{
    "paper_id": "W98-0142",
    "header": {
        "generated_with": "S2ORC 1.0.0",
        "date_generated": "2023-01-19T06:05:43.515355Z"
    },
    "title": "CONSISTENTDENDRIFICATION:TREESFROMCATEGORIES",
    "authors": [
        {
            "first": "A",
            "middle": [
                "M"
            ],
            "last": "Wallington",
            "suffix": "",
            "affiliation": {
                "laboratory": "",
                "institution": "UMIST",
                "location": {
                    "postCode": "M601QD",
                    "region": "Manchester",
                    "country": "UK"
                }
            },
            "email": ""
        }
    ],
    "year": "",
    "venue": null,
    "identifiers": {},
    "abstract": "I shall start by taking a fairly simple Combinatory Categorial Grammar (CCG) of the type developed by Steedrnan over the past decade or so (e.g. Steedman 1996) including rules of functional application, and functional composition. I shall have nothing to say about functional substitution in this paper, and shall assume that there are type-raised categories in the lexicon (e.g. S/(S\\NP)). I shal! also assurne, following Steedman, that syntactic symbols such as S, NP, S\\NP are in fact abbreviations for feature bundles.",
    "pdf_parse": {
        "paper_id": "W98-0142",
        "_pdf_hash": "",
        "abstract": [
            {
                "text": "I shall start by taking a fairly simple Combinatory Categorial Grammar (CCG) of the type developed by Steedrnan over the past decade or so (e.g. Steedman 1996) including rules of functional application, and functional composition. I shall have nothing to say about functional substitution in this paper, and shall assume that there are type-raised categories in the lexicon (e.g. S/(S\\NP)). I shal! also assurne, following Steedman, that syntactic symbols such as S, NP, S\\NP are in fact abbreviations for feature bundles.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Abstract",
                "sec_num": null
            }
        ],
        "body_text": [
            {
                "text": "From a Phrase Structure Grammar (PSG) perspective, a CCG derivation that uses functional composition, if interpreted as building a structural level cf representation, can give rise to some very strange looking trees containing some very unusual node labels. Whereas certain labels correspond to PSG ones (e.g. VP = S\\NP), others do not (e.g. S/NP), Furthermore, because certain analyses require a rule cf composition, such trees and labels will be required. 1f there is anything at all \"real\" about traditional PSG categories for languages such as English, then on the faceof it, CCG fails to capture them. There is a related point. Ifthese strange categories such as S/NP need to be assembled, then one would expect tl1at some lexical items would require such a category either as an argument or as the result. But, tltere seem to be curiously few such words and possibly no verbs.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "",
                "sec_num": null
            },
            {
                "text": "What we shall do in this paper is examine how CCG categories can correspond to trees (cf. Joshi & Kulick 1996 and Henderson 1992 for otlter approaches). We shall see that interpreting a lexical CCG category as a partial description of a tree using a number of very simple principles will allow a number of \"natural\" distinctions to fall out without being slipulated. In particular, subjects but not objects will be immediately dominated by the S, different types of \"empty\" categories will be predicted; and structural differences between raising and control verbs will be observed. lf the lexicon is constrained so that the categories can be interpretedas trees in tlte mannerwe shall describe, and ifduring the course ofa successful derivation such trees can tllen be combined with other trees, then we shall say that the lexicon is constrained by a principle cf \"Consistent Dendrification\".",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "",
                "sec_num": null
            },
            {
                "text": "As a start towards interpreting a lexical CCG category (e.g. X\\Y) as a partial description of a tree, we shall assume that a category does a maximum of three things: it \"names\" certain nodes within a subtree (a crucial point we shall return to is tltat these may not be unique nodes); it describes a rninimum of dominance relations (not necessarily immediate dorninance); and where appropriate it describes relative preccdence relations. For example, in the example given, X and Y would be two named nodes, X would dominate a subtree (is the root) which would contain tlle node Y and also a node dorninating tlte lexical item (general principles which we shall spell out later determine how tltis item is named). Finally, because oftlle direction cf slash, tlte Y argument subtree must be to the left cf another node.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Hypothesising Trees",
                "sec_num": "2."
            },
            {
                "text": "At this point the tree will be very under specified. However, we shall also assume a set of very general principles that can be applied to the minimum infonnation specified in the category and thesc will allow other nodes to be hypothesised, named, and related to still more nodes in the tree. Finally, when a tree cornbines with another tree during the course of a derivation the resulting tree will be further specified.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Hypothesising Trees",
                "sec_num": "2."
            },
            {
                "text": "I shall first give two principles governing how nodes that have been hypothesised are labelled, then give two mechanisms for hypothesising nodes in a tree, and finally state a principle of economy that limits the number of nodes that can be hypotl1esi sed.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Principles and Conventions of Tree Building",
                "sec_num": "2.1"
            },
            {
                "text": "Principlc of Full Correspondcncc: All (non-slash (and brackets)) labels in a category correspond to, i.e. they label, (not necessarily different)nodes in a tree.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Principles and Conventions of Tree Building",
                "sec_num": "2.1"
            },
            {
                "text": "For example, with the category S/(S/NP) (\"whom\"), nodes must have been hypothesised that can be labelled witlt an S. an S. and an NP. but cruciallv. the argument (l.e. SJNP) will not be used to labet a\u2022 node, because it has been separated into an S and an N. Suppose we were to an S/NP labe!; then, the tree will contain an S/NP node which does not correspond to any standardPSG node. Ifwe wanted to relate CCG to standard trees, then we would have to give an alternative category to words such as \"whom\" and a differentanalysis to long distance dependencies.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Principles and Conventions of Tree Building",
                "sec_num": "2.1"
            },
            {
                "text": "Naming Principle: Any node that has been hypothesised and does not correspond to a labet in the category will be labelled with the labe! of the dorninating node as the result part ofthe labet and with the label of the other daughter of the dominating node as the argurnent part of the labet. The position of this other daughter on the left or right will determine the direction ofthe slash.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Principles and Conventions of Tree Building",
                "sec_num": "2.1"
            },
            {
                "text": "Note that the Principle of Full Correspondence entails that functional nodes in the tree e.g. 'X:IY must be labelled by the Naming Principle. lt will often be the case that the dominating node referredto in the Naming Principle is the nodes mother, and the other daughter is the nodes sister.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Principles and Conventions of Tree Building",
                "sec_num": "2.1"
            },
            {
                "text": "Lexical Anchor: A node is hypothesised tJiat imrnediately dominates the lexical item.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Principles and Conventions of Tree Building",
                "sec_num": "2.1"
            },
            {
                "text": "Argument and Result Correspondencc: (Not necessarily different) Nodes will be hypothesised to correspond to every argument (i.e. the right-hand-side of a slash), and to every result (i.e. left-hand-side of a slash) in a category.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Principles and Conventions of Tree Building",
                "sec_num": "2.1"
            },
            {
                "text": "Note the important difference between this mechanism goveming the hypothesis of nodes in a tree and the Principle of Full Correspondence, goveming the Jabelling of nodes. A node will be hypothesised for the argument S/NP in the S/(S/NP) category (and for the NP argument and the S and S results). However, it will not be labelled with a S/NP labe!.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Principles and Conventions of Tree Building",
                "sec_num": "2.1"
            },
            {
                "text": "We might also note the importance of the lexical anchor. Trees hypothesised from categorial grammar categories will be binary branching. Consequently, a minimal subtree will consist of three nodes. Of these three, the root node will correspond to the result part <f the category and one of the daughter nodes will correspond to the argument part of the category. In higher reaches of the tree, the second daughter node will correspond to the root of a lower subtree. However, there are two situations in which this will not be the case. One such situation will be when the (functional) lcxical category is split into the result and argument categories. A root node and a sister node will be hypothesised to correspond to this division, but a second daughter node will not have been hypothesised. The Lexical Anchor fonns this node. The second situal.ion can arise when an arg-ument is itself a functional category. This will be the situation with the category of\"whom\" S/(S/NP). In this case, an S node will by hypothesised; an NP node, which must be on the right of some other node, will also be hypothesised, and a relation of domina:nce, although not necessarily immediate dominance, will be assumed betwcen the two nodes. Acx:ording to the Principle d Economy that we will introduce next, no other nocles can be hypothesised on the basis of the category d \"whom\". And, this is what we want, since if another daughter of S were hypothesised as a sister of the NP, then by the Naming Principle it would receive the label S/NP. lt would not correspond to any conventional PSG category, and nor would it be .found in trees hypothesised from simple transitive verbs, so preventing combination oftrees. Finally, the NP is the object NP being questioned and such an NP can be arbitrarily low in the tree. We do not want to hypothesise exactly what this NPs sister is until the tree for \"whom\" has combined with trecs hypothesised from other categories.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Principles and Conventions of Tree Building",
                "sec_num": "2.1"
            },
            {
                "text": "Principle of Economy: The smallest number ci hypotheses about nodes, and dominance and preccdence relations are niade.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Principles and Conventions of Tree Building",
                "sec_num": "2.1"
            },
            {
                "text": "This principle entails that nodes and relations between nodes are not hypothesised without evidence. It also entails that ifthere is reason to hypothesise two nodes and these two nodes will receive the sarne labet. then all things being equal the two labels will refer io the samenode.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Principles and Conventions of Tree Building",
                "sec_num": "2.1"
            },
            {
                "text": "Let us assume that the lexicon gives the following category forthe proper noun \"John\" foruse as a subject S/(S\\NP). The assumption of a Lexical Anchor leads to the hypothesis of a nodc dominating \"John\" although at the rnoment it cannot be named. Let us call this node l. By Argument and Result Correspondence, we can hypothesise two further nodes by splitting the category into a result part and an argument part. We shall call the node corresponding to the result node 3. Turning now to the argument, the right slash entails that there will be a node to the right of node 1 corresponding to the subtree hypothesised from the S\\NP. Let us call this node 2. This subtree can also be split into an argument and a result. Consequently, we can at this point hypothcsise two nodcs for the subtree. By the Principle of Full Correspondence, we can label these an S and an NP. Let us calt these nodcs 2: 1 and 2:2. Becausc ofthe left slash we also know that node 2:2 must appear on the left of some other, as yet unknown, node. Can we equatenodes 2 and2:1, i.c. is the sister ofthe lexical anchor an S? At this point, this question cannot be ansm~red since node 2: 1 could also be a higher node that dominates node 2. At this stage we cannot choose between these two options, so we will leavc the node unlabc!led.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "1 Type-Raised Subjects",
                "sec_num": "3."
            },
            {
                "text": "We can now turn to node 3, i.e. the node corresponding to the result part ofthe S/S\\NP category.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "1 Type-Raised Subjects",
                "sec_num": "3."
            },
            {
                "text": "Since the result cannot be split into a result and an argument, we can labet it with an S by the Principle ci Full Correspondence. W e can return to the earlier hypotheses. The node corresponding to the S\\NP argument (i.e. node 2) was required tobe dominated by an S (node 2:1). The just hypothesised root node (node 3) will dominate this node and so by the Principle of Economy we shall equate nodes 3 and 2: 1. Node 2: 1 dominates an NP, node 2:2, which must appear on the left. We have equated nodes 3 and 2: 1. There is an as yet unlabelled node on the left that is dominated by node 3 and that is node l, the lexical anchor. Consequently, we shall equate nodes l and 2:2. Node 2 has not yet been labelled. However, its sister is labelled NP, and its mother is labelled S. Consequently, by the Naming Principle, node 2 will be labelled S\\NP. In other words, the tree corresponding to a type-raised subject is the following:",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "1 Type-Raised Subjects",
                "sec_num": "3."
            },
            {
                "text": "1) s 3 = 2:1 I \\ l = 2:2 NP S\\NP 2 1 John",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "1 Type-Raised Subjects",
                "sec_num": "3."
            },
            {
                "text": "Assuming a correspondence between an S\\NP and a VP, this is the correct result.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "1 Type-Raised Subjects",
                "sec_num": "3."
            },
            {
                "text": "Suppose that the lexicon contained an S\\(SINP) category for a type-raised object. lt should be clear that if this were the case the resulting tree would be as",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "1 Type-Raised Subjects",
                "sec_num": "3."
            },
            {
                "text": "depicted in 2. 2) s / \\ SINP NP 1",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "1 Type-Raised Subjects",
                "sec_num": "3."
            },
            {
                "text": "Not only does such a tree contain the S/NP label that does not correspond to a PSG labe!, it will not be able to combine with any tree that does not also include a S/NP labet as the daughter ofthe S. In particular it will not be able to combine with the tree hypothesised from a simple transitive verb. In other words, if the categories in the lexicon will be interpreted as trees, then the type of category that may occur will be constrained. \\ 1 /e can say that the lexicon is conS'urained by a requirement of consistent dendrification.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "John",
                "sec_num": null
            },
            {
                "text": "We shall assume that categories for the question words \"who\" and \"whom\" are S/(S\\NP) and S/(SINP) respectively. Notice that in terms of major features thc category of a subject wh-word and tl1at of a type-raised subject are identical. However, we have assumed, following Steedman, that Iabels are in fact feature bundles, and we shall assume that an S labe! with interrogative force has a +int feature. Consequently, a fuller description of these categories would be: S+int/(S-int\\NP) and S+int/(S-int/NP).",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Wh-words",
                "sec_num": null
            },
            {
                "text": "I shall take the subject wh-word first. In the previous example, we assumed that the two Ss referred to . the same node. However, in these examples, they differ with respect to the int feature. Much of the procedure for hypothesising a tree proceeds as before, but since the two Ss are no langer identical nodes 3 and 2: l cannot be equated. If nodes 3 and 2:1 cannot be equated, then one S will be dominated by the o~er S and it will be nodes 2 (i.e. the node corresponding to the S\\NP argument) and 2:1 (i.e. the result part ofthe S\\NP argument) that will be equated. Nodc 2: 1 dominates an NP node 2:2. This time no other nodc has been hypothe~ised that can be equated with n~e 2:2. In particular, node 2:2 will not be equated wttll the lexical anchornode 1. A consequence ofthis is that no node has been hypothesised as a sister of the NP node. A$ discussed earlier, such a node will only be introduced when this tree combines with another tree that has an S root, an NP on the left (or right if the category is the object we-\\\\urd) and a sister of the NP. Again as cliscussed earlier, the absence of a sister node means that the NP may be arbitrarily far ftom the S. Finally, ifthe Iexical anchor (node 1) is not equa.ted with node 2:2, then it must be named by the Nanung Principle. Its mother is an S node (node 3) and its sister is also an S node (node 2: 1). Consequently, the node dominating the word \"whom\" has the category S/S. The tree then consists of the wh-word chomskyadjoined on the Ieft side of a declarative sentence as depicted in 3. This again is the result we want. ",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Wh-words",
                "sec_num": null
            },
            {
                "text": "I shall assume that if we restrict ourselves to major features then the category for a raising verb such as \"seem\" 'and the category of a control verb such as \"try\" is the same: S\\NP/(S\\NP) (cf. Jacobson 1990 for an alternative view).",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Subject Raising Verbs",
                "sec_num": "3.3"
            },
            {
                "text": "We shall proceed as usual. A lexical anchor will be hypothesised (node l). The category splits into an argument corresponding to the S\\NP (node 2) and result corresponding to another S\\NP (node 3). The argument also splits into a result (node 2: 1) and an argument (node 2:2). Node 2:1 will dominate node 2:2. Since both ofthe categories corresponding to these nodes are atoms, these nodes will be labelled with an S and an NP respectively.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Subject Raising Verbs",
                "sec_num": "3.3"
            },
            {
                "text": "In this case, the result node (node 3) corresponds to a functional category and so node 3 will not be immediately named, and will be dominated by a node correspondingto the result (node 3:1) which will also dorninate a node corresponding to the argument (node 3:2). The result of the result (i.e. the node corresponding to the S) cannot be split into an argument and result and so by the Principle of Full Correspondence, it will be labelled with an S. This is the root of the tree. Sirnilarly, the argument of the result cannot be split, and so node 3:2 will be labelled with an NP. By the Naming Principle, node 3, which has an S mother and NP sister will be labelled S).NP.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Subject Raising Verbs",
                "sec_num": "3.3"
            },
            {
                "text": "Ifwe have hypothesised nodes and labels for the result part of the lexical item, we can turn to the argument part. The node corresponding to this is node 2. The subtree corresponding to this node is dominated by an S (node 2:1). In this case node 3:1 is labelled with an S and dorninates (although not immediately dominates) node 2. There appears to be no reason in tenns of features not to equate nodes 3: 1 and 2: 1. However, if their daughter nodes 3:2 and 2:2 were labelled differently, then these could not be equated and as a consequence their rnothers could not be equated. ln this instance both are NPs and on the left. However, we rnight ask whether they differ in terms of minor features. In a raising construction, the subject NP has no independent theta-role projected by main verb. Its theta-role is projected from that ofthe subordinate verb. If we exarnine the lexical category, it is the subtree hypothesised from the result that will combine with the tree hypothesised from an adjacent verb. In other words NP 2:2 will be marked as taking an independent theta\u2022 role, and NP 3 :2 marked as not having an independent theta-rote. In such a situation, I shall assume that there is no possibility of theta\u2022roles clashing, node 2:2 equates with node 3:2. If on the other hand, both NPs had been marked as taking independent theta-roles, then I will assume that the nodes could not be equated.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Subject Raising Verbs",
                "sec_num": "3.3"
            },
            {
                "text": "What about the label f\u00fcr node 2? Since node 2 was hypothesised to be dominated by an S (node 2:1) which also dorninates an NP (node 2:2), it will also be labelled S\\NP. We can finally return to the lexical anchor. The node corresponding to the result (node 3) that dominates it is labelled with an S\\NP, and the",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Subject Raising Verbs",
                "sec_num": "3.3"
            }
        ],
        "back_matter": [
            {
                "text": "node corresponding to the argument is also labelled with an S\\NP, and so this node is labelled with an S\\NP\\(SINP). I shall assume that a verb such as \"try\" has the same category as \"seem\", the only difference being that the two NPs have independent theta\u2022roles. A consequence of this difference is that nodes 3:2 and 2:2 cannot be eq uated. This in turn entails that the two S nodes (3: l and 2:1) cannot be equated. Instead, node 2 will be equated with node 2: 1, and will dorninate node 2:2, which will have no hypothesised node yet as a sister. Finally, the label of the lexical anchor will be different from that given to it in the case of \"seem\". lt will be dominated by an S\\NP and its sister will be an S. Hence t11e labet will be S\\NP/S. ",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "annex",
                "sec_num": null
            }
        ],
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}