| { |
| "paper_id": "J75-2005", |
| "header": { |
| "generated_with": "S2ORC 1.0.0", |
| "date_generated": "2023-01-19T02:40:52.782785Z" |
| }, |
| "title": "American Journal of Computational Linguistics \"FORMULAE\" IN COHERENT TEXT : LINGUISTIC RELEVANCE OF SYMBOLIC INSERTIONS", |
| "authors": [ |
| { |
| "first": "Respunsa", |
| "middle": [], |
| "last": "Project", |
| "suffix": "", |
| "affiliation": { |
| "laboratory": "", |
| "institution": "Bar-Ilan Universi ty Ramat-Gan", |
| "location": { |
| "country": "Israel" |
| } |
| }, |
| "email": "" |
| } |
| ], |
| "year": "", |
| "venue": null, |
| "identifiers": {}, |
| "abstract": "Some difficulties in automatic analysis ~n d translat i o n bound to symbolic insertions in mathematical t e x t s a r e discussed. Rules dealins with these d i f f i c u l t i e s a r e proposed, These r u l e s are based on the use of the whole t e x t of the a~C i c l e incorporating a formula. For satisfactory automatic analysis of texts, it is necessary to provide in the dictionary exhaustive serriantical Information ascribed to i t s entries. But t h i s i n f o rmation can a p p e a r to be insufficient in cases where the meaning of! linauistic elements is a s c r i b e d to their occurrences by t h e very t e x t in whlch they. a r e encountered cf. I or example, pronouns. The o t h e r example is provided by symbolic insertions in mathematical t e x t s , which we shall call 'If ormulaeN. So n o t o n l y 'a= b , 'X 2 Y ' e t c. , but a l s o Ox* @ @ and so on are nforrnulaew. Mathematical formula resembles pronouns in one respect: it is semantically *voidqt being out of context. For example, @ G 9 may be * s e t H , \"~u b s e t * , N~r o u p l t , %peratorn, M f u n c t i m * , \" s t r i n g w , *elementu, 9qrule of grammarH, e t o. The meaning is ascribed ta a formula by the context. There are a f e w t y p e s of f o~m u l a e with f i x e d meanings. F'or example, *dx/dyf I s @derlVatlve8. B u t this s l t bt i o n 1 s n o t typical. One of t h e basic usages of formulae conSist's of naming by formula A s o m e individual object a belonging to s o m e class b of objects such t h a t t h e r e e x i s t s s o m e noun b l o c k C l (A) that names b. For example, i'n the expression 'set R' the formula *R' names some individual s e t belonging to the class of %etsN-. N o u n block @seta (consisting in this case-of a single-noun) names this class. So here c~(R) = *sete. Consider some d i f f i c u l t A e s arising in translation because of t h e absence in a source sentence of the Cl(f) f o r a formula E.", |
| "pdf_parse": { |
| "paper_id": "J75-2005", |
| "_pdf_hash": "", |
| "abstract": [ |
| { |
| "text": "Some difficulties in automatic analysis ~n d translat i o n bound to symbolic insertions in mathematical t e x t s a r e discussed. Rules dealins with these d i f f i c u l t i e s a r e proposed, These r u l e s are based on the use of the whole t e x t of the a~C i c l e incorporating a formula. For satisfactory automatic analysis of texts, it is necessary to provide in the dictionary exhaustive serriantical Information ascribed to i t s entries. But t h i s i n f o rmation can a p p e a r to be insufficient in cases where the meaning of! linauistic elements is a s c r i b e d to their occurrences by t h e very t e x t in whlch they. a r e encountered cf. I or example, pronouns. The o t h e r example is provided by symbolic insertions in mathematical t e x t s , which we shall call 'If ormulaeN. So n o t o n l y 'a= b , 'X 2 Y ' e t c. , but a l s o Ox* @ @ and so on are nforrnulaew. Mathematical formula resembles pronouns in one respect: it is semantically *voidqt being out of context. For example, @ G 9 may be * s e t H , \"~u b s e t * , N~r o u p l t , %peratorn, M f u n c t i m * , \" s t r i n g w , *elementu, 9qrule of grammarH, e t o. The meaning is ascribed ta a formula by the context. There are a f e w t y p e s of f o~m u l a e with f i x e d meanings. F'or example, *dx/dyf I s @derlVatlve8. B u t this s l t bt i o n 1 s n o t typical. One of t h e basic usages of formulae conSist's of naming by formula A s o m e individual object a belonging to s o m e class b of objects such t h a t t h e r e e x i s t s s o m e noun b l o c k C l (A) that names b. For example, i'n the expression 'set R' the formula *R' names some individual s e t belonging to the class of %etsN-. N o u n block @seta (consisting in this case-of a single-noun) names this class. So here c~(R) = *sete. Consider some d i f f i c u l t A e s arising in translation because of t h e absence in a source sentence of the Cl(f) f o r a formula E.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Abstract", |
| "sec_num": null |
| } |
| ], |
| "body_text": [ |
| { |
| "text": "L e t US try to translate from, Engllcsh-to 'Russian the sentence n \\ y n -- Similar examples a r e provicted by other languages:.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "", |
| "sec_num": null |
| }, |
| { |
| "text": ": ", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "German", |
| "sec_num": null |
| }, |
| { |
| "text": "In jeder Umgebung V von o X * .", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "German", |
| "sec_num": null |
| }, |
| { |
| "text": "'Let R be a ring with a unity I*.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "an expression From the same t e x t ) :", |
| "sec_num": null |
| }, |
| { |
| "text": "( 2 We deflne 3 and k by j = m + n; k = mno. 5The \"direct* translation of ( 5 ) t o Russian: ", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "an expression From the same t e x t ) :", |
| "sec_num": null |
| }, |
| { |
| "text": "'", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "an expression From the same t e x t ) :", |
| "sec_num": null |
| } |
| ], |
| "back_matter": [ |
| { |
| "text": "Ls a l s o appositive.T h e inverse also holds t r u e . U s i n g axioms A 3 9 A = , A 2 9 k g * A19 Az and A1 we can ascribe the meaning \"appositive\" to the link in ( 4 ) . ", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "f o r m u l a f R f'", |
| "sec_num": null |
| } |
| ], |
| "bib_entries": {}, |
| "ref_entries": { |
| "FIGREF0": { |
| "num": null, |
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| "text": "c i r s t find an x m e n t r of R v . (1) (Previous surface syntactical analysis is, assumed, i t s results being represented in dependency-tr-ee form).Syntactically, t h i s sentence (is very simple, but even an experienced \"humanq* interpreter would n o t be able t o properly understadd this expression and translate it.", |
| "type_str": "figure" |
| }, |
| "FIGREF1": { |
| "num": null, |
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| "text": "We can ascribe this meaning to t h e f o r m u l a * R n [.governed by the p r e p~s i t i o r r 'of'): , the process of translation is suspendea because of the f a c t t h a t in Russian t w o non-coordinate formulae cannot depend on the s a m e now.", |
| "type_str": "figure" |
| }, |
| "FIGREF2": { |
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| "text": "human interpreter does n o t usually hesitate to properly translate such expressions only because he understmnds their meaning from a general background or vast context. We can point out some characteristic construe-t i o n s in mathematical t e x t s that are sufficient as cont e x t s in such cases. Consider, f o r example, such a context.(i.e.", |
| "type_str": "figure" |
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| "FIGREF3": { |
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| "text": "a r expression (I), and l e t us formulate.;~very s i m e f is some flformulan, Na noun b l o c k , means syntactical irnlr,reads: 'if . . . the French and German examples abqve, L e t us n o w try to trans1at.e to Russian, the f o lpredicative adjective in Russian must be put In grammatical agreement With the subject of t h e seritence; an attributive adjectivewith the qoverning noun. T h a t Is, t h e Russian adjectives for cyclicp In ( 3 ) and for *smallestm in ( 4 ) mus* asree in gender with 'H' and * k t correspondingly. It is clear that t h e i n f brmation about the gender of a I t f omulafl can be proy i d e d by, Cl(f). Having defined. Cl(H) = 'matrixw for wh1chb..t;he translation 'KATRXTSAw is. remlnine, we receive f o r ( 3 ) t h e translation There exist numerous o t h e r ex,pre.ssions f o r which the finding o f Cl(f) is very desirable, for example:", |
| "type_str": "figure" |
| }, |
| "FIGREF4": { |
| "num": null, |
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| "text": "Qpredeltm j i k putjorn j = m + n ; k = mn b is not smooth enough; t h e translation: 'Opredelim J i k s pomosh ju s o~t n~s h e n i j 3 = m + n; k -= mn*, (*We ikefine j and k by correspondences j = m + n; k = mn\") is much b e t t e r . ~l ( f ] can be sometimes defined f r o m the very formula f. For example, 'a = b' is nequalityl,, , , ,*a ) b \" fs \"inequalityqt, and so on. Somet%mns t-he .he\"meming18 of a formula f ban be derived f r o m words syntactically linked to t h i s formula or from a more complex fo2niula F i n c o rp r a t i n g f. For example, f r o m the e2presSion we can derive t h a t T is a wtransformatianw and t h a t A and @ B W are w s e t s M . From the expression we can derive t h a t 'B' is a \"setu and that ' a p is an 'Subset of A' A @ i s a *.setN. In 'Differentiation (.or : integration.') w i t h respect t o x v , ' x ' IS a l%arlabldN, and s o on. Cl(f) f o r a formula f can be sometimes a more or less bulky expression consisting of a noun w i t h words depending on the noun d i r e c t l y or Indirectly. Pour les fonctlons x ( t ) de L g w i t h a context ,La partie c o r n w e L de tous l e s ensembles Li ' (Cl(L) is underlined), w e cannot reduce C 1 ( , L ) to only one w o r d upartlee, which I s i t s syntactical governor, 'St is very difficult t o formulate a general Pule ta discriminate between cases of typee ( 6 ) and ( 7 ) . The expression. ( 7 ) o m be translated using a synonym for C~( L ) , f o r example. 'ensemble', having in m i n d t h a t the intersection of several s e t s is also a s e t . The computability of such synonyms can, of course, In such cases m e qenitive link is r a r e ( 5 % of n all occurrences of constructions of type N f, i . e m several-dozen occurrences in a mathematical article). The t a s k of automatic cho1c.e h e r e is very d i f f i c u l t . It was solved o n l y partially. We can c h~o s e from the t e x t of an article about 70% of all occurrences of t h e appos i t i v e links and a l s o sowe occurrences of geni't-ive links, The rest of occurrences remain ambiguous. T h e proposed procedures w e r e checked in exhausting manual experiments, hue their aaaptation f o r computer is In t h e same Russian t e x t every t w o different 1 occurrences o f t.he same expsre,ssion of t y p e . -N f are or both appositive or both So, if we have s-ucceeded in clarifying the meaning of a link in one o c c u r r e m e of a construction, we can ascribe this meaning t o every occurrence of t h e same construction. ( A~) In a.construction of the t y p e where fl and f2 are two syntactt;cally co-_T ~rdinate formulae, the t w o l i n k s a r e b o t h appositive or both qenitive. cherez f * ( I *~e t us desiqnate N by f\") i n t r o d u c t o r y construotions. Every introductory construction ascr-ibes the meanizg t o the formula which It i n t r oduces. In every construc,ti.on N f, for which m . lntroductory c o n s t r u c t i o n exists i n the same t e x t . the ( A ) Sometimes the meaning is ascribed t o a formu-4 la without any introductory con.struction. The l i n k in an occurrence r of a construction n occurred in the t e x t berore. r,. In this case the formu3.a f must also not occur before r as any coherent part (subformula) of some other formula F , Because t -R e meaning can be ascribed t o a formula f by i t s place In F t s e e above). Sut t o use t h e distinction between a coherent and a non-coherent p a r t of a formula (Cf. 'a + b' in '(a + b)/d8 and in 'ca + b d 9 ) , we need a calculus of' all mathematical symbolic notations, of which o n l y small portions exist (Cf. arithmetic expresssionS 0f prograhming languages ) . Becaus-e of this Ah was formu1.ated in the above form). ( A ) Sometimes t h e r e occur in mathematical t e x t s 5 expressions where verbal and symbolic parts are interwoven so that i r l syntactic analysis a s-ymbolic insertion appears n o t as a single unit but as a complex construction having i t s own struct'ure. Some p a r t s of tr formula can have links of their o m wish t h e external verbal parts of the sentence. Examples : ( t m F u n o t i o n L H ( I 1 ) \" ).", |
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| "text": "is t h e predicate of .the sentence, 'Funs-tidn9 is iks subject and C H ( R ) *an i n d i~e c t object, The sentence Can be read as' 'F.unction L b e l o n~s to modif-ying the same word. B u t the whole string L E H(R) can a l s o be corlsidered an apposition m o d i f y i n g t h e w o r d 'functioh' . So, w e can formulate a r u l e : m If the link in some construction of t h e type N -A f I s apposiCt;'ve, then the link of t h e same N w i t h the formulaf R-f * . where R is one of the ~y m b o l s~, * , < , &~~, , 3 .~ a.c,C.f.% or 3. and f! is a (coherent) p a r t of the", |
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