Generation From Under - And Overspecified Structures

This paper describes informally an algorithm for the generation frolll un(|erall(| overspceified feature structures. The generator require~ a grammar, :t goal category m~et a feature structure mq input, and derives all strings whose corl'eSl)ondillg feature strlltCtllre is llot ill Colltrlu|iction to the input structure. 1 I n t r o d u c t i o n In this pape r I will present all algorithut for generation fronl underalld overspccitied feattlrc struetl tres in the Lr'(; fi 'amework 1. Tile a lgor i thm makes use of the concept of generation as slructuT~-driven derivatzon as it is described ill 114, 15, 16]. Most of tile t ime the a lgor i thm works top-down breadth-first , similar to the gcncra to r described ill [7] and [61. Only for thc creat ion of the final s t ruc tu re tile a lgor i thm works bottonl-Ill), 2 M o t i v a t i o n The a lgor i thm given ill [14] allows to genera te fi'om a fltlly specified feature s t ruc ture , e.g. tile input structure is equal to a s t ruc ture t ha t would be derived during parsing. For ai)plications otlter than test ing a granl lnar for overgenerat ion the equali ty-condit ion is too restrictive. The a lgor i thm given in [15] and [16] then Mlows to generate frolu all uuderspceified s t ruc ture , if there is a fully specified (semant ic) p red ica tc -a rgonten t s t ruc ture which is nnt ~dlowed to be extended during generat ion, e.g. tile l )redicate-argunlent s t ructure must be conqllete and coherent with respect to the ta rge t g r a m m a r , One of the disadvantages of this algor i thm is, tha t it must be marked for tile generator, which subs t ruc tu re is not allowed to be changed dur ing generat ion. Fur ther , in certain applications, the condition tha t there is a partiM feature s t ruc ture which is comple te and coherent with respect to the ta rge t g r a m m a r might be ,also too restrictive. The genera tor described in this paper had been deycleped for projects whielt are involved in machine translat ion. While one of the projects makes use only of syntact ic informat ion encoded in a feature structure the o ther in'eject uses semant ic information ~s well. In I)oth cases the inI)ut feature s t ruc ture for tile genera to r is at least undersl)eeified with respect to *The work reported here is part of the Sonderforschungsbereich 340 Sp~chtheo,'etische G~ltndlagen der ('omputerlingu£~tik l For details of the LFe, formalism see (1 b the ta rge t g r a m m a r , not only for al;omic a t t r ibu te value pail's but also fro' complex pairs. This means tile gencra tor has to in t roduce informat ion into the given feature s t ruc tu re to get a s t ruc tu re which is valid with l-espect to tile ta rge t gr tunmm~r . In both projects a similar archi tec ture is used: 2 1. parse a sentellCe and re turn the feature s t ruc ture Fp 2. extrat:t tile inforlnation for the t ranslat ion from Fp and build F,j 3. genera te fronl F 9 a sentence In such an archi tec ture the creat ion of Fg is usually independent of the ta rge t g r a m m a r , in the sense tha t the creat ion is not au tomat ica l ly coutroUed by tile t a rge t gralnular . In machiuc t raas la t ion the g r a m m a r s used for parsing and for generat ion are basically spccilic for tile two single languages one wants to t rans la te between. I t is usually desirable to sl)eeify F~ only in ,~s rud imen ta ry and ms general lnauller ;L~; possible. This lueans tile details of how to genera te a wdid surface s t r ing of tim ta rge t language are only known in the ta rge t grammar , ra ther than spelled out ill th" t ransla t ion relation. Ill o ther words, a single g r a m m a r G describes only the relation of a surface str ing of a language L and a feature s t ruc tu re valid for tile g r a m m a r G of L. ~ t r t h e r , a valid feature s t ruc tu re for G will represent only informat ion necessary for L, but not neeessarily information necessary for the lauguage to t rans la te into. For example, a g r a m l a a r fro' G e r m a n will describe a fl~atttre s t ruc tu re which h,'us informat ion for the tenses past, present, and future, but no information about progressive ms it is required for English. Therefore, ill tile t rans la t ion G e r m a n to English the genera to r has to genera te froln a feature s t ruc tu re which might be underspecified with respect to tense information, while ill the t ranslat ion Englislt to German the genera to r has to genera te from a feature s t ruc ture which might be overspecified with respect to tense information. ht general, in describing the t ranslat ion relation between two languages one lta.s to face tile probleuts of interfaces: • Infornmtion is missing and must be derived froin tim target g ra lnmar , e.g. tile input s t ruc tu re is uuder,~pecified. 2For the re~ons of this architecture see for example [4]. There are also other MT projects like GRADE (see [9], [10] and [8]) which nl~tke use of a similar architecture. ACRES DE COLING-92. NANTES. 23-28 AOt3T 1992 6 8 6 Prec. oF COLING-92. NANTES, AUG. 23-28, 1992 • There is more informat ion than defined by tile ta rge t g r a m m a r , e.g. there is no str ing of the target language for which the g r a m m a r describes a feature s t ruc ture which contains all a t t r ibutevahle pairs given ill the iuput s t ruc tu re FS 9. The input s t ruc tu re is overspccifled and the overspceif)cation could be ignored dur iug geuerat ion. • The re is informat iou which is incousisteut with the ta rge t g r a m m a r , e.g. the input s t ruc ture is illforrned with respect to the ta rge t g ramnla r . This requires some error t r e a tmen t . All a lgor i thm for generat ion then h~s to provide uwchanisms which allow geuerat ion from underspecifled s t ruc tures as well as f rom overspecilicd ones. This will allow to deal with cer tain types of trauslation mismatches as they are described for example in [2]. Further , the t r e a t m c u t of fllformed s t ruc tures shouhl be such. tha t the invldid elements of the input structure could he m a d e visible for debugging purposes, ills tead of just failing to genera te anything. As it turned o n t , even for u l e d i u u l s i z e d g r a l l l l n a r s i t Call b e c o n l e quite dill)cult for a linguist to debug the g r a m m a r if there is only a debugger available which had been develolled for the generM l)urpnse p r o g r a m m i n g language the sys tem is inq)lemented ill, e.g. prolog. 3 T e r m i n o l o g y The alger)tirol has been devehlped for g r a m m a r s wri t ten in the Ll.'c;-formalism. This uleal!s, it works on a eoutext-frec g r a m m a r G wi th anno t a t ed fcatm'e descriptions. Given a feature s t ruc tu re FSi , as input the a lgor i thm has to genera te all those surface strings, for which G ;Lssociates a feature s t ruc ture FS,j, with FSI~ coutpat ihle to FS,~. V~rhat co're, pal)hie means depends on tile kind of application the genera tor is used iu: • If the appl icat ion is to tes t a g r a m m a r for overgeu(,ration, FSin lnust lie equal to FSu, e.g. lie iuformat ion is in t roduced into or deleted from FSi,, dur ing geuerat ion, and ]i~Si,, unifies ill t e rms of feature unification with FS,j. • If the alll)licatiou is to test whe the r a s t ruc ture of a cer tain a t t r ibu te might be sufficient for generalieu, i.e. whe the r the senlautic s t ruc ture does not m'ergenera te , FSI,~ must I)e subsumed by FS,~, e.g. all informat ion of FSI,, nlust be required for generat ion, and it is only allowed to introduce iMonnat ion lute FSin. • If the appl icat ion is machiue t rauslat ion, FSi,, and FSI~ must unify, e.g. FSI,, might contain nlore inlorulat ion and ,also less iuforluatiou th~t.u FS u . Del)endiug on tile al)l)licati(m the a lgor i thm is i )arametr ized as to whe ther it allows the introduction of informat ion into FSi , and whe ther it allows FSI, to be overspecified. For those not famil iar with LFG I will give a short overview of tile e lements of the fea ture descriptious as I will use t hem af terwards . In general a feature deseril)tiou consists of a coujuuct ion of equations or a disjunction of feature descriptions. In this pape r I will only cousider feature descript ions wi thout disjunctious. The equat ions are dist inguished into • defining equat ions indicated by tile ope ra to r = • inequatimts indicated by the opera to r # • constra ining equat ions indicated by the opera to r =e All equation consists of a reference to a s t ruc ture , tile el)era)or , and ,'L,~ second argulueut of the opera t iou oue of • all a tomic v~due like raas • a semantic form, indicated by double quotes, with a n a t ou ) i c u a u l e a u d a l l o p t i o n a l a r g u u l e u t list,, i.e. " m a n " , "give (SuuJ,ot~J}" • a r e f e r e l l e e to a s t r u c t u r e A reference to a s t ruc ture is ei ther a mete-var iab le or a pa th applied to a mete-var iable . Examl)les are • the meta-wtr iable 1, which s tands for the structure assnciated with tile n lo ther l l ode , e.g. the ca tegory given on tile left hand side of a rule. • t tw meta-variMilc 1, which s tands fur tile structure a.ssociate(1 with a ( laughter uode of a rule, e.g. the nolle on the right hand side of a rule where tile feature description is an annota t ion of. • (~ GENI)ER), which refers to a s t ruc tu re under the a t t r i l lu te (;[.;NDI.~R ill tile feature s t ruc tu re associated with tile m o t h e r node. Equat ions , which have references on both sides of a equat iou arc called ree~ttr(trtey equations. Semant ic forms describe unique vMues, e.g. while two atoufic values unify if they are described by the same fern), two semant ic forms will not. The a rgumen t s of a semant ic form of at) a t t r i bu t e A are pa ths which are member s of the governable f~mctions of A. This set will be named as g f (A) . %) alh)w semant ic forms )~s possil)le values tilt ally a t t r i bu t e is a generalization of t h e Ilse of s l t n l an t i c forll lS a,s t h e y a r e g i v e n in [1] where semant ic forms are only values of the att r ihute PRED. Semant ic forms contain all informat ion ueeessary to test the conditiolm of COml)leteness and c o h e r e n c e . 3.1 C o h e r e n c e and C o m p l e t e n e s s Using the general izat ion tile conditious of completeness and coherence ms given in [3, pp. 211/212] are reformulated ~s • A feature s t ruc ture 5' is locMly comple te iff for each a t t r i bu t e A in S where g f ( A ) is non-empty tile governable functions defined by tile vMue of A exist ill S with a value for the a t t r i bu t e A, and if all values required are defined. A s t ruc tu re is conq)lcte if all of its subs t ruc tures are locally complete. • A feature s t ruc tu re S is loeMly coherent , iff for each a t t r ibu te G of S which is m e m b e r of g f (A) G is governed by the value of A, e.g. the argulueut list of the vMue of A contains G, and if ,all a t t r ibu tes of S are given by tile g r a m m a r . A s t ruc ture is coherent if ,all of its subs t ruc tu res are locally coherent . Ac~rEs DE COLING-92. NnivrI,kS. 23-28 ^olyr 1992 6 8 7 PRec. OF COLING-92. NANTES. AUG. 23-28. 1992 The s t ruet tn 'e FS derived in the genera t ion process mus t a t least fttllfiqll these contlit ions of comple teness and coherence, e.g. ally violat ion of one of these condit ions is t r ea ted as an error. Since the input s tructure FSi,, should be pa r t of the derived s t ruc ture , the condi t ions for a t t r i ba t e -va l ae pairs of the input s t ruc tu re are modif ied to be able to use the input s t ruc tu re to control the genera t ion process and to bc able to allow overspecif icat ion, a • I f an a t t r i b u t e A of FSi, is licensed by a defining equat ion or inequat ion in the rules of tile g r a m m a r which are no t explicit ly excluded by FSi,, it shouhl be checked tha t A is actual ly cons tnned d a r i n g generat ion. T h i s condit ion ex tends the condi t ion of coml)leteness. • If an a t t r i b u t e A of FSi, does not occur in any equat ion of the g r a u l m a r , t im inpu t s t ruc tu re is ovcrspecified. It depends on the applicat ion, whe the r this type of overspeeif icat ion is allowed, e.g. whe thc r it should be considercd a.s a violation of the coherence condi t ion or shoultl be ignored. • I f an a t t r i b u t e A of FSi, is not l ieeased by a defining eqna t ion or an inequat ion in the rules of the g r a n u n a r which are not explicit ly excluded by FSi, the input s t ruc tu rc is overspecified. I t depcnds on tbc allplication whe ther this type of overspecif ieat iml is allowed. In ease overspecificat ion is allowed, A and i ts value are ignored, o therwise it is t r ea ted ,as a violat ion of the coherence condition. As indicated by tile last extension to the coherence and comple teness condit ions, i t depends on the application w h a t kind of inpu t s t ruc tu re is considered to be a valid one for the t a rge t gra lonlar . Ill case a g r a m m a r should he tes ted for overgenera t ion a valid input s t ruc tu re is not allowed to be extended t lnriug genera t ion and is not anowed to be ow~rspecifictl. In the case of mach ine t rans la t ion the input s t ruc tu re can be considered as a valid one, even it is underspecified. Del)ending on the l anguage pair i t migh t be also apl)ropria te to consider an overspeeified input s t ructure ms valid. 4 T h e A l g o r i t h m The a lgo r i t hm works on a g r a n m m r tlescription and an input fea ture s t ruc tu re . T h e g r a m m a r descr ipt ion cuasis ts of context free rules wi th anno ta t ed fea ture descr ipt ions. For siml)licity it is a s sum ed tha t the anno ta t ed feature descr ip t ions do not contain dis junct ions. A disjunc t ion in a fea ture descr ipt ion can always be t ransformed into a dis junct ion of nodes on the c -s t ruc ture level. Fu r the rnmre , a siugle ode is a conca tena t ion of t e rmina l and uonte rmiua l nodes, and for each category C of a g r a m m a r the rules for C are t r ea ted as one dis junct ion. aThis mealm, it is not sufficient to require, that the inptlt structure has to Ilnify with a structure derived from the grammar to get a generatim~, since this would allow to produce sentences which do not contain all of the semantics given in the inptll structure as well ms to produce sentences with any kind of possible modifiers the grammar could derive, that is infinile many. T im a lgor i thm s t a r t s wi tb a current ca tegory C~, initialized wi th the gual category, and a cur ren t feature s t ruc tu re FS~, init ialized wi th the inpu t fea ture s t ruc tu re FSin. T h e a lgor i thm proceeds as follows: • Match the current fea ture s t rnc tu re FS~ with the cur ren t ca tegory C~ by ma teh iug FS~ with the feature descr ipt ions FDi of the nodes N i on the r ight hand side of tile rule for Cc, where FSc is bound to the m a t a variable T which deao ta t e s the s t ruc tu re associa ted wi th the nlother node C,, on the left hand side. The ma tch ing works top-down I)readth-first . Dur ing tile ma tch FS~ will lint be nmdif ied. • Eztend FS,. by the appl icat ion of a fea ture descript ion FD.