| { |
| "paper_id": "J74-2002", |
| "header": { |
| "generated_with": "S2ORC 1.0.0", |
| "date_generated": "2023-01-19T02:17:50.615390Z" |
| }, |
| "title": "SEMANTIC DIRECTED TRANSLATION t OF CONTEXT FREE LANGUAGES", |
| "authors": [ |
| { |
| "first": "H", |
| "middle": [ |
| "William" |
| ], |
| "last": "Buttelmam", |
| "suffix": "", |
| "affiliation": {}, |
| "email": "" |
| }, |
| { |
| "first": "", |
| "middle": [], |
| "last": "Columbus", |
| "suffix": "", |
| "affiliation": {}, |
| "email": "" |
| }, |
| { |
| "first": "", |
| "middle": [], |
| "last": "Ohio", |
| "suffix": "", |
| "affiliation": {}, |
| "email": "" |
| } |
| ], |
| "year": "", |
| "venue": null, |
| "identifiers": {}, |
| "abstract": "A formal d e f i n i t i o n f o r t h e semantics of a c o n t e x t free language, c a l l e d a phrase-structure semantics., i s given. The d e f i n i t i o n i s a model of t h e n o t i o n t h a t i t i s phrases which have meaning and t h a t t h e meaning", |
| "pdf_parse": { |
| "paper_id": "J74-2002", |
| "_pdf_hash": "", |
| "abstract": [ |
| { |
| "text": "A formal d e f i n i t i o n f o r t h e semantics of a c o n t e x t free language, c a l l e d a phrase-structure semantics., i s given. The d e f i n i t i o n i s a model of t h e n o t i o n t h a t i t i s phrases which have meaning and t h a t t h e meaning", |
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| "eq_spans": [], |
| "section": "Abstract", |
| "sec_num": null |
| } |
| ], |
| "body_text": [ |
| { |
| "text": ". . . . . . . . . . . ", |
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| "section": "", |
| "sec_num": null |
| }, |
| { |
| "text": ". T r a n s l a t i o n i s n e c e s s a r i l y concerned w i t h b o t h syntax and semantics, so we begin with a formal d e f i n i t i o n of semantics f o r context f r e e grammars.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "TRANSLATIONIV(1. + t 0 2 . + )", |
| "sec_num": null |
| }, |
| { |
| "text": "I n Section 2, a simple algorithm f o r t r a n s l a t i n g from one context free language t o another i s given. The algorithm i s \"controlled\" by a f i n i t e set of r u l e s which s p e c i f y how t o r e p l a c e phrases i n t h e source language with semantically e q u i v a l e n t phrases i n the t a r g e t language. The transl a t i o n algorithm, i t t u r n s o u t , i s s t t a i g h t f o r w a r d . The key p r o b l e~ is in \"finding\" t h e f i n i t e s e t of r u l e s which c a r r e c t l y s p e c i f y the t r a n s ' l a t i o n .", |
| "cite_spans": [], |
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| "eq_spans": [], |
| "section": "TRANSLATIONIV(1. + t 0 2 . + )", |
| "sec_num": null |
| }, |
| { |
| "text": "The main p a r t of t h i s paper, S e c t i o n 3, is concerned w i t h t h a t problem.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "TRANSLATIONIV(1. + t 0 2 . + )", |
| "sec_num": null |
| }, |
| { |
| "text": "Throughout t& paper, w e assume t h a t grammars and semantics a r e given.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "TRANSLATIONIV(1. + t 0 2 . + )", |
| "sec_num": null |
| }, |
| { |
| "text": "There i s nothing i n this paper t h a t t e l l s you. how t o go about w r i t i n g t h e", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "TRANSLATIONIV(1. + t 0 2 . + )", |
| "sec_num": null |
| }, |
| { |
| "text": "\"right\" grammar and semantics f o r a given cf 1.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "TRANSLATIONIV(1. + t 0 2 . + )", |
| "sec_num": null |
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| "text": "Meeting of t h e Association f o r Computational L i n g u i s t i c s a t Ann Arbor, Michigan, August, 1973. This research was supported i n p a r t by NSF g r a n t GN-534.1.", |
| "cite_spans": [ |
| { |
| "start": 79, |
| "end": 109, |
| "text": "Arbor, Michigan, August, 1973.", |
| "ref_id": null |
| } |
| ], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "t An e a r l i e r v e r s i o n of t h i s paper was presented t o t h e Eleventh Annual", |
| "sec_num": null |
| }, |
| { |
| "text": "Much of the presentation is formal. Some readers may find i t helpful t o read only through Example 1, and then t o peruse Section 4 (Sample Translations) t o pick up some i n t u i t i o n , before proceeding with t h e rest of the paper.", |
| "cite_spans": [], |
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| "section": "t An e a r l i e r v e r s i o n of t h i s paper was presented t o t h e Eleventh Annual", |
| "sec_num": null |
| }, |
| { |
| "text": "1. Phrase S t r u c t u r e Syntax and Semantics.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "t An e a r l i e r v e r s i o n of t h i s paper was presented t o t h e Eleventh Annual", |
| "sec_num": null |
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| "text": "I assume t h e reader i s f a m i l i a r w i t h the notions of \"derivation\" and I1 syntax tree1' ( a l i a s \"derivation tree\", a l i a s \"phrase marker\") f o r cf g ' s .", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "t An e a r l i e r v e r s i o n of t h i s paper was presented t o t h e Eleventh Annual", |
| "sec_num": null |
| }, |
| { |
| "text": "Several good texts on t h e s e s u b j e c t s a r e l i s t e d i n the bibliography.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "t An e a r l i e r v e r s i o n of t h i s paper was presented t o t h e Eleventh Annual", |
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| "text": "The d e f i n i t i o n of semantics which I am about t o give i s based oa the following two simple notions: 1) i t i s phrases which have m e w g (paragraphs, sentences, clauses, and morphs a r e s p e c i a l cases of' phrases) , Benson (1970) , Knuth (1968 Knuth ( , 1971 , some statements attributed t o Thompson (cf Benson, 1970) , and in* Tarski (1936) . Now t h e d e f i n i t i o n : D e f i n i t i o n 1.", |
| "cite_spans": [ |
| { |
| "start": 233, |
| "end": 246, |
| "text": "Benson (1970)", |
| "ref_id": null |
| }, |
| { |
| "start": 249, |
| "end": 260, |
| "text": "Knuth (1968", |
| "ref_id": null |
| }, |
| { |
| "start": 261, |
| "end": 275, |
| "text": "Knuth ( , 1971", |
| "ref_id": "BIBREF8" |
| }, |
| { |
| "start": 322, |
| "end": 335, |
| "text": "Benson, 1970)", |
| "ref_id": null |
| }, |
| { |
| "start": 346, |
| "end": 359, |
| "text": "Tarski (1936)", |
| "ref_id": "BIBREF10" |
| } |
| ], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "t An e a r l i e r v e r s i o n of t h i s paper was presented t o t h e Eleventh Annual", |
| "sec_num": null |
| }, |
| { |
| "text": "Let. G = (V, z, P , S) b e a c o n t e x t f r e e grammar where:", |
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| "ref_spans": [], |
| "eq_spans": [], |
| "section": "t An e a r l i e r v e r s i o n of t h i s paper was presented t o t h e Eleventh Annual", |
| "sec_num": null |
| }, |
| { |
| "text": "V is t h e f i n i t e nonempty vocabulary, C c -V i s t h e t e r m i n a l a l p h a b e t , S \u20ac (V -C) i s t h e axiom, and P is the finite nonempty set of grammar r u l e s , having the form W e a l s o r e q u i r e that X fI (M u A) = 0.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "t An e a r l i e r v e r s i o n of t h i s paper was presented t o t h e Eleventh Annual", |
| "sec_num": null |
| }, |
| { |
| "text": "+ A -t B , f o r A \u20ac (V -C) and B 6 V .", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "t An e a r l i e r v e r s i o n of t h i s paper was presented t o t h e Eleventh Annual", |
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| }, |
| { |
| "text": "There i s an example on t h e next page.", |
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| "eq_spans": [], |
| "section": "t An e a r l i e r v e r s i o n of t h i s paper was presented t o t h e Eleventh Annual", |
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| { |
| "text": "Example 1.", |
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| "eq_spans": [], |
| "section": "t An e a r l i e r v e r s i o n of t h i s paper was presented t o t h e Eleventh Annual", |
| "sec_num": null |
| }, |
| { |
| "text": "Coxfsider a cfg and phrase-structure semantics f o r well-formed addition expressions over t h e alphabet Z = {I, +). L(G) = {I, I+I, I+I+I, . . . I . ", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "t An e a r l i e r v e r s i o n of t h i s paper was presented t o t h e Eleventh Annual", |
| "sec_num": null |
| }, |
| { |
| "text": "G = (V", |
| "cite_spans": [], |
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| "eq_spans": [], |
| "section": "t An e a r l i e r v e r s i o n of t h i s paper was presented t o t h e Eleventh Annual", |
| "sec_num": null |
| }, |
| { |
| "text": "c = {I, +)", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "t An e a r l i e r v e r s i o n of t h i s paper was presented t o t h e Eleventh Annual", |
| "sec_num": null |
| }, |
| { |
| "text": "N i s t h e set of non-aegatiue i n t e g e r s ,", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "t An e a r l i e r v e r s i o n of t h i s paper was presented t o t h e Eleventh Annual", |
| "sec_num": null |
| }, |
| { |
| "text": "and f and I a r e r e c u r s i v e functions defined i n F below, + t", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "3-", |
| "sec_num": null |
| }, |
| { |
| "text": "M = {N, 1, f 1", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "3-", |
| "sec_num": null |
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| { |
| "text": "F contains just the following d e f i n i t i o n s : ", |
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| "eq_spans": [], |
| "section": "3-", |
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| "text": "1 ( i d e n t i t y function on N + N): 1 (x) = x + f (integer a d d i t i o n on N x N + N) : 1 ) f+(x ,Y) = ( f + ( X , Y ) ) (' i s the successor fn.) Note t h a t rS4+S (x1,x2,x3) = x (X ,X ) does", |
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| "section": "3-", |
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| "text": "+ + . I . J + X2 is i n v(+) = {f 1, then x2(x1,x3) = f (X x ) i s i n N and f i s defined", |
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| "section": "3-", |
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| "text": "Before explaining the example, let's f i r s t consider what t h e semantics i s used f o r . We will need t h e following n o t a t i o n for t r e e s : 0) a i s a tree, f o r all a f C. 1) a c t ... t > is a t r e e , f o r a l l a c Z and trees tl, ..., t .", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1' 3 primitive recursive,", |
| "sec_num": null |
| }, |
| { |
| "text": "n n t For r e a d a b i l i t y , we w r i t e the members of M without unnecessary braces -i . e . , \"1\" i n s t e a d of \"{l)\".", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1", |
| "sec_num": null |
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| "text": "The above i n d u c t i v e d e f i n i t i o n gives a \"standard\" parenthebized n o t a t i o n for trees. Let us denote t h e r o o t of a tree t , r t ( t ) and t h e frontier, f r ( t ) . W e s h a l l a l s o need t h e following non-standard n o t a t i o n : n i \" ' node of the f r o n t i e r of to, which can be done s i n c e t h i s node has the same label as the root of ti. Then 4 and t h e meaning f u n c t i o n p a r e used t o d e f i n e a meaning f u n c t i o n p on t h e sentences of G. F i r s t , w e d e f i n e 4, then u.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1", |
| "sec_num": null |
| }, |
| { |
| "text": "t I t ... t ] i s a tree i f t 0 1 n 0 ' n . . . ,", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1", |
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| }, |
| { |
| "text": "To d e f i n e $, w e must first d e f i n e the codomain of @, @. Informally, U u + i s t h e set of a l l n-ary f u n c t i o n s on 2 X * * * X Z~ + 2 , f o r arbitrary n.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1", |
| "sec_num": null |
| }, |
| { |
| "text": "Formally, l e t +n = {f:2 x * a *~2~ + 2 U f i s a function of n arguments).", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "U", |
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| }, |
| { |
| "text": "Then @ = U n=1,2, .. . @n . and l e t Bi +l...Bi = f r ( t ) f o r j = 1, ..., n , where A phrase form i s s i m i l a r t o a s e n t e n t i a l form, except t h a t i t need n o t be derived from t h e axiom. Formally, t h e set o f phrase. forms of G is t h e set determined by i t s s y n t a c t i c s t r u c t u r e . A s e n t e n c e can be semantically ambiguous i f i t has more than one syntax t r e e o r if a t l e a s t one of i t s cons t i t u e n t s is semantically ambiguous.", |
| "cite_spans": [], |
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| "eq_spans": [], |
| "section": "U", |
| "sec_num": null |
| }, |
| { |
| "text": "i = 0. j j 0 j -1 Then @(t0Itl...t ])(x1, ..., x ) : .~I ( B~) x \" * x~( B~ ) + v ( r t ( t O ) ) n i n n I n t u i t i v & l y ,", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "U", |
| "sec_num": null |
| }, |
| { |
| "text": "* * P(G) = I w I v C V and A a w f o r some A 6 v).", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "U", |
| "sec_num": null |
| }, |
| { |
| "text": "W e retyrn t o Example 1 on t h e next page.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "U", |
| "sec_num": null |
| }, |
| { |
| "text": "Now consider Example 1. L e t w b e the sentence \"L + I' + I\". It has the syntax tree Consider now any two c f g ' s and t h e i r a s s o c i a t e d semantics, 9, d l and G2, J2", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "U", |
| "sec_num": null |
| }, |
| { |
| "text": "One", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "U", |
| "sec_num": null |
| }, |
| { |
| "text": ". A t r a n s l a t i o n of L(G1) tjo L(G ) is a function 2 T: L(G,) + 2 L (G*) defined a s f o l l e w :", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "U", |
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| "text": "The codomain of a t r a n s l a t f o n must be t h e power set of t h e t a r g e t language, s i n c e every sentence i n L(G ) may have many semantically equivalent sen-1 tences i n L(G2). I n t h i s paper wel focus on b a n s l a t i o n s which a r e specified by a f i n i t e set of r u l e s . For these t r a n s l a t i o n s , t h e r e i s a simple and S<OS> \u20ac Tp; 0 \u20ac gen(Tp), and ScOS<B>> \u20ac ges(Tp). Note t h a t t can a l s o be written as t = s<OS<OS>> [OOS<B>] , and again, S<OScOS>> \u20ac gen mp), 0 f gen(Tp) , and S<B> \u20ac g e n (~~) .", |
| "cite_spans": [ |
| { |
| "start": 470, |
| "end": 478, |
| "text": "[OOS<B>]", |
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| } |
| ], |
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| "eq_spans": [], |
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| }, |
| { |
| "text": "To s p e c i f y a t r a n s l a t i o n from T(G ) t o T ( G~) w e proceed as fallows: 1 L e t r be any p a r t i a l function on VN -+ V , a n d l e t T be a generating set N, I L for T(GI). L e t ; be a f u n c t i o n on", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "U", |
| "sec_num": null |
| }, |
| { |
| "text": "T + T(Gp) x N + + 0", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "U", |
| "sec_num": null |
| }, |
| { |
| "text": "which s a t i s f i e s the following p r o p e r t i e s :", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "U", |
| "sec_num": null |
| }, |
| { |
| "text": "i f ; ( t ) = (t',", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "U", |
| "sec_num": null |
| }, |
| { |
| "text": "xl...x ) then n i ) r t { t ' ) = ; ( r t (t)), and i i ) n = 1 f r ( t t ) 1, and", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "U", |
| "sec_num": null |
| }, |
| { |
| "text": "i i i ) 0 < -x . < I f r ( t ) I , f o r i = 1, .", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "U", |
| "sec_num": null |
| }, |
| { |
| "text": ".., n, and A s with languages, w e w i l l c a l l a t r a n s l a t i o n only i f i t pre-T(G2) serves semantics, t h a t i s , T: T(G1) + 2 i s a t r a n s P a t i o n i f f f o r every t r e e t 6 T ( G~) and f o r every t r e e t ' E T ( G~) , i f f r ( t ) = wl...w and m f r ( t t ) = w; ... w', then n t N i s t h e set of non-negative i n t e g e r s . 0 W e will c a l l r f i h i t e l y s p e c i f i e d ( s p e c i f i e d by a f i n i t e set of r u l e s ) i f f the g e n e r a t i n g set T is f i n i t e . F i n a l l y , r is used t o d e f i n e a t r d n s l a t i o n r:", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "U", |
| "sec_num": null |
| }, |
| { |
| "text": "1 - i v ) xi # 0 * f r ( t r ) i = r ( f r ( t ) ), f o r i = 1, ..., n. X i T(Gg)", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "U", |
| "sec_num": null |
| }, |
| { |
| "text": "L(G1) -+ 2 L(%)", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "U", |
| "sec_num": null |
| }, |
| { |
| "text": "as follows:", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "U", |
| "sec_num": null |
| }, |
| { |
| "text": "L e t w \u20ac L(Gl) have syntax trees tl, .... \\. Then - r(w) = { w' 1 3 t ' i n T(G2) and 3 t i n T(G1) such that t'", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "U", |
| "sec_num": null |
| }, |
| { |
| "text": "is a syntax tree of w' and t i s a syntax tree of w and I f such a g e n e r a t i n g set T and f u n c t i o n s i and ; can be found, t h e job i s f i n i s h e d , s i n c e i t can then be shown t h a t t h e f u n c t i o n T defined by i and ; i s a t r a n s l a t i o n .", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "U", |
| "sec_num": null |
| }, |
| { |
| "text": "The procedure begins with t h e set Tp of production t r e e s o f G which 1' is indeed a f i n i t e generating s e t f o r T(G1) a I f t h e procedure can f i n d a ?? t r a n s l a t i o n \" for each t i n T i t w i l l be successful, and w i l l h a l t and P , output T, , and ; . The procedure s y s t e m a t i c a l l y p i c k s successive t r e e s t 0 i n T and searches T(G ) f o r a semantically e q u i v a l e n t tree t;) whose fron-P 2 t i e r i t can roatch up by some r u l e x. If i t f i n d s one, i t o u t p u t s the @a d e f i n i t i o n ;(to) = (tb, x ) , d e l e t e s t from T and tries one of t h e remain-0 P i n g trees. If i t succeeds in exhausting T i t i s s u c c e s s f u l .", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "U", |
| "sec_num": null |
| }, |
| { |
| "text": "Suppose, however, t h a t f o r some to i n Tp, t h e procedure can't find a \" t r a n s l a t i o n \" in T(G2). Then i f w e assume t h a t 7 does exist, i t must be", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "P'", |
| "sec_num": null |
| }, |
| { |
| "text": "t h e case t h a t t i s p a r t of a l a r g e r t r e e ( o r of each of a set of larger 0 trees) which can be \" t r a n s l a t e d \" .", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "P'", |
| "sec_num": null |
| }, |
| { |
| "text": "Furthermore , n o t c o n t a i n i n g t which i s a f i n i t e", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "P'", |
| "sec_num": null |
| }, |
| { |
| "text": "generating set f o r T(G ) -{ t o } . It cannot be t h e case t h a t t h e f r o n t i e r 1 of to is a s e n t e n c e i f we a l s o assume t h a t t h e e x i s t i n g ' ; i s t o t a l on il So, l o s i n g t o from T(G ) cannot delete any s e n t e n c e s from the 1 lang,uage r e p r e s e n t e d by T(G1).", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "O S", |
| "sec_num": null |
| }, |
| { |
| "text": "The procedure takes t h e set T as a new 1 g e n e r a t i n g s e t t o work w i t h and b e g i n s a g a i n . I t turns o u t t h a t f i n d i n g T depends heavily an t h e sequence i n which s u c c e s s i v e trees a r e chosen f o r t r a n s l a t i o n a t t e m p t s . Therefore, t o guarantee t h a t T will be found if i t e x i s t s , the procedure tries all possi b l e sequences af t r e e s . The procedure has t h e g e n e r a l s t e u c t u x e of a S e t i t Ci.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "O S", |
| "sec_num": null |
| }, |
| { |
| "text": "Define the ( f i n i t e ) set of trees ", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "O S", |
| "sec_num": null |
| }, |
| { |
| "text": "I f t h e execution of 11 step 3 returns success\", then r e t u r n \"success\". I f s t e p 3 r e t u r n s \" f a i l \" , then pick t h e next t i n Ti and execute step 3 againr If step -3 returns \" f a i l \" for all t in Ti, then return \"fail\".", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "O t h e w i s e execute step 3 f o r each t \u20ac T i '", |
| "sec_num": null |
| }, |
| { |
| "text": "step 3: Execute search.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "O t h e w i s e execute step 3 f o r each t \u20ac T i '", |
| "sec_num": null |
| }, |
| { |
| "text": "If search returns \"fail\" then execute expand. If expand returns \"fail\" then return \"fail\" t o step 2.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "O t h e w i s e execute step 3 f o r each t \u20ac T i '", |
| "sec_num": null |
| }, |
| { |
| "text": "If either search or expand returns success\" then return 1 I If s t e p 2 returns fail\" return \"fail\" t o step 3.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "I I", |
| "sec_num": null |
| }, |
| { |
| "text": "expand: rn Let Dam(;) denote the domain of t h e c u r r e n t v e r s i o n of the f u n c t i o h ?, i . e . , ~orn(?) = { t I ? i t ) has been defined bysome execution of s e a r c h i n t h e c u r r e n t p a t h of t h e search tree). L e t T$' denote t h e ( f i n i t e ) s e t (T. U ~o m ( i ) ) . Define i 1 t h e set T t o be t h e s m a l l e s t s e t of trees which i s a g e n e r a t i n g t s e t f o r (gen(~;) -I t ) ) , and which c o n t a i n s t h e set (TI -It}). Then when t h e PROCEDURE h a l t s , s i n c e T i s t o t a l on (T(G,) -E x c~) , i t Since t \u20ac gen om(;)), t can b e w r i t t e n a s t [ t . . . t ] where t o C om(;) 0 1 m and each of the t r e e s t . . , , t C g e n (~o m ( i ) ) . Let ; ( t o ) = (tb, xl. . .X ) .", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "I * maxs Test each tree t ' i n T t t o s e e i f i t s a t i s f i e s each of the", |
| "sec_num": null |
| }, |
| { |
| "text": "Then fram t h e d e f i n i t i o n of T , ~( t ) Thus r i s a t r a n s l a t i o x .", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1' m n", |
| "sec_num": null |
| }, |
| { |
| "text": "F i n a l l y , as w e showed in S e c t i o n 2 , s i n c e T i s a t r a n s l a t i o n (on the.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1' m n", |
| "sec_num": null |
| }, |
| { |
| "text": "syntax trees), r is a t r a n s l a t i o n (on t h e languages). given a s e n t e n c e w i n 7 L 1'", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1' m n", |
| "sec_num": null |
| }, |
| { |
| "text": "The p a r s e r produces a p a r s e tree t < w ) f o r w. ( I f w i s s y n t a c t i c a l l y ambiguous, t h e p a r s e r may produce all t h e p a r s e t r e e s of w.) I f t(w) i s i n t h e domain of tihe f u n c t i o n T d e f i n e d by t h e tree mapper, t h e tree mapper w i l l produce ~( t ( w ) ) whose f r o n t i e r i s a s e n t e n c e u i n L 2 '", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1' m n", |
| "sec_num": null |
| }, |
| { |
| "text": "r --- - -1", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1' m n", |
| "sec_num": null |
| }, |
| { |
| "text": "t r a n s f o r m a t i o n TRANSLATOR --------------F i g u r e 1. T r a n s l a t o r g e n e r a t o r and t r a n s l a t o r .", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1' m n", |
| "sec_num": null |
| }, |
| { |
| "text": "The importance of t h e argument t h a t the f u n c t i o n d e f i n e d By t h e PROCEDURE is a t r a n s l a t i o n , i s just t h a t w and u are guaranteed t o have t h e sgne meaning. i f they are unambiguous, and i f thev are ambiguous, w and u are guaranteed t o have meanings i n common -i . e . , t h a t u is, a bona f i'de -t r a n s l a t i o n of w, i n t h e o r d i n a r y s e n s e of t h e word The u s e f u l n e s s of such a method of t r a h s l a t i n g i s t h a t the generator, which has t o c o n s i d e t a l l i s s u e s of syntax and semantics, and t h e r e f o r e runs very slowly, need o n l y run once. The t r a n s l a t o r which it produces should run very f a s t , s i n c e , o t h e r than p a r s i n g , i t bhly has t o transform trees according t o t h e f i n i t e set of rules i n t h e t r e e transformation t a b l e ( t h e funct\"ion ;). No seman&c computing i s r e q u i r e d a t t r a n s l o t o t r a n s l a t i o n . A l l t h a t i s needed i s t o assume t h a t i f a symbol appears i n both semantics, i t r e p r e s e n t s t h e same semantic e n t i t y i n each, whatever that e n t i t y is. For example, consider t h e two t r e e s i n the t r a n s l a t i o n involving \"+\". Let t = S<S%O<+>>, and t ' = E<EO<+>T<F<(E)>>>.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1' m n", |
| "sec_num": null |
| }, |
| { |
| "text": "A l l we need t o know i s t h a t @(t) : (g(tl>, and i t t u r n s o u t we can f i n d + t h a t out without computing f :", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1' m n", |
| "sec_num": null |
| }, |
| { |
| "text": "t h a t , (g(t) : + ( t l ) .", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1' m n", |
| "sec_num": null |
| }, |
| { |
| "text": "Consider now the translation of ABC+*. The following shows that 3 0 -T(ABc+*) = A*(w(c)):", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1' m n", |
| "sec_num": null |
| }, |
| { |
| "text": "F T C F I I I A F 1 ( E l 1 TRANSLATION I1 ( E x p l i c i t * to i m p l i c i t *)", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1' m n", |
| "sec_num": null |
| }, |
| { |
| "text": "This translation i s i n t e r e s t i n g because i t shows t h e procedure has the a b i l i t y t o \"iiiscover\" that a word (*) i n L(C1) has no translation.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1' m n", |
| "sec_num": null |
| }, |
| { |
| "text": "But ,it can findsa phrase form involving that word which can b e translated to a phrase f o m in L(G2).", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1' m n", |
| "sec_num": null |
| }, |
| { |
| "text": "Explicit *: The translation is specified by:", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1' m n", |
| "sec_num": null |
| }, |
| { |
| "text": "E -t EOE x2(xI,", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1' m n", |
| "sec_num": null |
| }, |
| { |
| "text": "Note t h a t t o \"discover1' t h i s t r a n s l a t i o n , t h e procedure must' b e a b l e t o + compute t h e f u n c t i o n f , s i n c e i t needs t o know t h a t 2 = 1+1. Consider, fat example, @(S<2>) (~~ 2 ", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1' m n", |
| "sec_num": null |
| }, |
| { |
| "text": "TRANSLATION IV (1 ,+ t o 2 ,+)", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1' m n", |
| "sec_num": null |
| }, |
| { |
| "text": "Suppose t h e procedure were asked t o t r a n s l a t e from L(", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1' m n", |
| "sec_num": null |
| }, |
| { |
| "text": "G ) t o L(G ) i n 2 1", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1' m n", |
| "sec_num": null |
| }, |
| { |
| "text": "t h e previous examplei . e . , from t h e i n t e g e r s t o the even i n t e g e r s . It would never h a l t , but i t would \"discover\" t h a t t h e phrase \"1 + 1\" is t o be t r a n s l a t e d a s t h e word \"2\", \"1 give the f u n c t i o n s ; and ; which d e f i n e t h i s p a r t i a l t r a n s l a t i o n . compute an i n v e r s e t r a n s l a t i o n and g e t anything l i k e t h e original. That i s , if one $ t a r t s with sentence w i n L and t r a n s l a t e s t o w i n L2, then 1 t r a n s l a t e s w ' t o w\" back in L one would l i k e f o r -w and w\" t o have the 1' same meaning. But the scutt1ebut.t says i t i s n ' t s o , and t h i s model shows why. Note t h a t all t h a t is r e q u i f e d f o r T: L2 Ll + 2 t o B e a t r a n s l a t i o n is t h a t i f w' i s a tran&@ion of w, then pl(w) f l v 2 ( w t ) # fl, i . e . , t h a t t h e source sentence and i t s t r a n s l a t i o n have some commo' n meaning. Now --r L suppose T': L -+ 2 1 i s a l s o a t r a n s l a t i o n and t h a t w\" E r'(wl). Then we 2 have pl(w) n y ( w f ) # 0 and -y (wi!) n u (w\") # 0, but 3t does n o t follow 2 2 1 ---that u1(w) n b1(w1') @. I n ~d e r t o g e t back t o the o r i g i n a l meaning, each t r a n s l a t o r must produce the e n t i r e s e t ~( w ) , r a t h e r than j u s t some sentence i n T (w), and then a l l of these must be r e t r a n s l a t e d i n e n t i r e t y .", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1' m n", |
| "sec_num": null |
| }, |
| { |
| "text": "+ 1 + 1 + I\" a s \"2 + 2\",", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "1' m n", |
| "sec_num": null |
| }, |
| { |
| "text": "T r a n s l a t i o n programs don' t u s u a l l y do t h a t . Neither do human t r a n s l a t o r s , f o r t h a t matter! A l t e r n a t i v e l y , t h e t r a n s l a t o r should be a b l e t o give with the t r a n s l a t i o n , its p a r s e and t h e atomic morphemes a s s o c i a t e d w i t h t h e sentence. The 7rocedure i n t h i s paper provides f o r doing t h a t .", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Conclusion and Further Research.", |
| "sec_num": "5." |
| }, |
| { |
| "text": "The same d e f i n i t i o n of t r a n s l a t i o n , i f i t i s a c c u r z t e , a l s o explains another phenomenon of language t r a n s l a t -i o n -haw i t i s t h a t two very d i f f e r e n t t r a n s l a t i~n s can corn from t h e same source. If w t and w\" are t r a n s l a t i o n s o r w, then we have ul(w) n p2(wt) f (b and ul(w) fl u2Cwff) C fi, but i t doe; not follaw t h a t p 2 (~' ) fl v2(wvt) # 8 -", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Conclusion and Further Research.", |
| "sec_num": "5." |
| }, |
| { |
| "text": "For n a t u r a l language, one would l i k e t,opexte i t h e theory in t h i s paper t o a r b i t r a r y phrase s t r u c t u r e grammars and t o t r a n s f o r m a t i o n a l grammars. The ewlarlsion t o transformational gramanrs r e q u i r e s only", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Conclusion and Further Research.", |
| "sec_num": "5." |
| }, |
| { |
| "text": "The \" l o r e \" has i t t h a t someone f e d . t h e following sentence t o a t r a n s l a t o r from L t o Lp: 1 \"The s p i r i t indeed i s will-ing, but t h e f l e s h i s weak.\"", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "3-", |
| "sec_num": null |
| }, |
| { |
| "text": "Then lie took t h e t r a n s l a t i o n and fed i t i n t o a t r a n s l a t o r froui L, t o L LI, and g o t :", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "3-", |
| "sec_num": null |
| }, |
| { |
| "text": "\"The l i q u o r i s a l l r i g h t , but t h e meat i s s p o i l e d . \" f o r m a l i z i n g t h e n o t i o n of t h e transform p f a semantic f u n c t i o n t o be a s s o c i a t e d w i t h each syntax transformation. (For t r a n s f o r m a t i o n a l semantic t h e o r i e s which do n o t allow semantic change i n t h e t r a n s f o r m a t i o n s , t h e e x t e n s i o n t o a r b i t r a r y phrase s t r u c t u r e grammars i s s u f f i c i e n t , of course.) There are, of course, schemes f o r t r a n s l a t i o n other than: t h e one i n t h i s paper. One might t h i n k of computing t h e meaning of a source sentence, and then having some e f f e c t i v e way of g e n e r a t i n g the target s e n t e n c e d i r e c t l y from the meaning. The scheme i n t h i s paper, however, i s more a t t r a c t i v e a t present than such a \" d i r e c t \" scheme, for t h r e e reasons: 1 ) It i s i n t u i t i v e l y s a t i s f y i n g . I b e l i e v e I t r a n s l a t e by f i r s t t r a n s l a t i n g simple p h r a s e s and then p u t t i n g their s e p a r a t e t r a n s l a t i o n s together according t o some r e s t r u c t u r i n g r u l e s t h a t are guaranteed t o p r e s e r v e seaantics . Thus, one \"builds up\" t h e t r a n s l a t i o n of a sentence r e c u r s i v e l y . I a m more l i k e l y t o c a l l t h e r e s u l t which I g e t by f i r s t computing t h e whole meaning and t h e n producing a sentence (often it i s a sequence of s e n t e n c e s ) with t h e same meaning, a \"paraphrase\" l I o r an i n t e r p r e t a t i o n \" , r a t h e r than a t f t~a n s l a t i o n \" . 2) I f used much, thss scheme i s l i k e l y t o be more e f f i c i e n t than t h e \" d i r e c t \" scheme, since n o -s e m a n t i c computation i s r e q u i r e d a t t r a n s l a t e t-ime. AJl the semantic problems are examined once and for a l l i n t h e t r a n s l a t o r g e n e r a t o r ; a t t r a n s l a t i o n t i m e , only a sequence of t r e e mappings i s performedsimply a s t r u c t u r e matching and r e p l a c i n g technique. 3) The \" d i r e c t \" scheme r e q u i r e s knowing how to specify l i n k u i s t i c d e s c r i p t i o n s i n such a way that, given a meaning i n semantic n o t a t i o n , one can produce a sentence having t h a t meaning. This problem Ts a d i f f i c k l t one not y e t w e l l understood.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "3-", |
| "sec_num": null |
| }, |
| { |
| "text": "The", |
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| "ref_spans": [], |
| "eq_spans": [], |
| "section": "3-", |
| "sec_num": null |
| }, |
| { |
| "text": "Presumably, the research c u r r e n t l y under way i n t h e f i z l d of g e n e r a t i v e semantics w i l l e x p l i c a t e the i s s u e s involved.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "3-", |
| "sec_num": null |
| } |
| ], |
| "back_matter": [], |
| "bib_entries": { |
| "BIBREF0": { |
| "ref_id": "b0", |
| "title": "Syntax and semantics: a categorial view", |
| "authors": [ |
| { |
| "first": "D", |
| "middle": [ |
| "B" |
| ], |
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| "FIGREF0": { |
| "num": null, |
| "uris": null, |
| "text": "D e f i n i t i o n 1 (phrase-structure semantics) 6", |
| "type_str": "figure" |
| }, |
| "FIGREF1": { |
| "num": null, |
| "uris": null, |
| "text": "cfg and phrase-s t r u c t u r e semantics) 7 D e f i n i t i o n of semantic f u n c t i o n s 4: T(G) -+ CP . a . a . . . . 8 U D e f i n k t i o n o f meaning function;: L(G) + 2 . . . . . . . . 9 2 . T r a n s l a t i o n s as Tree Mappings . . . . . . . . . . . . . . . . 12 Dgfinition of general translation r: L(G1) + 2 L(G.2) . . . . 12 D e f i n i t i o n o f g e n C T ) . . . . . . . . . . . . . . . . . . . . 13 Example2 (gen(T)) . . . . . . . . . . . . . . . . . . . . . 13 D e f i n i t i o n of translatioh r: T(G ) -t 2 T (G2) . . . . . . . . 14 LCG2) Definition of t r a n s l a t i o n 7: L(G1) + 2 . . . . . . . . Example 3 ( f i n i t e l y s p e c i f i e d translation) . . . . . . . . . 3 . A Procedure f o r Finding Translations (Usually) . . . a . a . . PROCEDURE . . . . . . . . . . . . . . . . . . . . . . . . . Proof t h a t the function defined by PROCEDURE is a . . . translatiotl .", |
| "type_str": "figure" |
| }, |
| "FIGREF2": { |
| "num": null, |
| "uris": null, |
| "text": "Translator Generator and Translator . t o Precedence Infix) . . . . . . . . 27 TRANSLATION XI (Cxpliclt * t o I m p l i c i t *) . . . . a . m . .", |
| "type_str": "figure" |
| }, |
| "FIGREF3": { |
| "num": null, |
| "uris": null, |
| "text": "+) . . . . . . . . . . . . . . . .", |
| "type_str": "figure" |
| }, |
| "FIGREF4": { |
| "num": null, |
| "uris": null, |
| "text": "Conclusion and FurtherResearch . . . . . . . . . . . . .", |
| "type_str": "figure" |
| }, |
| "FIGREF5": { |
| "num": null, |
| "uris": null, |
| "text": "and 2) the meaning of a phrase i s a function of i t s s y n t a c t i c s t r u c t u r e and of t h e meanings of i t s c o n s t i t u m t s . Keeping i n mind t h a t a function is nothing but aq assignment of elements i n i t s csdemain t o elements i n its domain, t h i s d e f i n i t i o n w i l l provide for idiomatic and emotive meaning, as well as denotative or referential meaning, provided such meanings are s p e c i f i e d i n t h e universe of di,scourse. I wish t o add before giving the d e f i n s t i o n t h a t , although I have never seen i t i n t h i s form before, I do not b e l i e v e t h i s d e f i n i t i o n of semantics i s o r i g i n a l w i t h me. I believe i t incorporates the notions of semantics i n", |
| "type_str": "figure" |
| }, |
| "FIGREF6": { |
| "num": null, |
| "uris": null, |
| "text": "p h r a s e -s t r u c t u r e semantics f o r G i s a 7 b t u p l e d = (u, M, u, X, A, F, R), where: U i s a s e t , t h e u n i v e r s e of d i s c o u r s e , T T Mc 2\" i s a f i n i t e set of atomic morphemes, M p : V + 2 i s the vocabulary meaning function,", |
| "type_str": "figure" |
| }, |
| "FIGREF7": { |
| "num": null, |
| "uris": null, |
| "text": ") f o r some i n t e g e r n , R A is a f i n i t e set of n b e s of p a r t i a l r e c u r s i v e f u n c t i o n s , F i s a f i n i t e s e t of d e f i n i t i o n s f o r t h e p a r t i a l r e c u r s i v e f u n c t i o n s named i n A, R is a finite set of semantic r u l e s , with the p r o p e r t y that t o each grammar r u l e A -t B . . .B t h e r e i s assigned one 1 n semantic r u l e , having t h e form r A + B1. . .B (xl,*..,X ~l = P , n + where p \u20ac (M U X U A) , and r A + B1. .B ( x~,~~~, x n 1 = P n s p e c i f i e s a p a r t i a l r e c u r s i v e f u n c t i o n :", |
| "type_str": "figure" |
| }, |
| "FIGREF8": { |
| "num": null, |
| "uris": null, |
| "text": ", Z, P, S), and d = (U, M, , X, 4, F, R ) , where: semantics v = {S, I, +) + U = N U {f } U { I } , where:", |
| "type_str": "figure" |
| }, |
| "FIGREF9": { |
| "num": null, |
| "uris": null, |
| "text": "indeed s p e c i f y a r e c u r s i v e 2 1 3 function on v ( S ) xu(+) xv(S) -+ v ( S ) , s i n c e i f x, and x, are i n p(S) = N and if", |
| "type_str": "figure" |
| }, |
| "FIGREF10": { |
| "num": null, |
| "uris": null, |
| "text": "For example, t h e tree -A is denoted a<b<de>c>, and i t h a s a l l t h e following non-standard representat i o n s : a<bc> [b<de>c], a<b<de> c> [dec] , and a[a<bc>] [ b < d e > c L A s t h e r e a d e r can see, t h e \"box n o t a t i o n \" i s u s e f u l f o r i s o l a t i n g any rooted s u b t r e e . I n p a r t i c u l a r , n o t e t h a t S<S+S> [s<I>+s<I>] i s t h e syntax tree S<S<I>+S<I>> of t h e grammar of Example 1, with its dominating s u h t r e e S<S+S> i s o l a t e d . Now back t o t h e semantics. The semantic rules R are used t o define a f u n c t i o n 4 on t h e trees of t h e grammar which a s s i g n s t o each syntax tree t a semantic f u n c t i o n 4(t).", |
| "type_str": "figure" |
| }, |
| "FIGREF11": { |
| "num": null, |
| "uris": null, |
| "text": "The f u n c t i o n @:T(G) + @ a s s i g n s t o each t i n T(G) a semantic f u~c ti o n $ ( t ) on IJ(B~)x*.~x~(B ) + p ( r t ( t ) ) , where B1...B = f r ( t ) . To s name of t h e f u n c t i o n , (xl,. . . ,x ) i s the v e c t o r o f arguments, D i s t h e n domain, and C is t h e codomain.", |
| "type_str": "figure" |
| }, |
| "FIGREF12": { |
| "num": null, |
| "uris": null, |
| "text": "$ i s defined by t h e following i n d u c t i v e d e f i n i t i o n : t T(G) is t h e s e t of syntax t r e e s ( p a r t i a l and complete) of G.", |
| "type_str": "figure" |
| }, |
| "FIGREF13": { |
| "num": null, |
| "uris": null, |
| "text": "t h e semantic f u n c t i o n assigned t o each t r e e t i s t h e composit i o n of t h e semantic functions assigned t o t h e s u b t r e e s of which t i s composed. W e leave i t t o t h e reader t o v e r i f y t h a t $ i s well-defined.The meaning function p on sentences i s a s p e c i a l case of t h e meaning function v on a l a r g e r domain -t h e s e t of phrase forms of t h e grammar.", |
| "type_str": "figure" |
| }, |
| "FIGREF14": { |
| "num": null, |
| "uris": null, |
| "text": "function $ i s used t o d e f i n e t h e meaning function as follows. The u function p:P(G) + 2 i s defined by t h e following rule: Let w = w . . O W be 1 n a phrase form i n P (G) and l e t w have syntax trees tl, . . . , t . Then the m set of tueanings of w i s t h e set L(G), t h e language of G, i s a subset of P(G) , s o t h e meaning f u n c t i o n on.", |
| "type_str": "figure" |
| }, |
| "FIGREF15": { |
| "num": null, |
| "uris": null, |
| "text": "sentences, p:L(G) + 2 , i s j u s t the r e s t r i c t i o n of p t o L(G) .", |
| "type_str": "figure" |
| }, |
| "FIGREF16": { |
| "num": null, |
| "uris": null, |
| "text": "Since t h e t h r e e functions v, y, and II have d i s j o i n t domains, they can never be confused, s o w e s h a l l w r i t e v f o r all t h r e e . ) . I i s the meaning function, which assigns t o each sentence, phrase form, and symbol, one o r more meanings according t o the semantics d .Thus, we are assigning meaning t o a sentence by assigning t o i t t h e meanbgs which a r e computed by the semantic functions specified by i t s phrase s t r u c t u r e s , taking a s a r g u~ ments t h e meanings of t h e c o n s t i t u e n t s of t h e sentence. T h e most elementary c o n s t i t u e n t s of a sentence a r e the members of C which c o n s t i t u t e i t . One .may think of these as the l e x i c a l items of the language. Their meanings, wMch a r e t h e arguments of t h e semantic function, a r e among the morphemes of t h e language -those morphemes which cannot be furthe-r separated i n t o morphemes ( t h i s i s the s e t of \"atomic morphemes\", M) . Thus, the meaning of a sentence i s a function of i t s morphemes. l h i c h function t o use tq", |
| "type_str": "figure" |
| }, |
| "FIGREF17": { |
| "num": null, |
| "uris": null, |
| "text": "meaning oE w i s 4 (t) (P (I), P (+I, P (I), IJ (+.I, P ( I ) ) . F o r notational purposes, l e t tl, tq, 3, and t 4 be t h e s u b t r e e s of t c i r c l e d i n the p i c t u r e . Now compute this member o f P (w) : Note that \"I + I + I\" a l s o has t h e syntax tree b u t t h e sentenge i s n o t s e m a n t i c a l l y ambiguous since 2 . Translation9 A s Tree Mappings.", |
| "type_str": "figure" |
| }, |
| "FIGREF18": { |
| "num": null, |
| "uris": null, |
| "text": "algorithm f o r computing t h e trans lati011 of any sentence. This s e c t i o n p r e s e n t s th2 bethod f o r giving the f i n i t e s p e c i f i c a t i o n of T and the algorithm f o r computing t h e t r a n s l a t i o n . I n f a c t , i n s t e a d of s p e c i f y i n g a t r a n s l a t i o n on the languages, we s p e c i f y a t r a n s l a t i o n on t h e t r e e s of t h e syntaxes.To make p r e c i s e what i s meant by \" t r a n s l q t i o n s which a r e s p e c i f i e d by a f i n i t e set of r u l e s \" we Sntroduce t h e concept of a generating set f o r trees. Let T and T2 be two sets bf trees with l a b e l s from some alphabet 1 0 C. Define the set T t o be t h e s e t of all t r e e s w i t h single nodes and C l a b e l s from g, i . e . , = { a I a E E}. Informally, T i s a generating. set 1 0 f o r T j u s t i n case every tree i n T7 i s e i t h e r i n T o r i s constructed of a 2 -C f i n i t e number of trees of T and j u s t i n case every t r e e s o constructed is 1' in T t . Formally, l e t T be a s e t of trees w i t h l a b p l s from Z. The set gen(T) of trees generated by T is defined inductively %as fol'lows: 0 0) TI: -C gen(7) and Tc gen(T), 1) tO[tl.. . t ] E gen(T) if i t i s defined, n for a l l p o s i t i v e integer$. n , and for all trees to, , ..., t \u20ac gen(T). n T i s a generating s e t for gen(T). We leave i t to the reader to verify that every tree i n gen(T) can be written in the f orin to [ tl. . . t ] , where n n t \u20ac (T U T;) and each ti \u20ac gen(T), f o r i = 1, . . . . st. Example The s e t of production.trees of a cfg i s a generating set for the set of all the syntax trees of the grammar. L e t G = (V, C, P, S ) , l e t P of production t r e e s of G i s the .set The set T(G) of a l l syntax t r e e s of G i s the s e t gen(T,). A s a more concrete example, consider the cfg G given by the following Tp i s the s e t { S<OS>, S<B2, B<O>, Bcl> 1, or written p i c t o r i a l l y : T(G) = gen(Tp) contains all trees of the following forms:The tree t = S<OS<OS<B>>> i s 111 T(G) = gm(Tp) s i n c e t = S~O S~[ O S~O S~B~~}", |
| "type_str": "figure" |
| }, |
| "FIGREF19": { |
| "num": null, |
| "uris": null, |
| "text": "Then we d e f i n e the funktion r: T(G1) + 2 by t h e following i n d u c t i v e d e f i n i t i o n :0) t \u20ac T -r ( t ) = t , where ;(t) = (t', x).where i) ;(to) = (T ( t o ) , XIa t t h e codomain of T i s the power set of T(G2) because t h e r e may be t r e e s i n T(G ) whose n o n -t r i v i a l f a c t o r i n g s into t [ t . . . t ] a r e n o t unique.", |
| "type_str": "figure" |
| }, |
| "FIGREF20": { |
| "num": null, |
| "uris": null, |
| "text": "e s e t r e e s , ~( t ) = { +(t 0 [ t 1 . . . t m ] ) 1 t O [ t l . . . t 1 is a r e p r e~e n t a t i m m of t ).", |
| "type_str": "figure" |
| }, |
| "FIGREF21": { |
| "num": null, |
| "uris": null, |
| "text": "t t \u20ac ~( t ) I. It follows from t h e d e f i n i t i o n s t h a t 7 i s a t r a n s l a t i o n i f r i s . To see thtis, l e t w = wl.. .w and w' = wi m. . .w' and l e t w' E T(w). Then there exist n sy&tax trees t of w and t ' of w' such t h a t t ' C df). L e t = @(t)(ul(wl)9\".9u 1 (w m ) ) and E 2 = ( t f ) ( 2 , . . , 2 ( w ) .Then from t h e d e f i n i t i o n of 11, c1 1) = ( w ) I\u00a3 r is a G II (w) and c2 ----t r a n s l a t i o n , t h e n fl E2 # 0, so <(w) f l V~( T ( W ) ) 0, and s o r i s a t r a n s l a t i o n .", |
| "type_str": "figure" |
| }, |
| "FIGREF22": { |
| "num": null, |
| "uris": null, |
| "text": "The f u n c t i o n s ; and i a r e t h e method f o r s p e c i f v i n g t h e function r.The s p e c i f icati.cn i s f i n i t e j u s t i n case t h e generating set T i s f i n i t e .The i n d u c t i v e d e f i n i t i o n f o r Tgives the algorithm f o r computing t h e tpansl a t i o n of any tree in T(G ) , and the definition of y, t o g e t h e r w i t h t h i s 1 algorithm and a g e n e r a l c o n t e x t f r e e p a r s e r such as Floyd's o r E a r l y ' s algorithm, g i v e s the algorithm f o r computing t h e t r a n s l a t i o n of any sentence in L(G ) . The next example illustrates. 1 (In t h e following and i n a l l subsequent examples, w e s h a l l give ex-p l i c i t l y only the grammar r u l e s , t h e right-hand s i d e of t h e semantic r u l e s , t h e universes o f discourse, the meaning function, and those d e f i n i t i o n s of p a r t i a l recursive f u n c t i o n s t h a t are necessary. The r e a d e r can e a s i l y determine t h e rest of t h e s p e c i f i c a t i o n s f o r t h e grammars and semantics, i f he wishes. For c f g ' s we s h a l l follow t h e u s u a l convention t h a t a l l symbols which do n o t appear on t h e left-hand side o f some grammar r u l e are terminal symbols, and t h a t t h e axiom i s the f i r s t symbol appearing in t h e f i r s t rule. ) Example 3. W e present two c f g ' s and their semantics, and a finitely specified translation T on T(G ) + 2 1 T(G2) . To h e l p the intuition, consider that G , 1 describes well-parenthesized subtract ion expressions, and G2, presents us with two cfg's G and G and t h e i r 1 2 r e s p e c t i v e semantics and d2. Suppose also that a f i n i t e l y s p e c i f i e d 1 translation froq T(G1) t o T(G2) e x i s t s . Can w e find i t ? That i s , can we produce t h e f l n i t e s e t ofr r u l e s a e f i n i n g t h e f u n c t i o n s ? and ; ? Xn this s e c t i o n we consider a procedure which a c c e p t s two a r b i t r a r y c f g ' s and t h e i r phrase s t r u c t u r e semantics and tries t o f i~d a descript i o n of such a t r a n s l a t i o n . The procedure may n o t always work, i n thata i t may n o t h a l t o r t h e Function T i t d e s c r i b e s may.be only p a r t i a l . Kt T i s guaranteed t o be c o r r e c t ; t h a t i s , t h e d e f i n i t i o n s of i and ; pro-duced s p e c i f y a p a r t i a l f u n c t i o n r: T(G,.) + 2 T(G2) which i s a t r a n s l a t i o n A in t h e sense t h a t , f o r any t \u20ac T(G ), i f ~( t ) i s defined then ~( t ) i s a 1 t r a n s l a t i o n of t. F i r s t , t h e procedure i s presented; then we g i v e t h e arguments t h a t t i s 3 ( p a r t i a l ) t r a n s l a t i o n .I n t u i t i v e l y , t h e procedure works as follows: W e t r y t o f i n d a f i n i t e generatiog set T f o r T(G1) and a p a i r of f u n c t i o n s i: V N q + V and + T(G2) x Nwhich have the p r o p e r t y that f o r every t r e e t E T, i f ) = ( t , x , then t and t ' r e p r e s e n t t h e same semantic function. by to and t; r e p r e s e n t t h e same semantic function\" is i u s t t h i s :-I f ;(to) = C t & 5 ...x ) then 4 ( t O ) (~1 , e a m s~m ) = 4 ( t b ) (~i , a a a~' ) , n n provided y ' = i I n g e n e r a l , t o g e t semantic equivalence, one has t o be c a r e f u l how the s y n t a c t i c v a r i a b l e s on t h e f r o n t i e r of t a r e a s s o c i a t e d by t h e s t r i n g x 0 with t h e s y n t a c t i c v a r i a b l e s on t h e f r o n t i e r of t;), s i n c e these r e p r e s e n t p o s s i b l e t r e e s with mceming, and hence t h e domains of t h e semantic f w ct i o n s f o r t and t' 0 0 '", |
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| "FIGREF23": { |
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| "text": ", i f w e a l s o assume t h a t r i s f i n i t e l y s p e c i f i e d , this s e t i s f i n i t e . Thus, the procedure tries t o c o n s t r u c t a new set of trees, T1", |
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| }, |
| "FIGREF24": { |
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| "text": "I1 t r e e search\", and i s r e p r e s e n t e d by the s e a r c h t r e e p i c t u r e d . below. Each node i n t h e t r e e r e p r e s e n t s a subprocedure which i s d e s c r i b e d below the tree. -F Given two reduced c f g ' s G and G and t h e i r r e s p e c t i v e phrase-1 2 s t r u c t u r e semantics J1 and J2,, execute t h e s e a r c h tree below f a r a14 i n t e g e r p a i r s ( m a x i , m a x s ) = (1, 11, (1, 21, (2, 11, (2, 2), ... . I f f o r I t any p a i r s t e p 1 halts and o u t p u t s success\", then h a l t . t Reduced in t h e sense t h a t each nonterminal symbol i s d e r i v a b l e from t h e axiom an'd derives t e m i n a l . s t r i n g s . I t is well-known t h t every cfg rlfm be p u t i n t o t h i s form.", |
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| }, |
| "FIGREF26": { |
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| "text": "Define t h e ( f i n i t e ) set of a l l possible p a r t i a lfunctions . I , i,, ..., ; k } such t h a t f o r each j = 1, 2, ..., k, v + VN, and ;.(S1) = S . a n d f o r all A \u20ac VN e p 2 f o r each f u n c t i o n ; J (i.e., f o r each j = 1, 2, . . . , k). If f o r some j the execution 11 11 of s t e p 2 r e t u r n s success\", then h a l t and o u t p u t success\". If s t e p 2 r e t u r n s \" f a i l \" , i n c r e a s e j and continue. I f s t e p 2 r e t u r n s \"fail\" f o r a . ( i e , f o r a l l j ) , then h a l t and output \" f a i l \" .", |
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| }, |
| "FIGREF27": { |
| "num": null, |
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| "text": "(Nab.. T , is a f i n i t e set)It . If T = (8 then r e t u r n success\".", |
| "type_str": "figure" |
| }, |
| "FIGREF28": { |
| "num": null, |
| "uris": null, |
| "text": "If i > maki t h e n return \" f a i l t t .", |
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| }, |
| "FIGREF29": { |
| "num": null, |
| "uris": null, |
| "text": "the first (maxs) trees of T(G2) : T~ = {ti, ti, m e a , t'", |
| "type_str": "figure" |
| }, |
| "FIGREF30": { |
| "num": null, |
| "uris": null, |
| "text": "is a string of non-negative integers x = x x . . of the following i s true: b) xi # O = , f r ( t t ) i = ;(fr(t) ) for i = 1, t r e e t ' exists i n T', then return fail\" t o step 3. If such a tree t t does exist i n T' then define ;(t) = ( t t , x) s e t J . + i+l define the set T i = (Ti-lit)) execute a new version o f step 2. I I I1 If step 2 returns success\" return success\" t o step 3.", |
| "type_str": "figure" |
| }, |
| "FIGREF31": { |
| "num": null, |
| "uris": null, |
| "text": "i (Note t h a t Tt does n o t c o n t a i n t.) I I I f T i s n o t f i n i t e , r e t u r n f a i l \" t o s t e p 3 . t S e t i + i+l. S e t T + Tto i Execute a new v e r s i o n of s t e p 2.", |
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| }, |
| "FIGREF32": { |
| "num": null, |
| "uris": null, |
| "text": "t e p 2 r e t u r n s success\" r e t u r n success\" t o s t e p 3.", |
| "type_str": "figure" |
| }, |
| "FIGREF33": { |
| "num": null, |
| "uris": null, |
| "text": "t e p 2 r e t u m s \" f a i l \" r e t u r n f a i l \" t o s t e p 3.END OF PROCEDURENow w e want t o e x p l a i n how t h e PROCEDURI$ d e f i n e s f u n c t i o n s ( p o s s i b l y p a r t i a l f u n c t i o n s ) on T(G1) -+ 2 T(G2) and on L(G6 ) + 2 1 L(G2' , and prove that t h e f u n c t i o n s a r e t r a n s l a t i o n s . W e s h a l l a l s o show t h a t i f t h e PR0CEDZl.G h a l t s , t h e t r a n s l a t i o n i t t o t a l , except under c e r t a i n e a s i l y i d e n t i f i a b l e c o n d i t i o n s . Consider any p a t h i n t h e s e a r c h tree. It looks l i k e t h i s : s defined h e r e .) (To = Tp i s d e f i n e d here.) (; ( t ) = (t' , x) i s d e f i n e d h e r e i f t h e node i s s e a r c h . ) (T1 i s defined h e r e . ) (T i s defined h e r e . ) n W e need t o i d e n t i f y two p a r t i c u l a r s e t s of trees a s s o c i a t e d w i t h t h i s path.Both are f i n i t e . The f i r s t i s t h e domain of t h e f u n c t i o n i, andt h e second i s t h e set of trees \"excluded\" by the s u c c e s s i v e executions of expand. Note that each execution of t h e s u b r o u t i n es e a r c h adds one i t e m t o the d e f i n i t i o n of t h e function, ?, and t h e e n t i r e d e f i n i t i o n of ; i s given by t h e s e t of a l l t h e s e items d e f i n e d by e x e c u t i o n s of s e a r c h i n t h e p a t h . The domain of ?, then, i s t h e set ~orn(;) = {k I ; ( t ) i s defined by some execution o f t h e s u b r o u t i n e s e a r c h i n t h e path}. S i m i l a r l y , each e x e c u t i o n of t h e s u b r o u t i n e expand, i n i t s f i r s t s t e p , d e f i n e s a new set, T t s which daes n o t contain t h e t r e e t . This s t e p has t h e e f f e c t of excluding t h e tree t from any f u r t h e r c o n s i d e r a t i o n i n t h e t r a n s l a t i o n p r o c e s s . The s e t of a l l such trees i s t h e s e t Excl = { t I T i s d e f i n e d by some e x e c u t i o n of t h e t s u b r o u t i n e exclude i n the path}. Wow, t h e s e t om(;) U T ) i s a f i n i t e g e n e r a t i n g set f o r t h e s e t n (T(G1) -Excl), s o t h e f u n c t i o n s i and ? d e f i n e a p a r t i a l f u n c t i o n T : -T ( G~) + 2 T(GZ) according t o t h e d e f i n i t i o n i n Section 2 . Furthermore, if T = b then ; is t o t a l on .the g e n e r a t i n g s e t , and s o T i s t o t a l on n (T (GI) -Excl), and t h i s i s j us t t h e case when t h e PROCEDURE h a l t s . Since Excl i s a f i n i t e s e t , we have t h e r e s u l t that T i s defined on a l l b u t a finite number of elements i n T ( G~) , when t h e PROCEDURE h a l t s .Since T is. a p a r t i a l f u n c t i o n on T(G ) i n i t i o n of 7 i n Section 2 t h a t ? i s a p a r t i a l f u n c t i o n on P(G ) + 2 1 and t h e r e f o r e on L(G1) + 2 L(G*) . Lett P(Excl) denote t h e s e t of f r o n t i e r s of t h e t r e e s of Excl. Note t h a t each member of P(Exc1) i s a phrase form.", |
| "type_str": "figure" |
| }, |
| "FIGREF34": { |
| "num": null, |
| "uris": null, |
| "text": "o t a l on (P ( G~) -P (Excl) ) and on (L(G1) -P (Excl) ) .", |
| "type_str": "figure" |
| }, |
| "FIGREF35": { |
| "num": null, |
| "uris": null, |
| "text": "Thus, i s t o t a l on L(G1) i f PROCEDURE halts and i f none of t h e trees excluded by exclude are complete syntax trees. I f complete syntax trees are excluded, then t h e i r s e n t e n c e s are t h e only ones f o r which 7 i s n o t d e f i n e d .-W e have l e f t only t o show t h a t T i s a t r a n s l a t i o n . The r e a d e r may r e c a l l t h a t t h e r e may be s e v e r a l n o n t r i v i a l f a c t o r i n g s of trees i n t o a form f o r which T i s defined, and t h a t t h i s may lead t o non-unique transl a t i o n s . Furthermore, t h e languages may be semantically ambiguous. These condi.tions make t h e proof t h a t r i s a t r a n s l a t i o n l e s s l u c i d , s o w e s h a l l give h e r e t h e proof f o r t h e case where r i s defined f o r only one f a c t o r i n g of each tree and t h e r e i s no ambiguity. It w i l l be h e l p f u l i n t h e proof t o have t h e following n o t a t i o n : Let t \u20ac T(G1) have f r ( t ) = wl. . .w and l e t m t ' C T(G2) have f r ( t l ) = w i ... w ' . Then by a ( t ) : $ ( t l ) w e mean n Now t o t h e proof. L e t ~( t ) = t ' . W e wish t o show t h a t $ ( t ) r $(tl).", |
| "type_str": "figure" |
| }, |
| "FIGREF36": { |
| "num": null, |
| "uris": null, |
| "text": "t '[ t ' . . . t ' ] , where f o r each 0 1 nFor i n d u c t i ve hypothesis, assume t h a t f o r each j = 1,. . . r E 1, ..., m l e t y = $(t j ( v (W r r 1 jrm1+l * l j r 1 , and f o r i = 1, ..., n l e t y' = $ ( y ! ) ( y (v' i ), . ..,u (w' ) Then, if w e 1 2 kiWl+l ki define j = kg 0 = 0, t h e r e s u l t above demonstrates t h a t Thus, by t h e d e f i l i i g i o n of in s e a r c h ,", |
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| }, |
| "FIGREF37": { |
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| "text": "n programming terminology a g e n e r a t o r i s a program whose i n p u t i s a s e t of parameters and whose o u t p u t i s a s p e c i a l i z e d program (cf Brooks and I I Iverson (1969), p . 365). Then PROCEDURE c o n s t i t u t e s a t r a n s l a t o r generator\": i t s i n p u t i s two c f g ' s and t h e i r a s s o c i a t e d p h r a s e s t r u c t u r e semantics, and i t s o u t p u t i s a t a b l e of tree t r a n s f o r m a t i o n s which \"drives\" a s&andard tree-mapping program. The t r e e mapping program i s designed t obe p a r t of a t r a n s l a t o r system composed of a p a r s e r , t h e tree mapper, and a f r o n t i e r s t r i p p e r (see F i g u r e 1 ) . T r a n s l a t i o n proceeds as follows: Let G and a1 b e t h e cfg and semantics f o r t h e s o u r c e language, L1, and G2 a d the c f g an& semantics f o r t h e t a r g e t language L3. The t r~n s l a t o r is L.", |
| "type_str": "figure" |
| }, |
| "FIGREF39": { |
| "num": null, |
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| "text": "some examples of translations on context free languages. The tree search procedure outlined i n Section 3 i s programmed i n CPS and runs on the IBM ~/370/165 a t Ohio State. A l l of these trans-= real numbers = I R~, R2, Rg, ... 1 = ~f +~ f-, f * , \u00a3'I Meaning function assigning atomic morphemes t o lexicaL items and s v n t a c t i c variables:A1= A2 = {I}, and F1 = F contains j u s t t h e d e f i n i t i o n : I : N + N:~( x ) = x.The reader should be a b l e to f i g u r e o u t , a f t e r readingt h e d e f i n i t i o n i n + * / Section 1, that M l a H 2 = {R, R1, %I R3, F, f , f , f , f 1 and A number of finite s p e c i f i c a t i o n s f a r t r a n s l a t i o n s are possible. One is: It i s i n t e r e s t i n g t o n o t e t h a t the PROCEDURE does n o t have t o know how + * 1 t o corppute t h e f u n c t i o n s f , , f , and f i n order t o discover t h i s", |
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| }, |
| "FIGREF40": { |
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| "text": ") is the language of all addition expressions with 2, i.e., the 1 s e t of a l l strings of the form 2 + 2 + . . . + 2 . L(GZ) i s the s e t of a l l strings of the form 1 + 1 + ... + 1. Under a s t a n d a r d semantics, L(G ) 1 expresses the even i n t e g e r s and L(G ) the integers. The procedure 11 I! 2 \"discovers\" t h a t t h eword 2 in L(G ) must be translated as t h e phrase 1 X = positive integers = 11, 2, . . . ) F1 = F2, which coptains t h e following d e f i n i t i o n", |
| "type_str": "figure" |
| }, |
| "FIGREF41": { |
| "num": null, |
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| "text": "f+(x' ,y) = (f (x, Y)) ' ( ' is t h e successor fn+> I :N + N ( i d e n t i t y ) : I (x) = x", |
| "type_str": "figure" |
| }, |
| "FIGREF42": { |
| "num": null, |
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| "text": "To g e t t h e l a s t s t e p i n t h e e v a l u a t i o n of t h e second semantic f u n c t i o n , t h e procedure must b e a b l e t o + compute f ( 1 , l ) .", |
| "type_str": "figure" |
| }, |
| "FIGREF43": { |
| "num": null, |
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| "text": "e t c . I t wotild d e f i n e a t r a n s l a t i o n which i s t o t a l on t h e s t r i n g s in L(G ) whose v a l u e s 2 a r e even, and i t would continue t o look f0reve.r f o r p o s s i b l e t r a n s l a t i o n s f o r t h e odd-valued s t r i n g s . W e l e a v e i t a s an e x e r c i s e f o r t h e r e a d e r t o", |
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| "FIGREF44": { |
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| "text": "t t h e p r e s e n t time what i s needed more than anything else i n t h e a r e a of language t r a n s l a t i o n i s an understanding of t h e fonnal n a t u r e of semantics, i t s r e l a t i o n t o syntax i n language d e s c r i p t i o n , and i t s r o l e i n t r a n s l a t i o n .I b e l i e v e t h i s paper provides some of t h e b a s i s f o r t h a t understanding. I n c i d e n t a l l y , the r e a d e r might have observed t h a t t h e d e f i n i t i o n of phrase-s t r u c t u r e semantics i n Section 1 provides f o r s o l u t i o n s t o t h e semantic p r o j e c t i o n problem (cf Katz and Fodor (1964), and Langendoen (1969)) . The reqder i s c e r t a i n l y aware by now, i f n o t b e f o r e , t h a t t h e w are many grammars and semantics f o r a given language. A f t e r having played with w r i t i n g grammars and semantics f o r simple languages f o r q u i t e a while nov, I b e l i e v e t h a t , f o r most languages a t l e a s t , t h e r e a r e \" b e t t e r \" 11 grammars and semantics and worse\" ones. Some j u s t seem t o b e more 11 e l e g s n t o r simple, o r n a t u r a l \" than o t h e r s , f o r a given language. But I c a n ' t say much of a s p e c i f i c n a t u r e about what i t means f o r a grammar and I t semantics t o be \"elegant\", \"simple\", o r n a t u r a l \" . It seems t h a t some study ih t h i s a r e a might g i v e u s i n s i g h t i n t o c e r t a i n s k i l l s f o r maklng it e a s i e r t o w r i t e l i n g u i s t i c d e s c r i p t i o n s s u i t a b l e for. t r a n s l a t i o n . One phenomenon t h i s model explains is why i t i s s o d i f f i c u l t t o", |
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| "FIGREF45": { |
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| "text": "extension t o a r b i t r a r y phrase s t r u c t u r e grammars r e q u i r e s f i r s t a formal statement o.f the \"phrase s t r u c t u r e s \" of u n r e s t r i c t e d grammars, s i n c e these s t r u c t u r e s are n o t t r e e s . The a u t h o r ' s forthcoming paper, l i s t e d i n t h e b i b l i o g r a p h y , covers t h e s u b j e c t of t h e s y n t a c t i c s t r u c t u r e s f o r u n r e s t r i c t e d languages in d e t a i l .", |
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| "text": "Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . . . . . . .", |
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