00a7 \u00a6 0 $ \u00a7 & \u00a7 \u00a6 0",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Strict and Sloppy Identity",
                "sec_num": "7"
            },
            {
                "text": ") , and finally strict again (",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Strict and Sloppy Identity",
                "sec_num": "7"
            },
            {
                "text": "& \u00a7 \u00a6 \u00a5 0 $ & \u00a6 \u00a5 0 3 $ \u00a7 & 05",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Strict and Sloppy Identity",
                "sec_num": "7"
            },
            {
                "text": "). We have tacitly assumed that source pronouns are resolved before ellipsis resolution. No mechanism has been provided to propagate binding constraints in parallel structures. But note that the order of operations in anaphora resolution is also constrained by structure: Anaphors embedded in other anaphors need to be resolved first (van der Sandt, 1992) . Ellipsis resolution may be considered on a par with anaphora resolution in this respect.",
                "cite_spans": [
                    {
                        "start": 334,
                        "end": 355,
                        "text": "(van der Sandt, 1992)",
                        "ref_id": "BIBREF14"
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Strict and Sloppy Identity",
                "sec_num": "7"
            },
            {
                "text": "Anaphors can occur in phantom conditions as well (cf. sentence (15)).",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Strict and Sloppy Identity",
                "sec_num": "7"
            },
            {
                "text": "(15) John revised a paper of his before the teacher did, and Bill did too.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Strict and Sloppy Identity",
                "sec_num": "7"
            },
            {
                "text": "An extension of the copy rules for binding constraints along the lines of Section 6 is straightforward (see below). If the embedding quantifier gets wide scope (3",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Strict and Sloppy Identity",
                "sec_num": "7"
            },
            {
                "text": "\u00a2 3 \u00a5",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Strict and Sloppy Identity",
                "sec_num": "7"
            },
            {
                "text": "), source and target constraints collapse (sloppy), or the target constraint asserts self-binding (strict).",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Strict and Sloppy Identity",
                "sec_num": "7"
            },
            {
                "text": "sloppy 3 9 6 3 5 E \u00a7 3 5 $ 3 \u00a2 \u00a5 5 , 3 9 6 3 5 RT 3 4 1 3 \u00a2 \u00a5 5 , strict 3 9 6 3 5 E \u00a7 3 5 $ \u00a7 3 K 5 , 3 8 6 3 5 RT 3 8 6 3 K 5 $ 33\u00a2 \" @ 3 \u00a5 \u00a1 & 2 \u00a4 \u00a3 K 0 E K5 , \u00a5 $ 33\u00a2 \" @ 3 \u00a5 \u00a1 & 2 \u00a4 \u00a3 J 0 E J5",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Strict and Sloppy Identity",
                "sec_num": "7"
            },
            {
                "text": "There are, however, some problems with this extension. See Figure 7 for the strict-sloppy-strict reading of sentence (15). If the indefinite NP gets intermediate scope between \"before\" and \"and\", the context variable will be set to . To remedy this defect, we stipulate that resolving the strict/sloppy ambiguity may partially disambiguate the scope structure: If in the course of resolving a particular ellipsis several anaphors are copied with different choices in the strict/sloppy bifurcation, the conditional constraints are evaluated so that the anaphors cannot turn out to be the same. This condition ensures that in the strict-sloppy-strict reading illustrated in Figure 7 the indefinite NP gets narrow scope under \"before\".",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 59,
                        "end": 67,
                        "text": "Figure 7",
                        "ref_id": null
                    },
                    {
                        "start": 672,
                        "end": 680,
                        "text": "Figure 7",
                        "ref_id": null
                    }
                ],
                "eq_spans": [],
                "section": "Strict and Sloppy Identity",
                "sec_num": "7"
            },
            {
                "text": "The paper has presented a new approach to integrate ellipsis resolution with scope underspecification. In contrast to previous work (Crouch, 1995) l7: revise( x, y ) l7: revise( x, y ) Figure 7 : UDRS for sentence (15) (Egg et al., 2001 ) the proposed underspecified representation facilitates the resolution of anaphora by providing explicit representations of potential antecedents. To this end, a method to encode \"phantom conditions\" has been presented, i.e. subformulae whose presence depends on the scope configuration. Furthermore, a method to deal with scope parallelism in scopally underspecified structures has been proposed. The proposed method has no trouble accounting for cases where the scope order in antecedent clause and elliptical clause is not entirely identical (Erk and Koller, 2001 ). Finally, it has been shown that the approach can cope with a wide variety of test examples discussed in the literature.",
                "cite_spans": [
                    {
                        "start": 132,
                        "end": 146,
                        "text": "(Crouch, 1995)",
                        "ref_id": "BIBREF2"
                    },
                    {
                        "start": 219,
                        "end": 236,
                        "text": "(Egg et al., 2001",
                        "ref_id": "BIBREF4"
                    },
                    {
                        "start": 783,
                        "end": 804,
                        "text": "(Erk and Koller, 2001",
                        "ref_id": "BIBREF6"
                    }
                ],
                "ref_spans": [
                    {
                        "start": 185,
                        "end": 193,
                        "text": "Figure 7",
                        "ref_id": null
                    }
                ],
                "eq_spans": [],
                "section": "Conclusion",
                "sec_num": "8"
            },
            {
                "text": "If the antecedent of a pronoun is outside the source, the copied pronoun is bound to the source pronoun (strict interpretation), not directly to the antecedent, cf. the reading missing in sentence (14) in which Bill will say that Mary helped Bill before Susan helped John. (14) John will testify that Mary helped him before Susan did, and so will Bill.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "",
                "sec_num": null
            }
        ],
        "back_matter": [],
        "bib_entries": {
            "BIBREF0": {
                "ref_id": "b0",
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            },
            "BIBREF1": {
                "ref_id": "b1",
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                        "last": "Asher",
                        "suffix": ""
                    }
                ],
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                "ref_id": "b3",
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                        "suffix": ""
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        "ref_entries": {
            "FIGREF0": {
                "uris": null,
                "text": "Many thanks for discussion and motivation are due to the colleagues in Saarbr\u00fccken.",
                "type_str": "figure",
                "num": null
            },
            "FIGREF5": {
                "uris": null,
                "text": "3",
                "type_str": "figure",
                "num": null
            },
            "FIGREF6": {
                "uris": null,
                "text": "UDRS for sentence(6)",
                "type_str": "figure",
                "num": null
            },
            "FIGREF7": {
                "uris": null,
                "text": "UDRS for sentence (6)Figure 4illustrates a UDRS with a phantom condition (again representing sentence (6)). A graphical l6UDRS for sentence(12)representation of this UDRS can be seen in the first conjunct ofFigure 5. Contexts are marked by dotted boxes, conditional constraints by a dotted subordination link with an equation.If the subsequent discourse contains a plural anaphoric NP such as \"both solutions\", two or more discourse referents designating solutions are looked for. Two such discourse referents are found (",
                "type_str": "figure",
                "num": null
            }
        }
    }
}