Base_JSON/prefixC/json/C96/C96-1044.json

{
    "paper_id": "C96-1044",
    "header": {
        "generated_with": "S2ORC 1.0.0",
        "date_generated": "2023-01-19T12:51:28.183282Z"
    },
    "title": "Extended Dependency Structures and their Formal Interpretation",
    "authors": [
        {
            "first": "Marc",
            "middle": [],
            "last": "Dymetman",
            "suffix": "",
            "affiliation": {},
            "email": "dymetman@xerox.fr"
        },
        {
            "first": "Max",
            "middle": [],
            "last": "Coppcrman",
            "suffix": "",
            "affiliation": {},
            "email": "copperman@xerox.fr"
        }
    ],
    "year": "",
    "venue": null,
    "identifiers": {},
    "abstract": "We describe two \"semantically-oriented\" dependency-structure formalisms, t J-forms and S-forms. U-forms have heen previously used in nmchine translation as interlingual representations, hut without being provided with a formal interpretation. S-forms, which we introduce in this paper, are a scoped vet sion of U-fnrms, and we define a compositional semantics mechanism for them. Two types of semantic composition are basic: complement incorlgoration and modifier incorporation. Binding of variables is done at tire time of incorporation, permitting tnttch [lexibility in composition order and a simple account of the semantic effects of permuting several incorporations.",
    "pdf_parse": {
        "paper_id": "C96-1044",
        "_pdf_hash": "",
        "abstract": [
            {
                "text": "We describe two \"semantically-oriented\" dependency-structure formalisms, t J-forms and S-forms. U-forms have heen previously used in nmchine translation as interlingual representations, hut without being provided with a formal interpretation. S-forms, which we introduce in this paper, are a scoped vet sion of U-fnrms, and we define a compositional semantics mechanism for them. Two types of semantic composition are basic: complement incorlgoration and modifier incorporation. Binding of variables is done at tire time of incorporation, permitting tnttch [lexibility in composition order and a simple account of the semantic effects of permuting several incorporations.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Abstract",
                "sec_num": null
            }
        ],
        "body_text": [
            {
                "text": "U-fi)rms (Unscoped dependency form) arc a representation formalism which has been used (under a different name) as tire basis for the intermediary language in the machine mmshttion system CRITFER (lsahelle et at., 1988; l)ymetman, 1992; Isabelle, 1995) . U-forms account for two central aspects of linguistic structure: predicate-argument relations and headedness (complements vs. modifiers), and so form a middle ground between a \"semantic\" and a \"syntactic\" representation. This, combined with their formal simplicity, accotmts for much of the popularity of U-forms or related formalisms --such as the semantic and deep syntactic representations used in Mel'cuk's Meaning-Text Theory (Mel'+nk, 1981) --in applications such as [nitchine translation and text generation.",
                "cite_spans": [
                    {
                        "start": 196,
                        "end": 219,
                        "text": "(lsahelle et at., 1988;",
                        "ref_id": null
                    },
                    {
                        "start": 220,
                        "end": 236,
                        "text": "l)ymetman, 1992;",
                        "ref_id": null
                    },
                    {
                        "start": 237,
                        "end": 252,
                        "text": "Isabelle, 1995)",
                        "ref_id": null
                    },
                    {
                        "start": 686,
                        "end": 701,
                        "text": "(Mel'+nk, 1981)",
                        "ref_id": null
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "INTRODUCTION",
                "sec_num": "1"
            },
            {
                "text": "Although t J-fotn~s are strongly \"meaning-oriented\" their interpretation is never made explicit but is left to the computational linguist's intuition. This has two consequences:",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "INTRODUCTION",
                "sec_num": "1"
            },
            {
                "text": "\u2022 Operations performed on U-forms and related formalisms cannot he controlled for semantic va-lidity. So, for instance, it is comnlon practice to deline graph rewriting rules on these representations which are believed to produce semantically equivalent expressions. Without the check of for+ real interpretation, these rtdes may work in some cases, hut produce wrong results in other cases. So for instance, a rule rewriting (the representation of) \"John's salary is $25000 higher this year than last year\" into \"John's salary was $25000 lower last year than this year\" would seem intuitively valid until one considered the case of \"John's salary is 50% higher this year than last year\", where it does not work any rnore.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "INTRODUCTION",
                "sec_num": "1"
            },
            {
                "text": "\u2022 U-forms are not directly adapted to applications putting emphasis on denotational semantics and formal reasoning, like for instance some lmtural hmguage generation systems in well-formalized domains (l-htang and Fiedler, 1995; Ranta, 1995; I+evine, 1990) , see also (Alshawi, 1992) .",
                "cite_spans": [
                    {
                        "start": 201,
                        "end": 228,
                        "text": "(l-htang and Fiedler, 1995;",
                        "ref_id": null
                    },
                    {
                        "start": 229,
                        "end": 241,
                        "text": "Ranta, 1995;",
                        "ref_id": "BIBREF12"
                    },
                    {
                        "start": 242,
                        "end": 256,
                        "text": "I+evine, 1990)",
                        "ref_id": null
                    },
                    {
                        "start": 268,
                        "end": 283,
                        "text": "(Alshawi, 1992)",
                        "ref_id": null
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "INTRODUCTION",
                "sec_num": "1"
            },
            {
                "text": "A basic obstacle to providing a formal interpretation for U-forms is the fact that these representations leave the relative scopes of dependents implicit. The S-form representation (Scoped dependency form), which we introduce here, is an extension of U-form notation which makes scope explicit, by allowing dependents to be ordered relative to one another. Dependents (complements or modifiers) c~m move fi'eely relative to one another in the S-form structure, under certain binding-site constraints+",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "INTRODUCTION",
                "sec_num": "1"
            },
            {
                "text": "We then go on to provide it compositional interpretation mechanism for S-forms. Free vmiahles (generalizations of the argt, arg._,, atrg:+ annotations of standard dependency formalisms) are used to connect an argutnent to its binding-site inside a predicate. Binding of variables is done at tire time of incorporation, permitting much llexibility in composition order and at simple account of the semantic effects of permuting several incorporations. This liberal use of free wlriables is contrasted to the approach of Montague grammar, where the requirement that semantic expressions entering into at composition m'e closed (do not contain free vmiables) leads to a certain rigidity in the order of composition.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "INTRODUCTION",
                "sec_num": "1"
            },
            {
                "text": "Two kinds of senmntic composition are basic: coinplement incorporation, whine the complement fills a semantic role inside the head, and modifier incorporation, where the head fills a semantic role inside the modifier. The mechanism of actually deriving the semantic translation of the composition fi+oln tile semantic translations of its two components is handled through a list of type-sensitive composition rules, which determine the action to be taken on the basis of the component types. The flexibility of the approach is ilhlstr;.lted on an example involving proper names, quantitied noun phrases, adverbials and relative clauses.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "INTRODUCTION",
                "sec_num": "1"
            },
            {
                "text": "Formally. U-ferms are nnordered labelled n-ary trees such as tile one shown in The edge htbels me members of the set {det, 1,2, 3, .... -l,-2. -3 .... }, alld correspond either to determiners (label \"det') or to argument positions relative to a predicate node (other labels).",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "U-FORMS",
                "sec_num": "2"
            },
            {
                "text": "The U-form of Fig. 1 In order to extract the predicate-argument relations encoded into tile U-form, one needs to apply the following \"'rule\". Let's notate (A,L,B) an edge of the tree, where A is the upper vertex, B tile lower vertex, and L the edge label. With each node A in tile tree, one associates its set of predication edges, that is the set PAl of edges of the form (A,+i.X) or (X.i,A). One then considers tile predication tree T i made by forming the collection of edges (A,LX) where I, is positive and either (A.L,X) or (X.inverse(L),A) is a predication edge of A. Each predication tree denotes a predicate-argtnnent rehition among IJ,+fornl nodes. So for illstance, the tree ' l' l~;u<~ is lt/inled by forming tile edges (hate, l,peter) and (hate,2.woman), and this corresponds to the predicate-argunlent rehition tlate(peter.woman).",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 14,
                        "end": 20,
                        "text": "Fig. 1",
                        "ref_id": null
                    }
                ],
                "eq_spans": [],
                "section": "U-FORMS",
                "sec_num": "2"
            },
            {
                "text": "FORMS In order to be well-formed, a U-iorm Uf: has to respect tile following condition. For ;.lily node A of L!F. the predication tree T i must be such that:",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "WELL-FORMEDNESS CONIilTIONS (iN U-",
                "sec_num": null
            },
            {
                "text": "1. [No hoh, s comliti(m] If (A.i.B) is an edge of 1\" i.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "WELL-FORMEDNESS CONIilTIONS (iN U-",
                "sec_num": null
            },
            {
                "text": "then for any number j between I and i, T.I nlttst MORE ON U-FORMS Negative labels are a device which permits to reconcile the notalien of predicateargnnlenl structnre with the notation of syntactic depondoilcy, So, in the i..]-fornl considered above, while \"semantically\" tile 'wellqan' node is an ;.irglnl]oni of tile \"hate\" node, \"syntactically\" tile hate' node is a dependent of tile 'woman' node. Cases such as this one. where there is a conflict between predicate-argument directionality and dependency directionality are no tated ill the U form throngh negative labels, and correspond tO #llodifie#',','. Cases where tile directionality is parallel correspond to complement.s.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "WELL-FORMEDNESS CONIilTIONS (iN U-",
                "sec_num": null
            },
            {
                "text": "When used as interlingual representations in machine translation systems, U-forms have several advantages. The first is ttmt they neutralize certain details of syntactic structure that de not carry easily between languages. For instance. French and English expiess negation in syntactically different ways: \"Rachel does net like Claude\" vs. \u00b0'Rachel n'aime pas Claude\": this difference is neutralized in the U-fornl representation, for both negations are expressed through a single negation predicate in the U-feral.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "WELL-FORMEDNESS CONIilTIONS (iN U-",
                "sec_num": null
            },
            {
                "text": "A second advantage is that they represent a good compromise between paraphrasing potential and semantic precision. So. for instance, in tile CRITTEI,I system, the three sentences:",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "WELL-FORMEDNESS CONIilTIONS (iN U-",
                "sec_num": null
            },
            {
                "text": "John does not like every woman that Peter hates John does not like every woman hated by Peter Every woman whom Peter hates is not liked by John would be assigned the U-form of Fig. 1 . On the other hand, the sentence:",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 176,
                        "end": 182,
                        "text": "Fig. 1",
                        "ref_id": null
                    }
                ],
                "eq_spans": [],
                "section": "WELL-FORMEDNESS CONIilTIONS (iN U-",
                "sec_num": null
            },
            {
                "text": "Peter hates every woman that John does not like would be assigned tile t!-form or' f:i~,. 3, which is different from the previous U-form, although tile predicate-argument rehitions are exactly tile sanie in hoth cases.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "WELL-FORMEDNESS CONIilTIONS (iN U-",
                "sec_num": null
            },
            {
                "text": "]Idt{' 1// \"~ 2 / \\, /)('tg'r WOllldll -<Q d/ \\~\" every like ,/\\<",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "WELL-FORMEDNESS CONIilTIONS (iN U-",
                "sec_num": null
            },
            {
                "text": ".jolm m~t Rachel was given a book by Claude so that a direct syntactic translation is not possible. However, at tile level of U-form, this sentence is equivalent to the French sentence:",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "WELL-FORMEDNESS CONIilTIONS (iN U-",
                "sec_num": null
            },
            {
                "text": "Claude a donne un livre ~t Rachel and this equivalence can he exploited it) provide a translation of the first sentence.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "WELL-FORMEDNESS CONIilTIONS (iN U-",
                "sec_num": null
            },
            {
                "text": "One serious problenl with 1.]. [ornis, however, is tilat they do not have unainbiguous readhigs in cases where the rehliive scopes of constituents can result in clifl'erent semantic ii~terpretations. So, in the case of sen fence (S l), tile two readings: \"it is not the case thai John likes every woman hated by Peter\", and 'Lh)tl.n dislikes every woman thai Peter hates\" are not distinguished by tile t l-l:oi+nl Of l\"ig+ 1, The only differeiice hetween this tree aml the l,Jform of l:ig. l is thai the nodes of our new tree are considered ordered whereas they were considered tinordered in the I!-lorm+ The convention is now that (tepetlttent sister nodes are interpreted :is having ttil'l]2retlt scopes, with llarrower scope correspondillg to a position iilore It) tile right.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "WELL-FORMEDNESS CONIilTIONS (iN U-",
                "sec_num": null
            },
            {
                "text": "The tree of l:'ig. 4 can he glossed in the following way: John, it is not the case that he likes every woman that Pe+ ter hates I f we consider tile six l)mmulalions of lhe nodes under like. we can produce six differenl scopings. Be cause John teleis to an individual, not a quantified NP. these six pernmtations really corrcsl)ond to only the two interl)relaiiens given ahove. The tree of Fig. 4 corresponds to the lirst of Ihese interpretations, which is the preferred interpretation Ik)l sentence (S I).",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 390,
                        "end": 396,
                        "text": "Fig. 4",
                        "ref_id": null
                    }
                ],
                "eq_spans": [],
                "section": "WELL-FORMEDNESS CONIilTIONS (iN U-",
                "sec_num": null
            },
            {
                "text": "like //.-J ! 2 t .jolm ~u~t W()lll(lfl (q'dl'V ]lg.ll(\"",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "WELL-FORMEDNESS CONIilTIONS (iN U-",
                "sec_num": null
            },
            {
                "text": "Our discussion of scope being represented by node order has been infornml so far. In order to nlake it ['Oi'lllal, we need to encode our representation into a binary-tree fornmt ell which a compositioiml senlan tics can he delined. To tie that. in a lirst step we rephtce the at'gunlent nunibers of l:ig. 4 hy exl)lici! argument haines; ill a seColld slep we encode the resulting or dered mary free inh)a himuy forumt which makes explicit the order in which dependents are incorlmrated inlo their head. S-I\"ORMS Consider tile mary tree of Fig. 4 . For any node A in this tree, take the set of predication edges associated with A, that is the set of edges (a,+i,B,) and (Bi, i,A). By renaming each such node A into A(XI .... X,+). where X I ..... X, are hesh identiliers, and by renaming each such htbel +i (resp. +i) into +X,: (resp. -X,:), one obtains a flew tree where argunmnl numbers have been replaced by argument haines. [:or instance the previous representation now becomes tile tree of l\"ig. 5. This representation is called a scopeU depemh'm3' ,lotto, or Sqbrm.",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 539,
                        "end": 545,
                        "text": "Fig. 4",
                        "ref_id": null
                    },
                    {
                        "start": 646,
                        "end": 664,
                        "text": "of edges (a,+i,B,)",
                        "ref_id": null
                    }
                ],
                "eq_spans": [],
                "section": "WELL-FORMEDNESS CONIilTIONS (iN U-",
                "sec_num": null
            },
            {
                "text": "In order to encode tile ordered n-ary tree into a binary tree, we need to apply recursively the transfotnmtiou ilhlstrated in Fig. 6 , which consists in forming a \"head-line\", projecting in a north-west direction from tile head 11, and in \"attaching\" to this line \"dependent-lines\" D~, D2 ..... 1),,, with l-)l tile right- ] 511",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 126,
                        "end": 132,
                        "text": "Fig. 6",
                        "ref_id": null
                    }
                ],
                "eq_spans": [],
                "section": "BINARY TREE FNCODING OF S-FORMS: B-FORMS",
                "sec_num": null
            },
            {
                "text": "EQUATION",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [
                    {
                        "start": 0,
                        "end": 8,
                        "text": "EQUATION",
                        "ref_id": "EQREF",
                        "raw_str": "//l\\,N\\ ] +I]/i \"1 \"\\'N\\ // ,, //~'\\\\ 1,2// /)\\, // I l,/ .... ,,",
                        "eq_num": "D2 1 \""
                    }
                ],
                "section": "BINARY TREE FNCODING OF S-FORMS: B-FORMS",
                "sec_num": null
            },
            {
                "text": "\\ D1 Figure 6 : The translbrmation between S-forms and Bforms.",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 5,
                        "end": 13,
                        "text": "Figure 6",
                        "ref_id": null
                    }
                ],
                "eq_spans": [],
                "section": "BINARY TREE FNCODING OF S-FORMS: B-FORMS",
                "sec_num": null
            },
            {
                "text": "Applying this encoding to our example, we obtain the binary tree of Fig. 7 , which is called a B-form.",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 68,
                        "end": 74,
                        "text": "Fig. 7",
                        "ref_id": "FIGREF6"
                    }
                ],
                "eq_spans": [],
                "section": "BINARY TREE FNCODING OF S-FORMS: B-FORMS",
                "sec_num": null
            },
            {
                "text": "The B-form makes explicit the order of incorporation of dependents into the head-line. By permuting several dependent-lines along their head-line, this incorporation order is changed and gives rise to different scopings.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "BINARY TREE FNCODING OF S-FORMS: B-FORMS",
                "sec_num": null
            },
            {
                "text": "S-forms and B-forms are completely equivalent representations. Cle~ly, the encoding, called the Sform/B:fi~rm encoding, which has just been defined is reversible. The S-form is more compact ,and makes the dependency relations more conspicuous, whereas the B-form makes the compositionality more explicit.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "BINARY TREE FNCODING OF S-FORMS: B-FORMS",
                "sec_num": null
            },
            {
                "text": "and enriching it, we have informally introduced the notions of S-form and B-form. We now define them formally.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "WELL-FORMEDNESS CONDITIONS ON B-FORMS AND S-FORMS Stm'ting fromthe U-form",
                "sec_num": null
            },
            {
                "text": "We start by giving a rect, rsive definition of IBFs (incomplete B-forms), that is, B-forms which may contain unresolved flee variables. We use the notation ((D,Label),H) the labelled binary tree obtained by taking H as the right subtree, D as the left subtree, and by labelling the left edge with Label. We ,also use the notation fv(IBF) for the set of the free variables in IBF. ",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "WELL-FORMEDNESS CONDITIONS ON B-FORMS AND S-FORMS Stm'ting fromthe U-form",
                "sec_num": null
            },
            {
                "text": "The notion of S-form cart now be delined through the nse of the S-form/B-form encoding.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "DEFINITION OF B-FORMS A B-form is an IBF with an empty set of free variables.",
                "sec_num": null
            },
            {
                "text": "A S-form is an of demd labelled n-ary tree which can be obtained from a B-form through the inverse application of the S-form/Bform encoding.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "DEFINITION OF S-FORMS",
                "sec_num": null
            },
            {
                "text": "It can be easily verified that the representation of Fig. 7 is indeed a B-form, and, consequently, the representation of Fig. 5 is a valid S-form. More generally, it can be easily verified that enriching a U-form by ordering its nodes, and then replacing argument variables by argument names always results in a valid Sform) tThe converse is not true: not all S-forms can be obtained in this way from a U-form. For instance, there exists a S-fonn corresponding to the prefelTed reading for \"Fido visited most trashcans on every street\", which has \"every street\"",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 53,
                        "end": 59,
                        "text": "Fig. 7",
                        "ref_id": "FIGREF6"
                    },
                    {
                        "start": 121,
                        "end": 127,
                        "text": "Fig. 5",
                        "ref_id": null
                    }
                ],
                "eq_spans": [],
                "section": "DEFINITION OF S-FORMS",
                "sec_num": null
            },
            {
                "text": "We now describe the interpretation process on B-fl)rms. lnlerpretation proceeds by propagating semantic translations and their types bottom-up.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "THE INTERPRETATION PROCESS",
                "sec_num": "4"
            },
            {
                "text": "The first step consists in typing the leaves of the tree, while keeping track of the types of fl'ee variables, as in Fig. 8 . The types given to the leaves of the tree are the usual functional types formed starting with e (entities) and t (truth values). In the case where the leaf entity cot> tains flee variable arguments, the types of these free variables are indicated, and the type of the leaf takes into account the fact that these free variables have already been included in the functioned form of the leaf. Thus hate(h l,h2), which can be glossed as: \"hi hates h2\", is given type t, while hl and h2 are constrained to be free variables of type e. VARIABLE-BINDING RULES According to the well-formedness conditions tot B-forms, a complement incorporation ((D,+x),It) is only possible when H contains x among its fi:ee variables; the \"syntactic dependent\" D is seen as semantically \"filling\" the place that x occttpies in the +'syntactic head\" H. In the same way, a modifier incorporation ((D,-x),H) is only possible when D contains x among its fiee wuiables;",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 117,
                        "end": 123,
                        "text": "Fig. 8",
                        "ref_id": "FIGREF7"
                    }
                ],
                "eq_spans": [],
                "section": "THE INTERPRETATION PROCESS",
                "sec_num": "4"
            },
            {
                "text": "outscoping \"most trashcans\", and which is not obtained from a U-form in this simple way. However, thet+e exists a mapping fiom S-forms to U-h>rms, the scope-fi)rgetting mapping, which permits to deiine equiwtlence chtsses among Storms \"sharing\" the same U-form. This relation between S-R~rms and Uqbrms can be used to give a (not>deterministic) lbrmal interpretation to U-forms, by considering the interpretations of the various S-forms associated with it (see the technical report eolnpanion to this paper.) in this case the \"syntactic\" head I I is seen as semantically \"filling\" the place that x occupies in the \"syn-tactic dependent\" D. (This difference corresponds to the opposition which is sometimes made between syntactic and semantic heads and dependents: complements are dependents both syntactically and semantically, while modiliers are syntactically dependents but semantically heads.)",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "THE INTERPRETATION PROCESS",
                "sec_num": "4"
            },
            {
                "text": "In order to make formal sense of the informal notion \"filling the place of x in A.,,\" (where the notation A,: means that A contains the free variable x), we introduce the variable-binding rules of Fig. 9 .",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 197,
                        "end": 203,
                        "text": "Fig. 9",
                        "ref_id": null
                    }
                ],
                "eq_spans": [],
                "section": "THE INTERPRETATION PROCESS",
                "sec_num": "4"
            },
            {
                "text": "cotnllh, ntenl tntldilict dot c t L]IiI/CI i[iC~)l i)Ol [it{t,ll illCt )t pol [t[iOll { lit'o[ pOl ~It iOll / 7 \\ D' [[' I)', I[' I)' 1[' dot //]k l)'",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "THE INTERPRETATION PROCESS",
                "sec_num": "4"
            },
            {
                "text": ".\\x.l [i+ Ax,I)'~ H' IY H' Figure 9 : Variable-binding rules. D' and tl' con'espond to the senmntic translation of the subtrees rooted in 1)and 11 respectively.",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 27,
                        "end": 35,
                        "text": "Figure 9",
                        "ref_id": null
                    }
                ],
                "eq_spans": [],
                "section": "THE INTERPRETATION PROCESS",
                "sec_num": "4"
            },
            {
                "text": "These rules tell t,s how to \"get rid\" of the free vailable being bound during complement or tnodifier incorporation, namely by forming the abstraction ,Xx.A,: before actually performing the semantic composition between tile dependent and tile head. For completeness, detemainer incorporation, which does not inw)lve vmiable binding, is given along with complement and rnodifier incorporation.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "THE INTERPRETATION PROCESS",
                "sec_num": "4"
            },
            {
                "text": "Two things should be noted about this way of \"delaying\" variable-binding until the relevant dependent is incorporated:",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "THE INTERPRETATION PROCESS",
                "sec_num": "4"
            },
            {
                "text": "\u2022 Suppose that we had bound the variables appearing in the head predicate locally, that is to say, that, in the style of Montague grammar (Gamut, 1991 ), we had written )d21 l.like(l1,12) instead of like (11, 12) , and so forth, in Fig. 7 . Then each incorporation of a dependent into the \"head-line\" would have changed the type of the head; thus 'not' would have had to combine either with a head of type e--+e~t, or e--t, or t, depending on its scope relative to the other dependents; with the scheme adopted here, the type of the head renmins invariant along the head-line;",
                "cite_spans": [
                    {
                        "start": 204,
                        "end": 208,
                        "text": "(11,",
                        "ref_id": null
                    },
                    {
                        "start": 209,
                        "end": 212,
                        "text": "12)",
                        "ref_id": null
                    }
                ],
                "ref_spans": [
                    {
                        "start": 232,
                        "end": 238,
                        "text": "Fig. 7",
                        "ref_id": "FIGREF6"
                    }
                ],
                "eq_spans": [],
                "section": "THE INTERPRETATION PROCESS",
                "sec_num": "4"
            },
            {
                "text": "\u2022 tinder the same hypothesis, the incorporation of the second mgnment first and of the first argt,ment second would have been much simpler than the reverse incorporation order, and some mechanism would have had to be found to distinguish the two orders. Then permuting the relative order of two dependents along the head-line --corre-",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "THE INTERPRETATION PROCESS",
                "sec_num": "4"
            },
            {
                "text": "\u2022 O ' \"\"",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "THE INTERPRETATION PROCESS",
                "sec_num": "4"
            },
            {
                "text": "spondm~ to dttferent scope possibililies--wonld have had complex computational conseqttences+ In the scheme adopted here, these cases are handled in a tiniforna way.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "THE INTERPRETATION PROCESS",
                "sec_num": "4"
            },
            {
                "text": "The way free wu'iables are used in our scheme is somewhat remi n i scent of the nse ol:.vvitla\u00a2'li\u00a2' variables he,, in Montague glanlliiar. Montague gl+anlmar hits the general requirement that only closed lambda-tetms (lanibda terms containing only bound variables) are composed together. This requirement, however, is di fficult to reconcile with the flexibility needed for handling quantilier scope ambiguities. Syntactic variables are zt device which pertnit to \"'quantify Jim'>\" clauses at an arbitrary time, hypassing the normal functional compc~sition of lambda-terms, which requires a strict management of incorporation order. In our scheme. by contrast, this secondary mechanism of Montague o]ammar is graduated to a central position. Composition is always done between two lambda-terms one of which at least contains a free variable which gets bound at the time of incorporation. TYPE SENSITIVI~ COMPOSITION R.UI,ES If we apply the vat+table-binding rules to the snbtree PH = ((peter,-hl),hate(hi,h2)) of Fig. 8 , we lind that we mtisl compose the semantic transhttions peter and %h 1.hate(h I ,h2) in \"con+lplement\" (+) mode. The litst ftmction is of type e, while the second function is oi type e~t (lor hate(hi,h2) is of type t, and hl of type e).",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 1014,
                        "end": 1020,
                        "text": "Fig. 8",
                        "ref_id": "FIGREF7"
                    }
                ],
                "eq_spans": [],
                "section": "THE INTERPRETATION PROCESS",
                "sec_num": "4"
            },
            {
                "text": "ltow do we compose two such functions? A first so lution, in the spirit of Lambek calculus (Morrill, 1994) or of linear logic (Dah'ymple et al.. 1995) , would tie to define a general computational mechanism which would be able, through a systematic discipline of typechanging operations, to \"adapt\" atttomatically to the types of the functions undergoing composition.",
                "cite_spans": [
                    {
                        "start": 91,
                        "end": 106,
                        "text": "(Morrill, 1994)",
                        "ref_id": "BIBREF11"
                    },
                    {
                        "start": 126,
                        "end": 150,
                        "text": "(Dah'ymple et al.. 1995)",
                        "ref_id": null
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "THE INTERPRETATION PROCESS",
                "sec_num": "4"
            },
            {
                "text": "Such mechanisms are powerful, but they tend to be algorithmically complex, to be non-lncal, and also to give rise to spurious antbiguities (superficial variations in the proof process which do not correspond to di fferent semantic readinos) t\" \"",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "THE INTERPRETATION PROCESS",
                "sec_num": "4"
            },
            {
                "text": "Here, we will prefer to use a less general tnecha+ nism, but one which has two advantages. First, it is local, simple, and efficient. Second, it is flexible attd can tie extended to handle the semantics of sentences extracted fiom a real corpus of texts, which it might he perilous to constrain too strongly fi'om the starc The mechanism is the following. We establish a list of acceptable \"type-sensitive composition rules\", which tell us how to compose two flmctions according to their types. Such a (provisory) list is given be ow: e The entries in this list have the following fornmt. The lflst argtuncnt indicates tile type of composition (++' fl)r complement incorporation. \"-\" for modilier incorl)orath'm. \"++let\" for deter+miner incorporation): the second argument is of the Iklrln Lelt:l+eftTypc, where Left is the left translation entering the composition, and LeftTypc is its type: similarly, the second argument Right:RightType corresponds to the right subtree entclin ~r~. the composition: linallv+ the third atELl-, ment ~ives the resuh l,?,esuh:l,P, esultType of the composition, where the notation A(B) has been used to indi cate slandard functional application of function A on arguntent B. Uppercase letters indicate unifiable vari ahles.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "THE INTERPRETATION PROCESS",
                "sec_num": "4"
            },
            {
                "text": "It may be remarked thai if, in these rules, we neglect the functions themselves (1 +eft, Right, Resnlt) and con. centrate on their types (l+eflType, RightType, Result + l'ype), then the rules can be seen as itnl)osin,,+ constraints on what can count :is validly typed trees: these constrahlts can flow from nlother to daugthers as ,.veil as in the opposite direction. Thus. through these rules. knowing thai the head-line functions projecting l]tlnl it verbal head must he of type t imposes some constraints on wlmt are the possible types for the det)endents: this can be usefttl in partict, lar for constraining the types nf semantically ambiguot, s lexical elements.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "THE INTERPRETATION PROCESS",
                "sec_num": "4"
            },
            {
                "text": "If we now go back to our example, we have to con> pose in complement mode (+) the function peter, ol type e. with the ftmction th I .hate(h I .h2). of type e--t. Consnlting the list of composition rules, we see that the only applicable rnle is (C2). and that the result is Ahl.hate(h l,h2) (peter) = hate(peter.h2), of type t. Now that we have the semamic translation hate(peter, h2) for the subtree Pit, we can compute the translation for the suhtree ((PH,-h2).woman). By the variable-binding rnle for modiliers, we need lirst to form the abstraction Xh2.hate(peter.lt2). of type e~t. and compose it in '-' mode with wonmn, of type e--t. Consnlting the list of composition rules, we find that the only applicable rule is (C5). and that the result of this application is Ah2.woman(h=)Ahate(l~eter, h=).: e It is a matter for further research to propose principles lk)l\" ploducing such Ill]ON. SotllC t)t\" them can be seen as special cases of general type-raising principles, others (such as C5) are necessary it one accepts that the type of intersectivc adjectives and restrictive relative clauses has to be e -t.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "THE INTERPRETATION PROCESS",
                "sec_num": "4"
            },
            {
                "text": ":~Thc rule (C5) differs from the previous rules in ll~e list in that it introduces the logical connective A which does lint originate in functional material already present in either of the arguments. A possible justilication for the rule. however,",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "THE INTERPRETATION PROCESS",
                "sec_num": "4"
            }
        ],
        "back_matter": [
            {
                "text": "Thanks to Alain l,ecomtc and Frdddrique Segond fOl\" COITIIllOIIIS ~111(1 discussions,",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Acknowledgments",
                "sec_num": null
            },
            {
                "text": "noHc~ cpvl,\\h2 womamh2)/g~ateq~uh'rh2).M21ikclfl~h,,12))) I ~.tl //'/ ('2 ~, \\, of cvelvfAh2 ~omo lib2 , \\halc(l)eh't h2 AI2 til, c II I2 ) l:igur\u00a2 10: B form interpretation, l\"or \"cvcry', we make use of the gcner;tlized quantilier notation qmm l( n'.st ri cl i ou.SCOl)e ).Fhe process of semantic translalion tin>coeds in this way bottom Ul-~on the B form. The end restth is; shown in Fig. 10. ",
                "cite_spans": [
                    {
                        "start": 70,
                        "end": 76,
                        "text": "('2 ~,",
                        "ref_id": null
                    },
                    {
                        "start": 77,
                        "end": 79,
                        "text": "\\,",
                        "ref_id": null
                    },
                    {
                        "start": 80,
                        "end": 104,
                        "text": "of cvelvfAh2 ~omo lib2 ,",
                        "ref_id": null
                    },
                    {
                        "start": 105,
                        "end": 129,
                        "text": "\\halc(l)eh't h2 AI2 til,",
                        "ref_id": null
                    },
                    {
                        "start": 130,
                        "end": 139,
                        "text": "c II I2 )",
                        "ref_id": null
                    }
                ],
                "ref_spans": [
                    {
                        "start": 386,
                        "end": 394,
                        "text": "Fig. 10.",
                        "ref_id": null
                    }
                ],
                "eq_spans": [],
                "section": "annex",
                "sec_num": null
            }
        ],
        "bib_entries": {
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        "ref_entries": {
            "FIGREF0": {
                "num": null,
                "text": "Fig. l, corresponding to tile sentence: (S l) \"John does not like every woman hated by Peter\".",
                "type_str": "figure",
                "uris": null
            },
            "FIGREF1": {
                "num": null,
                "text": "Predicate-argument relations in a U-form.",
                "type_str": "figure",
                "uris": null
            },
            "FIGREF2": {
                "num": null,
                "text": "contain a node of form (A,i,C)+ 2. [No rdpe'tilioll comlimml No two edges of T.t can have tile salne label i.",
                "type_str": "figure",
                "uris": null
            },
            "FIGREF3": {
                "num": null,
                "text": "A dilf0renl t J-form ()he can take advantage of such paral)hrasing potential in cerlain cases of synlaclJc divergence belween languages, l:or instance, French does not have a syn tactic equivalent to the dative-lnoven/etlt + passive configuration o1:",
                "type_str": "figure",
                "uris": null
            },
            "FIGREF4": {
                "num": null,
                "text": "S-FORMS INTI,I()I)UCIN(; SC()I'E Lefs consider the trec represented in Iqg. 4.",
                "type_str": "figure",
                "uris": null
            },
            "FIGREF5": {
                "num": null,
                "text": "4: Inhoducing scope hy ordering the nodes.",
                "type_str": "figure",
                "uris": null
            },
            "FIGREF6": {
                "num": null,
                "text": "A B-form. 1. A node N of the form Pmd(xl,..,xn) is an IBF with the set of free variables fv(N) = { x I ,..,xn }; 2. If D and H am IBFs, fv(D) and fv(H) ale disjoint, and x ~ fv(H) then H'=((D,+x),H) is an IBF with fv(ll') = fv(D) U fv(H) \\ {x}; 3. If D and H are 1BFs, fv(D) and fv(H) ,are disjoint, and x C fv(D) then H'=((D,-x),H) is an IBF with fv(H') = fv(D) U fv(H) \\ {x}; 4. If D and H are IBFs, and fv(D) and D(H) are disjoint, then H'=((D,det),H) is an 1BF with fv(H') = fv(D) U fv(H).",
                "type_str": "figure",
                "uris": null
            },
            "FIGREF7": {
                "num": null,
                "text": ".' ?i ] +l)-+(u-~t)~t / Typing the leaves. The flee wu'iables and their types are indicated in brackets.",
                "type_str": "figure",
                "uris": null
            },
            "FIGREF8": {
                "num": null,
                "text": "(x) AL(\u00d7):e->t:)",
                "type_str": "figure",
                "uris": null
            }
        }
    }
}