| { | |
| "paper_id": "1993", | |
| "header": { | |
| "generated_with": "S2ORC 1.0.0", | |
| "date_generated": "2023-01-19T07:37:13.924439Z" | |
| }, | |
| "title": "Parsing English with a Link Grammar", | |
| "authors": [ | |
| { | |
| "first": "Daniel", | |
| "middle": [ | |
| "D" | |
| ], | |
| "last": "Sleator", | |
| "suffix": "", | |
| "affiliation": { | |
| "laboratory": "", | |
| "institution": "Carnegie Mellon University Pittsburgh", | |
| "location": { | |
| "postCode": "15213", | |
| "region": "PA" | |
| } | |
| }, | |
| "email": "" | |
| }, | |
| { | |
| "first": "Davy", | |
| "middle": [], | |
| "last": "Temperleyt", | |
| "suffix": "", | |
| "affiliation": {}, | |
| "email": "" | |
| } | |
| ], | |
| "year": "", | |
| "venue": null, | |
| "identifiers": {}, | |
| "abstract": "We define a new formal grammatical system called a link grammar. A sequence of words is in the language of a link grammar if there is a way to draw links between words in such a way that (1) the local requirements of each word are satisfied, (2) the links do not cross, and (3) the words form a connected graph. We have encoded English grammar into such a system, and written a program (based on new algorithms) for efficiently parsing with a link grammar. The formalism is lexical and makes no explicit use of constituents and categories. The breadth of English phenomena that our system handles is quite large. A number of sophisticated and new tec\u00b5niques were used to allow efficient parsing of this very complex grammar. Our program is written in C, and the entire system may be obtained via anonymous ftp. Several other researchers have begun to use link grammars in their own research.", | |
| "pdf_parse": { | |
| "paper_id": "1993", | |
| "_pdf_hash": "", | |
| "abstract": [ | |
| { | |
| "text": "We define a new formal grammatical system called a link grammar. A sequence of words is in the language of a link grammar if there is a way to draw links between words in such a way that (1) the local requirements of each word are satisfied, (2) the links do not cross, and (3) the words form a connected graph. We have encoded English grammar into such a system, and written a program (based on new algorithms) for efficiently parsing with a link grammar. The formalism is lexical and makes no explicit use of constituents and categories. The breadth of English phenomena that our system handles is quite large. A number of sophisticated and new tec\u00b5niques were used to allow efficient parsing of this very complex grammar. Our program is written in C, and the entire system may be obtained via anonymous ftp. Several other researchers have begun to use link grammars in their own research.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Abstract", | |
| "sec_num": null | |
| } | |
| ], | |
| "body_text": [ | |
| { | |
| "text": "The links do not cross (when drawn above the words).", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Most sentences of most natural languages have the property that if arcs are drawn connecting each pair of words that relate to each other, then the arcs will not cross [10, p. 36] . This well known phenomenon, which we call planarity, is the basis of link grammars our new formal lan guage system. A link grammar consists of a set of words ( the terminal symbols of the grammar), each of which has a linking requirement. A sequence of words is a sentence of the language defined by the gram mar if there exists a way to draw links among the words so as to satisfy the following conditions: Planarity:", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Satisfaction: The links satisfy the linking re quirements of each word in the se quence. ", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Connectivity: The links suffice to connect all the words of the sequence together.", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Each of the intricately shaped labeled boxes is a connector. A connector is satisfied by match ing it to a compatible connector ( one with the appropriate shape, facing in the opposite direc tion). Exactly one of the connectors attached to a given black dot must be satisfied ( the others, if any, must not be used). Thus, cat requir\ufffds a D connector to its left, and either an 0 connector to its left or a S connector to its right. Plugging a pair of connectors together corresponds to draw ing a link between that pair of words. The following diagram shows how the linking requirements are satisfied in the sentence", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "1. In a link grammar each word of the lexicon is given a definition describing how it can be used in a sentence. The grammar is distributed among the words. Our second result is the construction of a link grammar dictionary for English. The goal we set for ourselves was to make a link grammar that can distinguish, as accurately as possible, syntac tically correct English sentences from incorrect ones. We chose a formal or newspaper-style En glish as our model. The result is a link grammar of roughly eight hundred definitions (formulas) and 25000 words that captures many phenomena of English grammar. It handles: noun-verb agree ment, questions, imperatives, complex and irreg ular verbs, many types of nouns, past-or present participles in noun phrases, commas, a variety of adj ective types, prepositions, adverbs, relative clauses, possessives, coordinating conjunctions, unbounded dependencies, and many other things.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "We can roughly divide our work on link gram mars into three parts: the link grammar fo rmal ism and its properties, the construction of a wide coverage link grammar for English, and efficient algorithms and techniques for parsing link gram mars. We now touch briefly on all three of these aspects. Link grammars are a new and elegant context free grammatical formalism 12 , and have a unique combination of useful properties:", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The third result described in this paper is a program for parsing with link grammars. The program reads in a dictionary (in a form very similar to the tables above) and will parse sen tences according to the given grammar. The pro gram does an exhaustive searchit finds every way of parsing the given sequence with the given link grammar. It is based on our own O(n 3 ) algo rithm ( n is the number of words in the sentence to be parsed). The program also makes use of sev eral very effective data structures and heuristics to speed up parsing. The program is comfortably fast -parsing typical newspaper sentences in a few seconds on a modern workstation.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "We can roughly divide our work on link gram mars into three parts: the link grammar fo rmal ism and its properties, the construction of a wide coverage link grammar for English, and efficient algorithms and techniques for parsing link gram mars. We now touch briefly on all three of these aspects. Link grammars are a new and elegant context free grammatical formalism 12 , and have a unique combination of useful properties:", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "report [14] . Note that context-free systems can differ in many ways, including the ease with which t_he same grammar can be expressed, the efficiency with which the same grammar can be parsed, and the usefulness of the output of the parser for further processing. [14) .", | |
| "cite_spans": [ | |
| { | |
| "start": 7, | |
| "end": 11, | |
| "text": "[14]", | |
| "ref_id": "BIBREF13" | |
| }, | |
| { | |
| "start": 265, | |
| "end": 269, | |
| "text": "[14)", | |
| "ref_id": "BIBREF13" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Both our program (written in ANSI-C) and our dictionary are available via anonymous ft p", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Certain other constructs are difficult to han dle only using the basic link grammar framework.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "There are a number of common English phe nomena that are not handled by our current sys tem. Our technical report contains a list of these, along with the reason for this state of affairs. The reasons range from the fact that ours is a pre liminary system to the fact that some phenom ena simply do not fit well into the link grammar framework. Coordinating conjunctions such as and pose a problem for link grammars. This is because in a sentence like The dog chased and bit Mary there should logically be links between both dog and bit and chased and Mary . Such links would cross. We have devised a scheme that handles the vast majority of uses of such conjunctions and in corporated it into our program. The existence of such a conjunction in a sentence modifie s the grammar of the words in it. The same parsing algorithm is then used on the resulting modified grammar.", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "2 Notation and terminology", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "One example is the non-referential use of it: It is likely that John will go is correct, but The cat\" is likely that John will go is wrong. It is possiblebut awkwardto distinguish between these with a link grammar. To deal with this ( and a num ber of other phenomena), we extended the ba sic link grammar formalism with a post-processor that begins with a linkage, analyzes its structure, and determines if certain conditions are satisfied. This allows the system to correctly judge a num ber of subtle distinctions (including that men tioned here).", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "way to draw links among the words so as to sat isfy each word's formula, and the following meta rules:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "The link grammar dictionary consists of a collec tion of entries, each of which defines the linking requirements of one or more words. These re quirements are specified by means of a fo rmula of connectors combined by the binary associative operators & and or. Presidence is specified by means of parentheses. Without loss of general ity we may assume that a connector is simply a character string ending in + or -. When a link connects to a word, it is associ ated with one of the connectors of the formula of that word , and it is said to satisfy that connector. No two links may satisfy the same connector. The connectors at opposite ends of a link must have names that match, and the one on the left must end in + and the one on the right must end in -. In basic link grammars, two connectors match if and only if their strings are the same (up to but not including the final + or -) . A more general form of matching will be introduced later. The connectors satisfied by the links must serve to satisfy the whole formula. We define the notion of satisfying a formula recursively. To sat isfy the & of two formulas, both formulas must be satisfied. To satisfy the or of two formulas, one of the formulas must be satisfied, and no connec tors of the other formula may be satisfied. It is sometimes convenient to use the empty formula (\" ()\"), which is satisfied by being connected to no links. A sequence of words is a sentence of the lan guage defined by the grammar if there exists a", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Planarity: The links are drawn above the sen tence and do not cross.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "The link grammar dictionary consists of a collec tion of entries, each of which defines the linking requirements of one or more words. These re quirements are specified by means of a fo rmula of connectors combined by the binary associative operators & and or. Presidence is specified by means of parentheses. Without loss of general ity we may assume that a connector is simply a character string ending in + or -. When a link connects to a word, it is associ ated with one of the connectors of the formula of that word , and it is said to satisfy that connector. No two links may satisfy the same connector. The connectors at opposite ends of a link must have names that match, and the one on the left must end in + and the one on the right must end in -. In basic link grammars, two connectors match if and only if their strings are the same (up to but not including the final + or -) . A more general form of matching will be introduced later. The connectors satisfied by the links must serve to satisfy the whole formula. We define the notion of satisfying a formula recursively. To sat isfy the & of two formulas, both formulas must be satisfied. To satisfy the or of two formulas, one of the formulas must be satisfied, and no connec tors of the other formula may be satisfied. It is sometimes convenient to use the empty formula (\" ()\"), which is satisfied by being connected to no links. A sequence of words is a sentence of the lan guage defined by the grammar if there exists a", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The links suffice to connect all the words of the sequence together.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Connectivity:", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Ordering: When the connectors of a formula are traversed from left to right, the words to which they connect proceed from near to far. In other words, consider a word, and consider two links connecting that word to words to its left. The link connecting the nearer word (the shorter link) must satisfy a connector appearing to the left (in the for mula) of that of the other word. Similarly, a link to the right must satisfy a connector to the left (in the formula) of a longer link to the right .", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Connectivity:", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Exclusion: No two links may connect the same pair of words.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Connectivity:", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The use of formulas to specify a link grammar dictionary is convenient for creating natural lan guage grammars, but it is cumbersome for mathe matical analysis of link grammars, and in describ ing algorithms for parsing link grammars. We therefore introduce a different way of expressing a link grammar called disjunctive fo rm.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Disj unctive form", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "In disjunctive form, each word of the grammar has a set of disjuncts associated with it. Each dis junct corresponds to one particular way of satis fying the requirements of a word. A disjunct con sists of two ordered lists of connector names: the left list and the right list. The left list contains connectors that connect to the left of the current word ( those connectors end in -) , and the right list contains connectors that connect to the right of the current word. A disjunct will be denoted:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Disj unctive form", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "((L 1 ,L2 ,. \u2022 \u2022 ,L m ) (Rn ,Rn -1 , \u2022 \u2022 \u2022 ,R 1 )) Where L 1 , L 2 , \u2022\u2022\u2022 , L m", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Disj unctive form", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "are the connectors that must connect to the left , and R 1 , R2 , ... , R n are connectors that must connect to the right. The number of connectors in either list may be zero. The trailing + or -may be omitted from the con nector names \u2022 when using disjunctive form, since 281 the direction is implicit in the form of the dis junct.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Disj unctive form", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "To satisfy the linking requirements of a word, one of its disjuncts must be satisfied ( and no links may attach to any other disjunct). To satisfy a disjunct all of its connectors must be satisfied by appropriate links. The words to which L 1 , L 2 , It is _ easy to see how to translate a link gram mar in disjunctive form to one in standard form. This can be done simply by rewriting each dis junct as and combining all the disjuncts together with the or operator to make an appropriate formula.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Disj unctive form", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "\u2022", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Disj unctive form", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "It is also easy to translate a formula into a set of disjuncts. This is done by enumerating all ways that the formula can be satisfied. For example, the formula: ", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Disj unctive form", | |
| "sec_num": "2.2" | |
| }, | |
| { | |
| "text": "To streamline the difficult process of writing the dictionary, we have incorporated several other features to the dictionary language. Examples of all of these features can be found in section 3-.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Our dictionary language", | |
| "sec_num": "2.3" | |
| }, | |
| { | |
| "text": "It is useful to consider connector matching rules that are more powerful than simply requir ing the strings of the connectors to be identical. The most general matching rule is simply a ta blepart of the link grammar -that specifies \u2022 all pairs of connectors that match. The resulting link grammar is still context-free.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Our dictionary language", | |
| "sec_num": "2.3" | |
| }, | |
| { | |
| "text": "In the dictionary presented later in this pa per, and in our larger on-line dictionary, we use a matching rule that is slightly more sophisticated than simple string matching. We shall now de scribe this rule.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Our dictionary language", | |
| "sec_num": "2.3" | |
| }, | |
| { | |
| "text": "A connector name begins with one or more upper case letters followed by a sequence of lower case letters or *S. Each lower case letter ( or *) is a subscript. To determine if two connectors match, delete the trailing + or -, and append an infinite sequence of *S to both connectors. The connectors match if and only if these two strings match under the proviso that * matches a lower case letter ( or *).", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Our dictionary language", | |
| "sec_num": "2.3" | |
| }, | |
| { | |
| "text": "For example, S matches both Sp and Ss, but Sp does not match Ss. Similarly, D*u, matches Dmu and Dm, but not Dmc. All four of these con nectors match Dm.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Our dictionary language", | |
| "sec_num": "2.3" | |
| }, | |
| { | |
| "text": "The formula \"((A-& B+) or () )\" is satis fied either by using both A-and B+, or by using neither of them. Conceptually, then, the the ex pression \"(A+ & B+)\" is optional. Since this oc curs frequently, we denote it with curly braces, as follows:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Our dictionary language", | |
| "sec_num": "2.3" | |
| }, | |
| { | |
| "text": "{A+ & B+}.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Our dictionary language", | |
| "sec_num": "2.3" | |
| }, | |
| { | |
| "text": "It is useful to allow certain connectors to be able to connect to one or more links. This makes it easy, for example, to allow any number of ad jectives to attach to a noun. We denote this by putting an \"\u00a9\" before the connector name, and call the result a multi-connector.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Our dictionary language", | |
| "sec_num": "2.3" | |
| }, | |
| { | |
| "text": "Our dictionaries consist of a sequence of en tries, each of which is a list of words separated by spaces, followed by a colon, followed by the formula defining the words, followed by a semi colon.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Our dictionary language", | |
| "sec_num": "2.3" | |
| }, | |
| { | |
| "text": "Perhaps the best way to understand how to write a link grammar for English is to study an ex ample. The following dictionary does not cover the complete grammar of the words it contains, \ufffdut it does handle a number of phenomena: verb noun agreement, adjectives, questions, infinitives, prepositional phrases, and relative clauses. ", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "An example", | |
| "sec_num": "3" | |
| }, | |
| { | |
| "text": "We develop an explanation of how this works in stages. Let's first restrict our attention to the following connectors: S, O, A, D. (Imagine the dic tionary with all of the other connectors removed.)", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Some Simple Connectors", | |
| "sec_num": "3.1" | |
| }, | |
| { | |
| "text": "The Sis used to connect a noun to its verb. The 0 connector is used to connect a verb to its object. The A connector is used to connect an adjective to its noun. ", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Some Simple Connectors", | |
| "sec_num": "3.1" | |
| }, | |
| { | |
| "text": "The M-connector on chased allows it to act as a participle phrase modifying a noun, as shown in these examples. (L, .. Now suppose that the region between L and R contains at least one word. In order to attach the words of this region to the rest of the sen tence there must be at least one link either from L to some word in this region, or from R to some word in this region ( since no word in this region can link to a word outside of the [L, ... , R] range, and something must connect these words to the rest of the sentence) .", | |
| "cite_spans": [ | |
| { | |
| "start": 112, | |
| "end": 118, | |
| "text": "(L, ..", | |
| "ref_id": null | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Participles", | |
| "sec_num": "3.3" | |
| }, | |
| { | |
| "text": "Since the connector l' has already been used in the solution being constructed, this solution must use the rest of the connectors of the dis junct in which l' resides. The same holds for r'. The only connectors of these disjuncts that can be involved in the (L, .. ", | |
| "cite_spans": [ | |
| { | |
| "start": 258, | |
| "end": 264, | |
| "text": "(L, ..", | |
| "ref_id": null | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": ". , R).)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Suppose, for the moment, that l is not NIL. We know that this connector must link to some disjunct on some word in the region (L, . . ", | |
| "cite_spans": [ | |
| { | |
| "start": 126, | |
| "end": 133, | |
| "text": "(L, . .", | |
| "ref_id": null | |
| } | |
| ], | |
| "ref_spans": [], | |
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| "section": ". , R) region are those in the lists beginning with l and r. (The use of any other connector on these disjuncts in this region ' would violate the ordering requirement.) In fact, all of the connectors of these lists must be used in this region in order to have a satisfactory solu tion.", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The situation is shown in the following dia gram. (W, ... , R) from all the other words, and (2) they serve to connect the words W and R together.", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 50, | |
| "end": 62, | |
| "text": "(W, ... , R)", | |
| "ref_id": null | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": ". , R). (It can't link to R because of the exclusion rule.) The algorithm tries all possible such words and disjuncts. Suppose it finds a word W and a dis-junct d on W such that the connector l matches left[ d]. We can now add this link to our partial solution.", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "We need to consider one other possibility. does a third recursive call, solving a third problem analogous to our original problem. In this prob lem the word range is (W, ... ", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 43, | |
| "end": 175, | |
| "text": "does a third recursive call, solving a third problem analogous to our original problem. In this prob lem the word range is (W, ...", | |
| "ref_id": null | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "How do we determine if this partial solution can be extended to a full solution? We do this by solving two problems similar to the problem we started with. In particular, we ask if the solution can be extended to the word range (L, ... , W) using the connector lists beginning with next[l] and next[left[d]]. We also ask if the solution can be extended to the word range (W, ... , R) using the connector lists beginning with right[d] and r. Notice that in the latter case, the problem we are solving seems superficially different: the bound ary words have not already been connected to gether by a link. This difference is actually of no consequence because the pair of links (L to R and L to W) play the role that a direct link from W to R would play : ( 1) they separate the region", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "A very similar analysis suffices to handle the case when l is NIL. oization ((2, p. 312] ). l and r. (These uniquely determine L and R.) The cost of a given call is bounded by the total number of disjuncts in the sequence of words. If we let d be the number of disjuncts and c be the number of connectors, then the running time is O(c 2 d) . For a fixed link grammar, d = O(N) and c = O(N), so the running time is O(N 3 ).", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 67, | |
| "end": 88, | |
| "text": "oization ((2, p. 312]", | |
| "ref_id": null | |
| }, | |
| { | |
| "start": 92, | |
| "end": 136, | |
| "text": "l and r. (These uniquely determine L and R.)", | |
| "ref_id": null | |
| }, | |
| { | |
| "start": 141, | |
| "end": 344, | |
| "text": "cost of a given call is bounded by the total number of disjuncts in the sequence of words. If we let d be the number of disjuncts and c be the number of connectors, then the running time is O(c 2 d)", | |
| "ref_id": null | |
| }, | |
| { | |
| "start": 347, | |
| "end": 381, | |
| "text": "For a fixed link grammar, d = O(N)", | |
| "ref_id": null | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": ", R) and the connec tor lists to be satisfied begin with next[right[d]] and left[r].", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The set of disjuncts left ( after pruning is com plete) is independent of the order in which the steps are applied. (The pruning operation has the Church-Rosser property.) We therefore choose an ordering that can be efficiently implemented. It would be ideal if we could achieve a running time for pruning that is linear in the number of connec tors. The scheme we propose satisfies no useful a-priori bound on its running time, but in prac tice it appears to run in linear time.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
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| "section": "Our first approach is based on the following obser vation: In any particular sequence of words to be parsed, most of the disjuncts are irrelevant for the simple reason that they contain a connector that does not match any other connector on a word in the sequence. To be more precise, suppose that a word W has a disjunct d with a connector C in its right list. If no word to the right of W has a connector (pointing to the left) that matches C, then the disjunct d cannot be in any linkage. This disjunct can therefore be deleted without chang ing the set of linkages. Deleting such a disjunct is called a pruning step. pruning consists of re peating the pruning step until it can no longer be applied.", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "A series of sequential passes through the words is made, alternately left-to-right and right-to-left . The two types of passes are analogous, so it suffices to describe the left-to-right pass. The pass processes the words sequentially, starting with word 1. Consider the situation after words Each right connector of each remaining disjunct of W is now incorporated into the set S. This completes the processing of word W.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Our first approach is based on the following obser vation: In any particular sequence of words to be parsed, most of the disjuncts are irrelevant for the simple reason that they contain a connector that does not match any other connector on a word in the sequence. To be more precise, suppose that a word W has a disjunct d with a connector C in its right list. If no word to the right of W has a connector (pointing to the left) that matches C, then the disjunct d cannot be in any linkage. This disjunct can therefore be deleted without chang ing the set of linkages. Deleting such a disjunct is called a pruning step. pruning consists of re peating the pruning step until it can no longer be applied.", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The function computed by this left-to-right pass is idempotent, which is another way of say ing that doing the operation twice in a row will be the same as doing it once. Therefore if ( as we alternate left-to-right and right-to-left passes) a pass ( after the first one) does nothing, then all further passes will do nothing. This is how the algorithm decides when to stop.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
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| "section": "Our first approach is based on the following obser vation: In any particular sequence of words to be parsed, most of the disjuncts are irrelevant for the simple reason that they contain a connector that does not match any other connector on a word in the sequence. To be more precise, suppose that a word W has a disjunct d with a connector C in its right list. If no word to the right of W has a connector (pointing to the left) that matches C, then the disjunct d cannot be in any linkage. This disjunct can therefore be deleted without chang ing the set of linkages. Deleting such a disjunct is called a pruning step. pruning consists of re peating the pruning step until it can no longer be applied.", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The data structure used for the set S is sim ply a hash table, where the hash function only uses the initial upper-case letters of the connec tor name. This ensures that if two connectors get hashed to different locations, then they definitely don't match.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Our first approach is based on the following obser vation: In any particular sequence of words to be parsed, most of the disjuncts are irrelevant for the simple reason that they contain a connector that does not match any other connector on a word in the sequence. To be more precise, suppose that a word W has a disjunct d with a connector C in its right list. If no word to the right of W has a connector (pointing to the left) that matches C, then the disjunct d cannot be in any linkage. This disjunct can therefore be deleted without chang ing the set of linkages. Deleting such a disjunct is called a pruning step. pruning consists of re peating the pruning step until it can no longer be applied.", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Although we know of no non-trivial bound on the number of passes, we have never seen a case requiring more than five. Table 1 shows a typ ical example of the reduction in the number of disjuncts achieved by pruning. 10 3 81 391 20 423 104 391 10 3 81 163 8 381 25 357 3 3 25 25 3 25 4 12 3 3 25 21 3 21 3 8 3 3 25 21 3 21 3 8 2 2 2 6 1 4 2 1 Table 1 : This table shows the number of disjuncts remaining on each word of the sentence Now this vision is secular, but deteriorating economies will Javor Is lamic radicalism. (The first number is for the wall which has not been described in this paper. Of course the comma also counts as a word.) The fourth pass of pruning has no effect, so pruning stops. The last row in the table shows the number of disjuncts that remain after power pruning.", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 118, | |
| "end": 125, | |
| "text": "Table 1", | |
| "ref_id": null | |
| }, | |
| { | |
| "start": 216, | |
| "end": 379, | |
| "text": "10 3 81 391 20 423 104 391 10 3 81 163 8 381 25 357 3 3 25 25 3 25 4 12 3 3 25 21 3 21 3 8 3 3 25 21 3 21 3 8 2 2 2 6 1 4 2 1 Table 1", | |
| "ref_id": null | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "Our first approach is based on the following obser vation: In any particular sequence of words to be parsed, most of the disjuncts are irrelevant for the simple reason that they contain a connector that does not match any other connector on a word in the sequence. To be more precise, suppose that a word W has a disjunct d with a connector C in its right list. If no word to the right of W has a connector (pointing to the left) that matches C, then the disjunct d cannot be in any linkage. This disjunct can therefore be deleted without chang ing the set of linkages. Deleting such a disjunct is called a pruning step. pruning consists of re peating the pruning step until it can no longer be applied.", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The inner loop in the algorithm described in sec tion 4 searches for a word W and a disjunct d of this word whose first left connector matches l, or whose first right connector matches r. If there were a fast way to find all such disjuncts, significant savings might be achieved. The fas t match data structure, which is based on hashing, does precisely this. The speed-up afforded by this technique is roughly the number of different con nector types, which is roughly 30 in our current dictionary.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "The fast-match data structure", | |
| "sec_num": "5.2" | |
| }, | |
| { | |
| "text": "Power pruning is a refinement of pruning that takes advantage of the ordering requirement of the connectors of a disjunct, the exclusion rule, and other properties of any valid linkage. It also interacts with the fast-match data structure in a beautiful way. Unfortunately, these details are beyond the scope of this paper 4 \u2022 Table 1 shows outcome of pruning and power pruning on a typ ical sentence. Each of the refinements described in this sec-_ tion significantly reduced the time required to do search for a linkage. The operations of pruning, power pruning, and searching for a linkage all take roughly the same amount of time.", | |
| "cite_spans": [], | |
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| { | |
| "start": 327, | |
| "end": 334, | |
| "text": "Table 1", | |
| "ref_id": null | |
| } | |
| ], | |
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| "section": "Power pruning", | |
| "sec_num": "5.3" | |
| }, | |
| { | |
| "text": "6 Dependency and categorial grammars", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Power pruning", | |
| "sec_num": "5.3" | |
| }, | |
| { | |
| "text": "There is a large body of work based on the idea that linguistic analysis can be done by drawing links between words. These are variously called dependency systems [5] , dependency syntax [10] , dependency grammar [3, 4] , or word grammar [6, 7] . In dependency grammar, a grammatical sen tence is endowed with a dependency structure, which is very similar to a linkage. This struc ture, as defined by Me l cuk [10) , consists of a set of planar directed arcs among the words that form a tree. Each word ( except the root word) has an arc out to exactly one other word, and no arc may pass over the root word. In a linkage ( as opposed to a dependency structure) the links are labeled, undirected, and may form cycles, and there is no notion of a root word.", | |
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| "end": 166, | |
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| "section": "Dependency formalisms", | |
| "sec_num": "6.1" | |
| }, | |
| { | |
| "text": "Gaifman (5) was the first to actually give a formal method of expressing a dependency gram mar. He shows that his model is context-free.", | |
| "cite_spans": [ | |
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| "start": 8, | |
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| "section": "Dependency formalisms", | |
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| { | |
| "text": "Me l cuk's definition of a dependency structure, and Gaifman 's proof that dependency grammar is context free imply that there is a very close re lationship between these systems and link gramroars. This is the case.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Dependency formalisms", | |
| "sec_num": "6.1" | |
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| "text": "It is easy to take a dependency grammar in Gaifman 's notation and generate a link grammar that accepts the same language. In this corre spondence, the linkage that results from parsing a sentence is the same as the corresponding depen dency structure. This means that our algorithm for link parsing can easily be applied to depen dency grammars. The number of disjuncts in the resulting link grammar is at most quadratic in the number of rules in the dependency grammar. None of the algorithms that have been described for dependency parsing [3, 15, 7] seem to bear any resemblance to ours. It is therefore plausible to conjecture that our algorithms and techniques could be very useful for directly parsing depen dency grammars.", | |
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| "start": 543, | |
| "end": 546, | |
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| "section": "Dependency formalisms", | |
| "sec_num": "6.1" | |
| }, | |
| { | |
| "text": "Gaifman's result shows that it is possible to represent a link grammar as a dependency gram mar (they're both context-free) . But this corre spondence is of little use if the parsed structures that result are totally different.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Dependency formalisms", | |
| "sec_num": "6.1" | |
| }, | |
| { | |
| "text": "One problem with constructing a dependency grammar that is in direct correspondence with a given link grammar is that a linkage in a link grammar my have cycles, whereas cycles are not allowed in dependency grammar. If we restrict ourselves to acyclic linkages, we run into another problem. This is that there is an exponential blow-up in the number of rules required to express the same grammar. This is because each disjunct of each word in the link grammar requires a sep arate rule in the dependency grammar.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Dependency formalisms", | |
| "sec_num": "6.1" | |
| }, | |
| { | |
| "text": "Gaifman 's model is not lexical. The method classifies the words into categories. One word can belong to many categories. Roughly speaking, for each disjunct that occurs in the dictionary, there is a category of all words that have that disjunct. The notation is therefore in a sense orthogonal to the link grammar notation.", | |
| "cite_spans": [], | |
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| "eq_spans": [], | |
| "section": "Dependency formalisms", | |
| "sec_num": "6.1" | |
| }, | |
| { | |
| "text": "We are not aware of any notation for depen dency systems that is lexical, or that is as terse and well suited for a natural language grammar as link grammars. There has been work on creat ing dependency grammars for English [7, 3] , but we are not aware of an implementation of a de pendency grammar for any natural language that is nearly as sophisticated as ours.", | |
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| "section": "Dependency formalisms", | |
| "sec_num": "6.1" | |
| }, | |
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| "text": "Another grammatical system, known as a catego rial grammar [1] bears some resemblance to link grammars. Below we show how to express any cat ego rial grammar concisely as a link grammar. It appears to be more difficult to express a link grammar as a categorial grammar.", | |
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| "section": "Categorial grammars", | |
| "sec_num": "6.2" | |
| }, | |
| { | |
| "text": "Just as in a link grammar, each word of a cat egorial grammar is associated with one or more symbolic expressions. An expression is either an atomic symbol or a pair of expressions combined with one of two types of binary operators: / and", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Categorial grammars", | |
| "sec_num": "6.2" | |
| }, | |
| { | |
| "text": "A sentence is in the language defined by the categorial grammar if, after choosing one expres sion associated with each word, there is a deriva tion which transforms the chosen sequence of ex pressions into S, a single expression consisting of a special atomic symbol. The derivation proceeds by combining two neighboring expressions into one using one of the following rules: e e\\f f/e e f f Here e and f are arbitrary expressions, and f\\e and f /e are other expressions built using e and f. In both cases the two expressions being combined ( the ones shown above the line) must be adjacent in the current sequence of expressions. Each combinational operation produces one ex pression (the one below the line), and reduces the number of expressions by one. After n -1 oper ations have been applied, a sentence of length n has be reduced to one expression.", | |
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| "text": "For example, consider the following categorial grammar [9] : The set of languages that can be represented by categorial grammars ( as they are described here) is the set of context-free languages [1] 5 This fact alone sheds no light on the way in which the formalism represents a language. To get a bet ter understanding of the connection between cat egorial grammars and link grammars, the follow ing paragraphs explain a way to construct a link 289 grammar for a given categorial grammar. The re verse ( constructing a categorial grammar from a given link grammar) seems to be more difficult, and we do not know of an elegant way to do this.", | |
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| "end": 58, | |
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| "text": "To simplify the construction, we'll use a mod ified definition of a link grammar called a special link grammar. This differs from an ordinary link grammar in two ways: the links are not allowed to form cycles, and there is a special word at the beginning of each sentence called the wall. The wall will not be viewed as being part of any sen tence.", | |
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| "text": "Let d be a categorial grammar expression. We 'll show how to build an equivalent link gram mar expression E(d). If a word w has the set { d1 , d2 , .\u2022. , dk } of categorial expressions, then we'll give that word the following link grammar expression:", | |
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| "text": "The function E( \u2022) is defined recursively as fol lows: E(J /e) = f /e-or f /e+ or (e+ & E(J)) E(e\\f) = e\\f-or e\\f+ or (e-& E(J))", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "E(d1 )orE(d2 )or \u2022 \u2022 \u2022 orE(dk)", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Here A stands for any atomic symbol from the categorial grammar, and A, f /e and e\\f are con ..: nector names in the link grammar formulas.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "E(A) = Aor A+", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The wall has the formula S+.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "E(A) = Aor A+", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Here is the link grammar corresponding to the categorial grammar above: (Here we have replaced parentheses in the cate gorial gramm\ufffdr expressions with brackets when using them inside of a link grammar expression.) This link grammar gives the following analysis of the sentence shown above:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "E(A) = Aor A+", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "WALL Harry likes peanuts passionately Notice that in this construction, both the size of the link grammar formula, and the number of disjuncts it represents are linear in the size of the original categorial grammar expressions. This suggests that a very efficient way to parse a cate gorial grammar would be to transform it to a link grammar, then apply the algorithms and heuris tics described in this paper.", | |
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| "eq_spans": [], | |
| "section": "(\ufffd \ufffd9", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "6 Personal communication.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "(\ufffd \ufffd9", | |
| "sec_num": null | |
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| { | |
| "text": "Link grammars have become the basis for sev eral other research projects. John Lafferty [11] proposes to build and automatically tune a prob abilistic language model based on link grammars. The proposed model gracefully encompasses tri grams and grammatical constraints in one frame work. Andrew Hunt 6 has developed a new model of the relationship of prosody and syntax based on link grammars. He has implemented the model, and in preliminary tests, the results are much bet ter than with other models. Tom Brehony 6 has modified our parser to detect the kinds of errors that Francophones make when they write in En glish.", | |
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| "section": "Remarks", | |
| "sec_num": "7" | |
| }, | |
| { | |
| "text": "Link grammars resemble dependency grammars and categorial grammars. There are also many significant differ ences. Some light is shed on the relationship in section 6. 2 The proof of the context-freeness of link grammars is not included in this paper, but appears in our technical", | |
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| "text": "The directory is /usr/sleator/public on the host spade .pc.cs.cmu . edu (128.2.209.226). Our technical re ports[14,11] are also available there.", | |
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| "text": "Although they do appear in our technical report(14].DANIEL SLEATOR AND DAVY TEMPERLEY", | |
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| "text": "There are other variants of categorial grammars which are mildly context-sensitive[9] . Of course the construction presented here does not work for those languages.", | |
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| "volume": "", | |
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| "FIGREF1": { | |
| "uris": null, | |
| "type_str": "figure", | |
| "num": null, | |
| "text": "The unused connectors have been suppressed here.) It is easy to see that Mary chased the cat, and the cat ran are also sentences of this gram mar. The sequence of words: the Mary chased cat is not in this language. Any attempt to sat isfy the linking requirements leads to a violation of one of the three rules. Here is one attempt:" | |
| }, | |
| "FIGREF2": { | |
| "uris": null, | |
| "type_str": "figure", | |
| "num": null, | |
| "text": "\u2022\u2022 are linked are to the\u2022 left of the current word, and are monotonically increasing in distance from the current word. The words to which R 1 , R 2 , \u2022\u2022\u2022 are linked are to the right of the current word, and are monotonically increasing in distance from the current word. \u2022" | |
| }, | |
| "FIGREF3": { | |
| "uris": null, | |
| "type_str": "figure", | |
| "num": null, | |
| "text": "A-or ()) & D-& (B+ or ()) & (0or S+)corresponds to the following eight disjuncts:" | |
| }, | |
| "FIGREF4": { | |
| "uris": null, | |
| "type_str": "figure", | |
| "num": null, | |
| "text": "0-or (({C-or CL-} &: S+) or SI-) ; dog cat park bone stick : DANIEL SLEATOR AND DAVY TEMPERLEY {\u00a9A-} &: Ds-&: {\u00a9M+ or (C+ &: Bs+)} &: (J-or 0-or ({C-or CL-} &: Ss+) or Sis-) ; dogs cats parks bones sticks : {\u00a9A-} &: {Dm-} &: {\u00a9M+ or (C+ &: Bp+)} &: (J-or 0-or ({C-or CL-} &: Sp+) or Sip-) ; has : (Sis+ or Ss-or (Z-&: B-)) &: (((B-or 0+) &: {\u00a9EV+}) or T+) ; did : (SI+ &: I+) or ((S-or (Z-&: B-)) &: (((B-or 0+) &: {\u00a9EV+}) or I+)); can may will must : (SI+ or S-or (Z-&: B-)) &: I+; is was : (Ss-or (Z-&: Bs-) or Sis+) &: (AI+ or O+ or B-or V+ or Mp+) ; touch chase meet : (Sp-or (Z-& Bp-) or I-) &: (0+ or B-) &: or CL+}) or B+ or Ss+ ;" | |
| }, | |
| "FIGREF5": { | |
| "uris": null, | |
| "type_str": "figure", | |
| "num": null, | |
| "text": "First of all, if there are no words in this region (i.e. L = R + 1 ) then the partial solution we've built is certainly invalid if either l =/= NIL or r =/= NIL. If l = r = NIL then this region is ok, and we may proceed to construct the rest of the solution." | |
| }, | |
| "FIGREF6": { | |
| "uris": null, | |
| "type_str": "figure", | |
| "num": null, | |
| "text": "1, ... , W -l have been processed. A set S of connectors has been computed. This is the set of connectors that exists on the right lists of the dis juncts of words 1, ... , Wl that have not been deleted. To process word W, we consider each disjunct d of W in turn. For each connector c on the left list of d, we search the set S to see if it contains a connector that matches c. d matches nothing in S, then we apply the pruning step to d ( we remove d) ." | |
| }, | |
| "FIGREF8": { | |
| "uris": null, | |
| "type_str": "figure", | |
| "num": null, | |
| "text": "or <S\\NP>/<S\\NP>+ or (S\\NP-& (S\\NPor S\\NP+ or (S-& (NPor NP+) )));" | |
| }, | |
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| "num": null, | |
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| "content": "<table><tr><td/><td>283</td></tr><tr><td/><td>(os y ss y-zv \ufffd \ufffd the dog arrived with a bone</td></tr><tr><td>Sim ilarly, the S connector is subscripted to ensure verb-noun agreement. The ordering of the terms in these expressions is often important. For example, the fact that on nouns, the A-occurs to the left of the D-means that the adjective must be closer to the noun than the determiner. Here are some judgements that can be ren dered by what we have described so far:</td><td>(\u00b0\ufffd \ufffd the dog with a bone arrived Notice that, as with A-connectors on nouns, a \u00a9 is used for M-connectors on nouns and EV-con nectors on verbs, allowing multiple prepositional phrases, such as</td></tr><tr><td>lf \ufffds-@ the ugly black dog chased a big cat</td><td/></tr><tr><td>r s \ufffd dogs died</td><td/></tr><tr><td>,s \ufffd dogs chase cats</td><td/></tr><tr><td>*a dog chase a cat *black the dog died *a/*the Mary chased the cat *a dogs died *dog died</td><td/></tr><tr><td>3. 2 Prepositions</td><td/></tr><tr><td>The J, M and EV connectors allow prepositional phrases. The J connector connects a preposition to its object. Notice that in nouns, the J-is an alternative to the 0-. This means that a noun cannot both be an object of a verb and of a prepo sition. The M connector is used when a preposi tional phrase modifies a noun and the EV connec tor is used when a prepositional phrase modifies a verb. The following two examples illustrate this:</td><td/></tr></table>", | |
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| "text": "The Dis for connecting a determiner to its noun. Notice that this connector is omitted from proper nouns, is optional on plural nouns, and is mandatory on singular nouns. Also notice that the subscripts allow the to act as the de terminer for both plural and singular nouns, but a can only work with the singular nouns." | |
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| "content": "<table><tr><td>[\u00b0\u2022hEV1:\ufffd l the dog chased in the park arrived</td></tr><tr><td>/\u00b0\ufffd\ufffd l the dog chased in the park arrived</td></tr><tr><td>The I connector is used for infinitives, as in:</td></tr></table>", | |
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| "text": "MaryNotice that the I connector is an alternative to the S connector on plural verb forms. Thus we take advantage of the fact that plural verb forms are usually the same as infinitive forms, and in clude them both in a single dictionary entry.In a similar way, the T connector is used for past participles.Past participles have a T-; forms of the verb have have a T+. The GI connector is used for present participles. Present participles have a GI-connector; forms of the verb be have a GI+. The AI connector is used for predicative ad jectives. Adjectives have a AI -connector; forms" | |
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| "content": "<table><tr><td/><td>DANIEL SLEATOR AND DAVY TEMPERLEY 2 8 5</td></tr><tr><td>*The dog chased cats died *The dog who chase cats died *The dog who John chased cats died *The dog John chased cats died *The dog who chased died This allows \ufffdx\ufffd did John chase the dog Wh -questions work in various different ways; only questions involving who will be discussed here. For subject-type questions, where who is substituting for the subject, who simply has an The following incorrect constructions are ac cepted, but can be weeded out in post-processing: *The dog did John chase died *The dog who John died Mary chased died S+ connector. This allows 1 ss\ufffd For object-type questions, where who is sub stituting for the object, the B connector is used. Tr ansitive verbs have B-connectors as an alter native to their O+ connectors. Wh o has a B+ con nector. This allows \ufffd7 who did John chase The following incorrect sentences are rejected: *Did John chase *Who did John chase Mary *John did Mary chase *Chased John Mary The following incorrect construction is ac cepted. In our on-line system, post-processing is used to eliminate this. 3.5 Relative Clauses For subject-type relative clauses, where the an tecedent is acting as the subject of the clause, a B connector serves to connect the noun to the verb of the relative clause. Nouns have a B+ connector. Notice that this is optional; it is also &ed with the shown in the following diagram: next[l'] and next[r'] respectively. The situation is N -1.) For convenience, we define l and r to be sequence to be parsed are numbered from O to a connector r' on word R. (The words of the proposed between a connector l' on word L and works, consider the situation after a link has been To give some intuition of how the algorithm *Who John chased would be NIL. Similarly, right [d] = NIL. point to the connector D, and next[next [left[d]]] would point to the connector \u25a1, next[left [d]] would ()) (using the notation of section 2) . Then left[d] For example, suppose the disjunct d = ( (D , 0) The algorithm is most easily explained by has the value NIL. its list. The next field of the last pointer of a list next [ c] will denote the next connector after c in left[d] and right[d]. If c is a connector, then lists of connectors. These pointers are denoted juncts. A disjunct d has pointers to two linked specifying a data structure for representing dis is above a link already in the partial solution. will never add a link (to a partial solution) that lution in this section) in a top down fashion: It tries to build up a linkage (which we'll call a so triangulation of a convex polygon [2, p. 320] . It programming algorithm for finding an optimal ative in the standard literature is the dynamic on dynamic programming. Perhaps its closest rel Our algorithm for parsing link grammars is based who chased the dog 4 The algorithm</td><td>S+, SI-, O+, and J+ connectors, meaning that one of these connectors must be used whether or not the noun takes a relative clause. Verbs have a B connector which is orred with their S-connec tors; if a verb is in a subject-type relative clause, it may not make an S connection as well. For subject-type relative clauses, the relative pronoun who is mandatory. For this purpose, verbs have a Z-connector anded with their B L R connector. Who has a Z+ connector; therefore it can fulfill this need. However, it also has a C connector anded with its Z+ connector; this must connect back to the C+ connector on nouns. This allows the following: Here the square boxes above the words L and R represent a data structure node corresponding to the word. The rectangular box above each of these represents one of the (possibly many) dis juncts for the word. The small squares pointed to by the disjuncts represent connectors. r\u00b0\"\ufffdY\ufffd I the dog who John chased died This system successfully rejects the following incorrect sentences: For object-type relative clauses, the same B+ connector on nouns is used. However, this time it connects to the other B-connector on verbs, the one which is orred with the O+ connector and which is also used for object-type wh-questions. In this case, the relative pronoun who is op tional. Notice that nouns have optional C+ and CL-connectors which are anded with their S+ con nectors. These are used when the noun is the who is not present, the C+ connector on the an tecedent noun connects directly to the C-on the subject of the relative clause: the dog John chased died When who is present, the C+ on the antecedent connects to the C-on who; this forces the CL+ to connect to the CL-on the subject of the clause: (\u00b0\" \ufffd \ufffd subject of an object-type relative clause. When (\u00b0-\ufffd\ufffd \ufffd I the dog who chased John died How do we go about extending the partial so lution into the region strictly between L and R? (This region will be denoted</td></tr></table>", | |
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| "text": "The SI connector is used for questions where there is subject-verb inversion. On nouns SI-is an alternative to S+, and on invertible verbs (is, has, did, must, etc.) SI+ is an alternative to S-." | |
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