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<?xml version="1.0" standalone="yes"?> <Paper uid="C65-1017"> <Title>A SYSTEM FOR TRANSFORMATIONAL ANALYSIS</Title> <Section position="2" start_page="0" end_page="0" type="metho"> <SectionTitle> i. Introduction </SectionTitle> <Paragraph position="0"> Numerous systems for the automatic recognition procedures of context-free languages have been proposed: 1 among them, two systems are in operation with comparatively large English grammars. One is J. Robinson's English parser 2 based on J. Cocke's algorithm, 3 and the other is the Kuno-Oettinger predictive analyzer of English. 4'5,6 The proponents of neither of the two systems have been satisfied with simply assigning phrase-structure descriptions to each given sentence. A paraphrasing routine has bec~ ~i(~d to Robinson's English parser 7 so that a set of kernel sentences can be obtained in addition to the phrase-structure description of the sentence. For example, the analysis outputs of &quot;X commands the third fleet.&quot; &quot;The third fleet is commanded by X.&quot; and&quot;X is commander of the third fleet.&quot; would all contain the information that the kernel is &quot;S -- X, V -- cQmmands, 0 -- third fleet&quot;. In connection with the Kuno-Oettinger predictive analyzer, three kernelizing routines have been proposed by J. Olney, 8 B. Carmody and P. Jones, 9 and D. Foster, lO which accept as input the output of the predictive analyzer and produce either kernel sentences or pairs of words which are in certain defined syntactic relationships. The SMART information retrieval system, ll,12,13,14,1~ Salton's Magic Automatic Retriever of ~exts, has a routine which compares the structure diagram (part of the analysis output of the predictive ~his ~ork has been supported in ~srt by the N~tional Science Founds tion under Gr~nt GN-329.</Paragraph> <Paragraph position="1"> Kuno-2 analyzer) of a request sentence with the structure diagrams of sentences to be retrieved, so that paraphrases of the same kernel sentence can be identified.</Paragraph> <Paragraph position="2"> The aim of the present paper is to investigate the role of the predictive analyzer in a transformational grammar recognition system, and to propose a system for analysis of a language of a given transformational grammar. Before going into details of the proposed system, it is worthwhile to discuss briefly two other systems so far proposed as transformational grammar recognizers.</Paragraph> <Paragraph position="3"> 2. General Solution to Recognition Problems of Transformational Languages (i) Analysis by Synthesis D. E. Walker and J. M. Bartlett 16 have proposed a system which parses the language of a given transformational grammar. Their system is essentially based on ~atthews' proposal 17 for analysis by synthesis. Analysis of a sentence is performed by generation of all possible strings from the initial symbol &quot;Sentence&quot; by means of a phrase-structure component, a transformational component, and a phonological component. Each of the terminal strings thus generated is matched against the input sentence. When a match is found, the path which has led to the matched terminal string represents an analysis of the input sentence. Certain heuristics are used to distinguish transformations which could have been applied to generate the sentence under analysis from those which could not have. For example, if a sentence ends in a question mark, then it is certain that at some point the question transformation was used.</Paragraph> <Paragraph position="4"> Kuno-2 The Walker-Bartlett *system, although drastically improved in efficiency compared to the proto-type proposed by Matthews, seems to be still far from being practicable because of an astronomical number of sentences that will have to be generated before the match is found.</Paragraph> <Paragraph position="5"> (ii) From Derived P-markers to Base P-markers Two similar parsing methods have been independently proposed by S. Petrick 18 and the MITRE Language Processing Techniques Subdepartment (Zwick, A. M., Hall, B. C., Fraser, J. B., Geis, M. L., Isard, S., Mintz, J., and Peters, P. S.) directed by Walker 19 as a general solution for the recognition problem of the language generated by a given transformational grammar. A transformational generative grammar G T has three components: the phrase-structure component , the transformational component, and the phonological component (see Diagram 1). The output of the phrase-structure compo~ent are generalized P-markers which have grammatical and .</Paragraph> <Paragraph position="6"> lexical forms emanating from the lowest nodes in the trees. The function of the transformational rules is to map generalized ?~ ~kers into derived P-markers. If the transformational rules map the generalized P-marker M G into the final derived P-marker ~ of the sentence X, then M G is the deep structure (base P-marker) of X and M D is its surface structure. The M D is then transferred to the phonological component, whose output is the plain terminal string X. 20 A slightly outdated model of a transformational grammar is presented here for the purpose of avoiding delicate arguments not directly connected with the aim of the present paper.</Paragraph> <Paragraph position="7"> Consider the (probably infinite) set of derived P-markers obtainable from a given transformational grammar GT. Each P-marker has at the bottom a string of symbols from which no branch emanates. Regard the set of all such strings corresponding to all derived P-markers as constituting language L D. It has been shown by Hall that, given the original transformational grammar GT, one can automatically construct a context-free grammar G S which accepts all the strings in ~ and assigns the corresponding derived P-markers to them. It is generally the case, however, that G S accepts nonsentences in ~ as well as sentences in ~, and also assigns some incorrect P-markers, as well as the correct one(s), to sentences in ~.** The analysis procedure works as follows (see Diagram 2).~Given a sentence in L(GT) , the dictionary lookup program, whichessentially plays the role of the inverse of a phonologicalcomponent, converts the sentence into a string in ~. A context-free analyzer with grammar G S assigns one (or more if the string is ambiguous in G S) derived P-marker(s) to the string. Then, each such P-marker is transferredto the inverse transformational component of G T. A test is made to see which of the transformational rules could have been applied to map some previous P-marker into the current @ Private communication. The author is greatly indebted to Barbara C. Hall, who read a preliminary draft of this paper and gave him numerous valuable suggestions.</Paragraph> <Paragraph position="8"> ** Actually, the context-free grammars for derived P-markers in both Petrick's and the MITRE group's systems have been manually compiled.</Paragraph> <Paragraph position="9"> Hall's automatic procedure does not guarantee an optimal context-free grammar for derived P-markers of a given transformational grammar.</Paragraph> <Paragraph position="10"> ***The analysis procedure described here is that of the MITRE group, with some simplifications for the sake of clarity of explanation. Petrick's procedure is conceptually similar to, but actually deviates significantly from, the model described here.</Paragraph> <Paragraph position="12"> P-marker in the course of generation of the given sentence. If a rule is .</Paragraph> <Paragraph position="13"> found whose derived constituent structure index matches the P-marker, the inverse of the structural change specified by the rule is applied to the P-marker, and a new P-marker is obtained which matches the original structural index* of the rule. If no moretransformaticnal rules can be applied inversely to the current P-marker, either the P-marker is a base P-marker, or the P-marker assigned by G S was not a final derived P-marker assigned to any sentence by G T. The latter case is due to the condition that G S accepts nonsentences as well as sentences in ~ and can give incorrect P-markers to sentences that are in ~. In order to identify whether the P-marker under consideration is a real base P-marker or not, a test has to be made to see if the P-marker is obtainable by the phrase-structure component of G T. If not, the original derived P-marker, which initiated the inverse transformational analysis path, is abandoned. If it is obtainable, the forward application of the transformational rules which were inversely applied confirms that it is in fact the base P-marker of the sentence under analysis. The base P-marker, the set of inversely applied transformational rules, and phonological rules contained in the dictionary entries constitute the analysis of the input sentence.</Paragraph> <Paragraph position="14"> Each transformational rule contains a structural index and a derived constituent structure index. The former specifies the condition that a P-marker has to fulfill in order for the rule to be applied to it. The latter specifies the structure of the P-marker into which the original * F-marker is to be mapped by the transformation.</Paragraph> </Section> <Section position="3" start_page="0" end_page="0" type="metho"> <SectionTitle> 3. A Predictive Analyzer and Transformational Analysis </SectionTitle> <Paragraph position="0"> The system of transformational analysis which is proposed below aims at obtaining a set of base P-markers almost simultaneously as a set of surface P-markers is obtained. Rules of the analytical context-free grammar for the system have associated with them information pertaining to the transformational histories of their own derivation. For example, assume that the base P-marker of &quot;I met a young prince&quot; in a given transformational grammar is the one shown in Fig. l, and that the transformational component of the grammar maps this base P-marker into the derived Then, the analytical context-free grammar for derived P-markers will have a rule which identifies a noun phrase consisting of an article (art), an adjective (adJ), and a noun. To this rule, we can assign the information that the base P-marker image of this noun phrase is the subtree corresponding to &quot;art @ the noun be adj # noun&quot; of Fig. 1. We can say that each such rule in the analytical context-free grammar draws a subtree of some base P-marker' When a derived P-marker of a sentence is obtained, the set of phrase-structure rules used for the analysis draws a set of subtrees which, when combined together, constitute the base P-marker corresponding to the derived</Paragraph> <Paragraph position="2"/> <Paragraph position="4"> The system is designed with the predictive analyzer A'5 as its core.</Paragraph> <Paragraph position="5"> The predictive analyzer uses a predictive grammar G' whose rules (called &quot;predictive rules&quot;) are of the following form:</Paragraph> <Paragraph position="7"> where Z, Yi are intermediate symbols (i.e., syntactic structures, also called predictions), c is a terminal symbol (i.e., syntactic word class) and ~ denotes the absence of any symbol, d Z, c,~ is called an argument pair.</Paragraph> <Paragraph position="8"> riSE, prn> I VP PD, for example, indicates that a sentence (SE) can be initiated by a prn (personal p~anoun in the nominative case) if the prn is followed by a predicate (VP) and a period (PD). A fragment of our current English grammar is shown in Kuno and Oettinger. 4'5 It is proved by Greibac h that G' is an exact inverse of a standard-form grammar G whose rules are of the form: Z-~>cY l...Ym where<Z, c> I YI&quot; &quot;Ym is a rule in G', or Z ~c where(Z, c~l ~ is a rule in G'.</Paragraph> <Paragraph position="9"> Since Greibach has proved that every context-free language can be generated by a standard-form grammar, the predictive analyzer could accept any . context.free language given a suitabl e predictive grammar.</Paragraph> <Paragraph position="10"> Given a context-free grammar G&quot;, we can automatically construct a standard-form grammar G which generates the same language as G&quot; does. However, it is to be noted that the structural descriptions assigned to a given sentence by G are not the same as those assigned to the same sentence by G&quot;. In such a case, we say that G and G&quot; are weakly equivalent with respect to the structural description.</Paragraph> <Paragraph position="11"> Kuno-lO Consider a predictive grammar which does not contain more than one rule with the same argument pair, and an input string of words each of which is associated with a unique terminal symbol. The analysis of the sequence of terminal symbols Cl.-.c n is initiated with a pushdown store (PDS) containing some designated initial symbol (&quot;SE&quot; in the case of a natural language. See Fig. 2 for an example). At word k in the course of the analysis of the string, an argument pair CZk, Ck> is formed from the intermediate symbol Z k topmost in the PDS and the current terminal symbol c k. If a rule with this argument pair is not found in the grammar, the input string is ill-formed (ungrammatical). If it is found, we say that the prediction Z k is fulfilled by the rule <Zk, c~> I Y.'&quot;Y ~ I m (or ink, Ck$ I 4), or simply that Z k is fulfilled by c k. A sequence of new intermediate symbols Y1 &quot;''Ym (or ~) then replaces the topmost intermediate symbol Z k of the PDS and the analysis moves to word k+ 1. The input string is well-formed if the last terminal symbol c n is processed yielding an empty PDS. A set of standard-form rules corresponding to the predictive rules used for the analysis of the string gives the derivational history of the string in the original standard-form grammar.</Paragraph> <Paragraph position="12"> Actually, a grammar may have more than one rule with the same argument pair. Also, a word in an input string may be associated with more than one terminal symbol. Therefore, a mechanism for cycling through all possible combinations of these rules and terminal symbols must be superimposed on the simple pushdown store machine described ~n the previous paragraph.</Paragraph> <Paragraph position="13"> We are not concerned here, however, about how such a mechanism is designed in the current predictive analyzer (see Sec. 1 of Kuno 6 for the analysis Kuno-ll algorit~hm). In the following discussions, only those analysis paths which lead to the end of the sentence are considered, and all abortive paths will be ignored in order to avoid unnecessary complications of the important question under discussion.</Paragraph> <Paragraph position="14"> Assume that the input sentence &quot;A young prince met a beautiful girl.&quot; is to be analyzed. Also assume that Rules i - 6 (see Fig. 2) have been used for the predictive analysis of the sentence. The configuration of the PDS prior to and immediately after the application of the rule at a given word position is shown in the preceding and succeeding lines of the column &quot;PDS Configuration&quot; of Fig. 2. The structural description (P-marker) assigned to this sentence by the set of standard-fo~i~l rules corresponding to the utilized predictive rules is shown in Fig. 3.</Paragraph> <Paragraph position="15"> Let us assume that the base P-marker that we want to have assigned to this sentence is not the one shown in Fig. 3, but the one in Fig. 4.</Paragraph> <Paragraph position="16"> Since a mapping of one P-marker into another P-marker involves shifting, removing, and adding of nodes in P-markers, it is important to have a device available to refer to any position in a P-marker. Names of branches in a P-marker are defined in the following way. If there are m branches emanating from a given node in a P-marker, the leftmost branch is named i, the second leftmost branch 2, and so forth. The rightmost branch is named m (see Fig. 4). Given a node y in a P-marker, the branch number of y is obtained by the concatenation to the right of each successive number assigned to each successive branch which leads from the topmost node to node y. For example, the branch number of adj for &quot;young&quot; in Fig. 4 is 1211, the branch number of noun for &quot;girl&quot; is 22221, and so on. Similarly, if we are given</Paragraph> <Paragraph position="18"> ......................................................................................................................... &quot;i NP PD: Rule 5 <~. NP, art> NP' a ................... i NP ' PD beautiful Rule 2 I <NP' adj > N i ! ! ............ * girl Rule 3 &quot;N, noun)~ Rule 6 -~PD, prd> ,~ a set of ordered pairs of (branch number, node) such as (1, A), (2, B), (3, C), (ll, D), (12, E), (31, F), (32, G), (33, H), the P-marker shown in Fig. 5 can be automatically constructed given the initial symbol S. To each prediction in each rule of the predictive grammar is assigned a set of ordered pairs (x, y) where y indicates the name of a node and x the branch number of y in a P-marker. For example, Rule 1 will have the @ following sets of ordered pairs assigned to its predictions: Rule l- qSE, artk i N P' VP (12, NP,) i (2, vP)</Paragraph> <Paragraph position="20"> The set of ordered pairs assigned to the prediction of the argument pair in Rule 1 represents the names of nodes and branch numbers leading from the prediction of the argument pair to the final node &quot;art&quot;. The set of ordered pairs associated with each new prediction shows the relationship of new predictions with the word class &quot;art&quot; of the argument pair (see Fig. 6). If in an ordered pair (x, y) associated with a prediction in a rule, y is not equal to the prediction itself (or to the word class of the argument pair in case the prediction is also in the argument pair), then the ordered pair plays the role of adding a new node y in a P-marker.</Paragraph> <Paragraph position="21"> In the course of predictive analysis of a sentence, the set of ordered pairs associated with the argument oair's prediction is stored in In Rule l~ each of the new predictions NP', VP, and PD has a one-member set of ordered pairs, Examples of sets of more than one ordered pair the output work area. The set of ordered pairs associated with each new .</Paragraph> <Paragraph position="22"> prediction is stored in the PDS together with the prediction.</Paragraph> <Paragraph position="23"> The branch number of an ordered pair in a rule does not have to be a constant as is the case with all the ordered pairs of Rule 1. For example, see Rule 2.</Paragraph> <Paragraph position="24"> The expression &quot;argument pair's prediction&quot; is used as distinct from the expression &quot;fulfilled prediction 'r. The former is prediction Z of<Z, ck, while the latter refers to the prediction which is topmost in the PDS and fulfilled by the rule &quot;Z, cP I YI'&quot;Ym (or J A ). The fulfilled prediction was a new prediction of a rule which was used at some preceding word position, and has associated with it in the PDS a set of ordered pairs.</Paragraph> <Paragraph position="25"> Although the fulfilled prediction itself at a given word position is always the same as the argument pair's prediction of the rule used at the same word position, it is convenient to distinguish the two for our subsequent discussions because the set of ordered pairs associated with the fulfilled prediction in the PDS is different from the set of ordered pairs associated with the argument pair's prediction in the rule (see explanation of Rule 2).</Paragraph> <Paragraph position="27"> This rule is used for the processing of &quot;young&quot; and &quot;beautiful&quot; of the example &quot;A young prince met a beautiful girl.&quot; (see Fig. 2). The branch number that the node NP' which dominates &quot;young&quot; is to receive is different ~T from the branch number that the node ~P' which dominates &quot;beautiful&quot; is to receive in the base P-marker. Since NP' can be a recursive symbol, there is no way of assigning all the possible branch numbers that NP' can be associated with in any finite number of rules. Instead, we use a variable x whose value is determined by the branch number of the immediately dominating node in a P-marker. The notation {(x, y)~ is used to indicate that the prediction appearing above the notation is to Be assigned the same set of ordered pairs as the fulfilled prediction used to have in the PDS.</Paragraph> <Paragraph position="28"> In our example, the first NP' (&quot;young&quot;) has f(12, NP') I due to Rule 1 when it becomes topmost in the PDS. In the case of the second NP' (&quot;beautiful&quot;), )to it will be shown later that it has i(222, NP' Similarly, the branch number that the node ad~ for &quot;young&quot; is to receive in a base P-marker is different from the branch number that the node _ad_i for &quot;beautiful&quot; is to receive. In fact, each of the two branch numbers depends upon the branch number which its respective immediately dominating node NP' is associated with (see Fig. 4). Yet, if NP' is to be regarded as the initial node, the branch numbers to be associated with A and adj for &quot;young&quot; and N and noun for &quot;prince&quot; are exactly the same as those to be</Paragraph> <Paragraph position="30"> associated with A at,d adj For &quot;beautiful&quot; and N and noun for &quot;\[~ir\]&quot;, respectively. Therefore, in ftule 2, the branch numbers domit~ated by N?' are given as constants, and branch numbers emanating from the initial symbol and leading to NP' fire ~iven as variables. The notation (xl~ A), for example, indicates that whatever the branch number \['rom the initial node t,o NP' might be, A is to receive i as the rightmost di~it For f, be ~ntire branch number from the initLal node to A. It is to ~ noted that ordered r~airs with variables a~pear only in rules in the grammar whose argument pairs do not contain the initial prediction SE. Once a rule is used for the analysis of a sentence, all the variables for branch numbers in the set of ordered r~airs associated with this rule will I~ changed into some numerical branch numbers.</Paragraph> <Paragraph position="31"> In general, (~m, Z) (m >_ i) not in a !~air of braces indicates the follo~ing: Take the maximum value* of branch numbers (max x) in .!( ~ ~ . X~ jj; of the fulfilled prediction. (i{emember tha~ the branch numbers of ordered pairs associaL~ed ~ith the fuli'i\].led prediction are all numerical, and do not corttain any variables. ~egard numeric branch rmmbers as integers to obtain the &quot;maximum value&quot;.) Concatenate m to the ri\[~ht of max x.</Paragraph> <Paragraph position="32"> Form an ordered oair ~ith Z.</Paragraph> <Paragraph position="33"> The concatenation mark is suppressed where no confusion can result. .',hen (C-m, Z)a pe rs p ir races, the x Y)!i or the .\['uifill.ed ored:i_ction, not the maximum w~lue, are used t,o :form a set of new ordered pairs with m concatenated to the right oi' each w~luo of x (see kule 5a for example) ~ Why max x is used among values oF x in )'(x, y~'i will be explained in Sec. 5. Ordered pairs with variables (x, y), (x'~m, y) can be regarded as a notation for some function whose value depends upon the previously obtained value of the same function. It is this recursive nature of ordered pairs in the grammar that allows the proposed system to work for an infinite number of sentences in the language.</Paragraph> <Paragraph position="34"> In the case under discussion, the fulfilled prediction NP' corre-O sponding to &quot;young&quot; has ~12, NP')~ associated with it in the PDS. Therefore, max x = 12. So, (xl, A) and (xll, adj) are changed into (12~, A) and (12 ii, adj), respectively, and the latter two are stored in the output work area. As explained in the previous paragraph, ~x, y)~ associated with the argument pair's prediction is replaced by (12, NP')~ which also is stored in the output work area. The new prediction N of Rule 2 is assigned the ordered pair (12~2, N). N, (122, N) replaces the fulfilled prediction NP' and its ordered pair (12, NP') in the PDS. Now the output work area contains (i, NP), (ii, T), (IIi, art) due to Rule 1 and (12, NP'), (121, A), (1211, adj) due to i<ule 2. This set of ordered pairs corresponds to a partial P-marker shown in Fig. 7.</Paragraph> <Paragraph position="35"> Rule 3 is shown below with ordered pairs: Rule 3 : <N~ noun &quot;~.</Paragraph> <Paragraph position="36"> (xl, noun) When ~{ule 3 is used for the processing of the third word &quot;prince&quot; of the example, the fulfilled prediction has associated with it the ordered pair (122, N). Therefore, (122, N) and (122~i, noun) are stored in the output</Paragraph> <Paragraph position="38"> it is to be noted that the set of ordered pairs in the output work area in Fig. 8 is isomorphic ~o ~'~ne P-marker shown in ~mg. '~&quot; 4.</Paragraph> <Paragraph position="39"> Le~ us go back to the traasformational grammar previously mentioned wn~c~, assigns the base P-marker of Fig. ! to &quot;I met a young prince &quot;</Paragraph> <Paragraph position="41"/> <Paragraph position="43"> /< associated with a prediction in a rule performs the function of eliminating the node for the prediction from a P-marker.</Paragraph> <Paragraph position="45"> The argument pair's pred~c~o.. ,', ' ...... &quot;'~'~'~ with it a set of ordered pairs xl, noun * ~ ~s to be noted that ..... ' - ~ .........</Paragraph> <Paragraph position="46"> &quot;~ &quot;' &quot; &quot; the fulfilled of P.ule z/. ~:'nen 2~ule 5a ~.s used to process '~prince, prediction N has associated with it ordered pairs (222, N) and (221312, N). Therefore, ~(xl, noun)} is changed into noun) and (2213121, noutu).</Paragraph> <Paragraph position="47"> In comparing Rule 3a, for example, with Fig. l, one may wonder why (x2, N) and (xl312, N) are associated with the new prediction N, and not with the argument pair's prediction NP. If the latter alternative were chosen, N would have no ordered pairs in Rule 3a. Then, when Rule 5a is used for the processing of &quot;prince,&quot; there would be no way of obtaining desired branch numbers for the noun in \[(xl, noun)~. The concatenation operation x~m introduced in the previous paragraphs is not enough to deal with coordinate structures. Assume that the base P-marker of Fig. 9 is to be assigned to &quot;She is young and</Paragraph> <Paragraph position="49"> However, if the predicate has three adjectivez :*young and beautiful and intelligent,&quot; the inadequacy of a con~e~#o-free gra~u~-r manifests itself. The P-marker that we want to obtain is not that of Fig. 10(a), but of Fig. 10(b). Yet, we car~uot include in the predictive grammar a rule such as</Paragraph> <Paragraph position="51"> because we will face the same problem for coordinate predicates with more than three coordinated members, and because we carmot have an infinite n~mber of rules pertair~ing to i-member coordinate structures where i = 2,3,...,~.</Paragraph> <Paragraph position="52"> In order to obtain P-markers of the type shown in Fig. 10(b) with a fir~Ite set of rules, a new operation &quot;/&quot; is introduced. If a prediction in a rule has (x+m, u), max x is chosen among the values of x of ~(x, Y)3 associated with the fulfilled prediction: m is numer'ocally Actu~lly, the difficulty under discussion is not only of a context-free analyzer, but also of the phrase-structure component of a transformatio~=aL grammar. A base P-marker of the type shown in Fig. 10(b) c~ot be obtained by any phrase-structure grammar if an infinite number of coordinated members is to be accounted for. One solution for a transformational ~enerative grammar is to have in its phrase-structure component a re~vriting schema such as PRED-->A (AND A)*, where (AND A)* can be repeated any number of times (including zero). T~his is done in the :J~ITP~ procedure in both the generative phrase structure component of GT and the context-free analysis component G S. In the generative component, the only starred rule is S'----~S (AND S)*; in the recognition component, all compoundable intermediate symbols have rules of this type.</Paragraph> <Paragraph position="53"> added to the rightmost position of max x. (If more than nine constituents are to be accepted in a construct, it is necessary to use more than one digit for the name of each branch, but this does not cause any additional complexities.) For example, when the second adjective &quot;beautiful&quot; of the example &quot;She is young and beautiful and intelligent.&quot; fulfills the prediction A, Rule i0 is usedt Rule i0- <A~ ad~ I AND A i m , , (x/l, AND) (~2, A)&quot; {(x, y)} for the fulfilled prediction is (223, A); therefore, (x+l~ AND) and (x+2, A) are changed into (224, AND) and (225, A), respectively (224 = 223 + i, 225 = 223 + 2), and are stored in the PDS with the corresponding predictions AND and A. If the predicate has four adjectives as in &quot;young and beautiful and intelligent and bright,&quot; Rule i0 will be used again for the processing of &quot;intelligent.&quot; This Kuno-27 time, max x = 225. Therefore, new predictions AND and A will be stored in the PDS with the new ordered pairs (226, AND) and (227, A), respectively.</Paragraph> <Paragraph position="54"> It should now be noted that the concatenation operation x~m plays the role of generating a subtree whose initial node has the branch number max x, while x+ m plays the role of adding a branch to the right of a branch whose branch number is x, and whose immediately dominating node also dominates the added branch.</Paragraph> </Section> <Section position="4" start_page="0" end_page="0" type="metho"> <SectionTitle> 4. Salient Features of the Proposed System for Transformational Analysis </SectionTitle> <Paragraph position="0"> What are the salient differences between the transformational analysis system (see Sec. 2(ii) of this paper) proposed by the MITRE group and Petrick (to be referred to as M-P system) and the one proposed in the present paper (to be referred to as K-system)? The M-P system is based on the condition that a transformational grammar is given. A context-free analysis component is automatically constructed on the basis of the transformational grammar; the context-free analysis component assigns one or more derived P-markers to a sentence to be analyzed; transformational rules are applied inversely to each P-marker step by step until the base P-markers of the sentence are obtained.</Paragraph> <Paragraph position="1"> For example, after a derived P-marker is assigned to &quot;He met a beautiful girl.&quot;, the M-P system will compare the P-marker with the derived See the second footnote on page 4-</Paragraph> <Section position="1" start_page="0" end_page="0" type="sub_section"> <SectionTitle> Kuno~-28 </SectionTitle> <Paragraph position="0"> constituent structure indices of transformational rules, and find that this derived P-marker is the result of the transformational rule which places an adjective in front of a noun. Therefore, by applying this rule inversely, an intermediate P-marker corresponding to &quot;#He met a girl beautiful#&quot; is obtained. Next, this new P-marker is compared with derived constituent structure of transformational rules, and it is found that this is the result of the transformational rule which deletes a relative pronoun and a copula. Therefore, by applying this rule inversely, an intermediate P-marker corresponding to &quot;#He met a girl who was beautiful#&quot; is obtained. Next, this intermediate P-marker is compared with the derived constituent structure indices of transformational rules again and is identified as being the result of a relativization rule. Therefore, the rule is applied inversely, and a new P-marker corresponding to &quot;#He met a girl # the girl was beautiful#&quot; is obtained, which in turn is identified as originating from a rule which places an embedded #S# dominated by DET after the noun. A new P-marker corresponding to &quot;#He met a # the girl was beautiful #girl#&quot; is thus obtained. AZ'ter comparing this P-marker again with rules in the transformational component, it is found that there is no rule whose derived constituent structure index matches the P-marker. It is also found that the P-marker is derivable from the phrase-structure component of the transformational grammar. Thus, the P-marker is identified as being a base P-marker, and forward application of the transformations which were inversely applied confirms that it is in fact the base P-marker of the sentence under analysis.</Paragraph> </Section> <Section position="2" start_page="0" end_page="0" type="sub_section"> <SectionTitle> Kuno-29 </SectionTitle> <Paragraph position="0"> With regard to the K system, on the other hand, a predictive grammar which accepts all the sentences of a given transformational grammar G T (and probably nonsentences in addition) is manually compiled. A derived P-marker assigned to a given sentence by the predictive grammar is usually not equal to the derived P-marker which is assigned to the same sentence by 9&quot; The mapping of such a distorted P-marker into the base P-marker is not performed step by step through intermediate P-markers as is the case with the M-P system. Instead, it is performed in one step by means of ordered pairs. For example, the fact that the predictive rule <lq?, art~! A N has been used for assigning a distorted P-marker to the sentence &quot;He met a beautiful girl.&quot; indicates immediately that an embedded sentence which constitutes a relative clause is involved here, that the subject of the embedded sentence is the same as a noun (&quot;girl&quot; in our example) which fulfills N of the predictive rule, and that the adjective (&quot;beautiful u) which fulfills A is the predicate adjective of the embedded sentence. The predictive rule has associated with it a set of ordered pairs which draws a subtle of the base P-marker image of this NP. The summation of such subtrees drawn by all the rules used for obtaining the distorted P-maker yields the base P-maker of the sentence.</Paragraph> <Paragraph position="1"> The K system does not achieve this one-step mapping without cost. The sacrifice is paid in the simplicity of the context-free Kuno- 30 analysis component. For example, in order to obtain desired base Look at the girl who is dancing the mazurka.</Paragraph> <Paragraph position="2"> This is the girl whom everyone likes.</Paragraph> <Paragraph position="3"> This is the glrl by whom he was ruined.</Paragraph> <Paragraph position="4"> the predictive grammar must have three different rules pertaining to a noun phrase initiated by the definite article &quot;the.&quot; Each rule specifies a different position, in the embedded sentence, of the predicted N (see circled N's in Fig. ll).</Paragraph> <Paragraph position="5"> Rule (i): <NP, the></Paragraph> <Paragraph position="7"/> <Paragraph position="9"> Moreover, in order to deal with sentences such as (iv) Look at the ~irl dancing the mazurka. (v) Look at the dancinK_g_irl.</Paragraph> <Paragraph position="10"> (vi) This is the girl liked by ever ~X_ ~. additional rules have to be recognized which have the same argument pair <NP, the> but which have different sequences of new predictions and the different sets of ordered pairs from those in Rules (i), (ii) and (iii). Depending upon the nature of the original transformational grammar GT, the number of such rules with the same argument pair can become very large. However, when a given sentence with a noun phrase is analyzed, only one of these rules will lead to the end of the sentence (unless the sentence is ambiguous with respect to the noun phrase), and all the other rules of <NP, the> Kuno-33 will come to an impasse before the end of the noun phrase is reached. Moreover, once an analysis of the sentence is obtained, the derived P-marker can be unambiguously mapped into the corresponding base P-marker.</Paragraph> </Section> </Section> class="xml-element"></Paper>