Interaction Grammars

ISSN 0249-6399 ISRN INRIA/RR--6621--FR+ENG Thème SYM INSTITUT N A TION AL DE RECHERCHE EN INFORMA TIQUE ET EN A UTOMA TIQUE Interaction Grammars Bruno Guillaume — Guy Perrier N° 6621 Septembre 2008 Centre de recherche INRIA Nancy – Grand Est LORIA, T echnop ôle de Nancy-Brabois, Campus scientiﬁque, 615, rue du Jardin Botaniqu e, BP 101, 54602 V illers-Lès-Nancy Téléphone : +33 3 83 59 30 00 — Télécopie : +33 3 83 27 83 19 In teraction Grammars Bruno Guillaume ∗ , Guy Perrie r † Th` eme SYM — Syst` emes symboliques ´ Equip e-Pro jet Calligramme Rapp ort de recherche n ° 6621 — Septemb re 20 0 8 — 37 pages Abstract: Int era c tion Gra mmar (IG) is a gr ammatical formalism based o n the notion of p olarity . Polarities express the resourc e sensitivity of natural languages by mo delling the distinction b etw een saturated and unsa turated syntactic struc- tures. Syntactic comp osition is repr esented as a chemical r e a ction guided by the saturation of pola rities. It is expr essed in a mo del- theoretic framework wher e grammar s are constraint sy stems using the notion of tree descr iption and par s- ing appea rs as a pro ce s s o f building tree desc r iption models satisfying criteria of s aturation and minimality . Key-w ords: Grammatical fo r malism, Categorial Grammar , Uniﬁcation, Po- larity , T ree description ∗ LORIA, INRIA Nancy Grand-Est ( Brun o.Guillaume@ loria.fr ) † LORIA, Universit ´ e N ancy 2 ( Guy.Perri er@loria.fr ) Les Grammaires d’In teraction R´ esum´ e : Les grammaires d’interaction sont un formalisme grammatica l bas ´ e sur la notion de p olarit´ e. Les pola rit´ es expriment la sens ibilit´ e aux ressources de la langue naturelle en distinguant les structures syntaxiques satur´ ee s et insa- tur´ ees. La comp osition syntaxique pe ut ˆ etr e v ue comme une r´ eactio n c himique control ´ ee par la satura tion des po larit´ es. Les grammaires sont exprim ´ ees par un syst` eme de co nt ra intes utilisant la notion de description d’arbre. L’analyse syntaxique appara ˆ ıt alor s comme un proce s sus de construction de mo d` eles sa- tisfaisant des cr it` eres de ne utr alit´ e et de minimalit´ e. Mots-cl´ es : F o rmalisme grammatical, Grammaire s cat´ egor ie lle s, Polarit ´ e, Description d’arbre Inter action Gr ammars 3 In tro duction Int era c tion Gr ammar (IG) is a grammatica l forma lism ba sed on an old idea of O. Jes pe r sen [20], L. T esni` ere [46] and K. Adjukiewicz [2]: a sentence is viewed as a mo le c ule with its words as the atoms; every word is equipp ed with a v alence which expresse s its capacity of in teraction with o ther w ords, so that s y nt actic comp osition a pp ears as a chemical reaction. The ﬁrst g rammatical forma lism that exploited this idea w as Categor ial Grammar (CG) [39]. In CG, co ns tituen ts are equipp ed with t yp es, which ex- press their in teraction ability in terms of syn tactic categor ies. A way of high- lighting this or iginality is to use po larities: s yntactic types can b e represented by par tially spec iﬁe d syntactic trees , which are decorated with po larities that express a proper ty of non sa turation; a positive no de repr esents an a v a ila ble grammatica l constituen t whereas a nega tive no de represents an expe cted gram- matical constituent; nega tive no des tend to merge with po sitive no des of the same type and this mechanism of neutralizatio n betw een opp osite po larities drives the comp os itio n of syntactic trees to pro duce saturated tree s in whic h all po larities hav e been neutraliz ed. The notion of p olar it y in this sense w as not used explicitly in computationa l linguistics until recently . T o our k nowledge, A. Nas r w as the ﬁrst to pro p o se a formalism using p olariz e d s tructures [31]. Then, nea rly a t the sa me time, R. Muskens [30], D. Duc hier and S. Thater [15], and G. Perrier [33] prop os e d grammatica l formalis ms using p ola rities. The latter was a ﬁr st version of IG, presented in the framework of linear logic. This version, whic h cov ers only the syntax of natural lang ua ges, was ex tended to the semantics o f na tur al lan- guages [35]. Then, S. Kahane show ed that all well k nown forma lisms (CF G, T AG, HPSG, LFG) can b e viewed as p olar ized forma lisms [21]. Unlike the pre- vious appro a ches, polarities are used in a non monotono us w ay in Minimalist Grammar (MG). E . Stabler [4 3] pro po ses a for ma lization of MG which highligh ts this. Polarities are as so ciated with syntactic features to co ntrol mo vemen t inside syntactic structures: strong features ar e used to drive the movemen t of phonetic forms (o vert mov ement ) and weak featur es a re used to drive the movemen t of logical for ms (cov ert mov emen t). With IG, we highlight ed the fundament al mechanism of satura tion betw een po larities underlying CG in a more reﬁned wa y , because p olar ities are attached to the feature s used to descr ib e constituents and not to the constituents them- selves — but the essential diﬀerence lies in the change of framework: CG are usually formalized in a gener ative deductiv e framework, the hear t of which is the La mbek Calculus [23], wherea s IG is for malized in a mo del-theoretic frame- work. A pa rticular interaction g r ammar app ears as a se t of constraints, and parsing a sen tence with suc h a g rammar reduces to solving a constr aint s atis- faction problem. G. K. Pullum and B. C. Scholz highlighted the adv antages of this c hange o f framework [37]. Here, we are esp ecia lly interested in some of these adv antages:  syntactic ob jects a re tree descr iptions which combine indepe ndent ele- men tary pro pe r ties in a very ﬂexible way to repr esent families of syn tactic trees;  undersp eciﬁcation can b e repr esented in a natural wa y b y tree descriptions; RR n ° 6621 4 B. Guil laume & G. Perrier  partially well-formed sentences hav e a syntactic representation in the sense that, even if they hav e no complete parse trees, they can be characterized by tree descriptions. The no tion of tr ee description, which is central in this appro ach, w as in tro- duced b y M. Mar cus, D. Hindle and M. Fleck to reduce non- deter minism in the parsing o f natural la nguages [27]. It w as used again by K. Vija y-Shanker to represent the adjoining o pe r ation of T A G in a monotonous w ay [4 8]. Then, it was studied systematically from a mathematical p oint of view [4 0] and it gav e rise to new grammatica l fo r malisms [2 2, 3 8]. If mo del theory provides a declarative framework fo r IG, polar ities provide a step by step o p erational metho d to build mo de ls of tr ee descriptions: par- tially sp eciﬁed trees are s upe r p osed 1 under the con trol of polar ities; so me no des are merged in or der to satur a te their p olar ities and the proces s ends when all po larities are saturated. A t that time, the r esulting des c ription repres ents a completely sp eciﬁed syntactic tree. The ability of the formalism to superp os e trees is v ery imp orta nt fo r its expr essiveness. Moreover, the control of supe rp o- sition b y pola rities is interesting for computational eﬃcie ncy . In na tural lang uages, synt ax is a wa y to ac c ess sema nt ics and a linguistic formalism w orthy of the name must take this idea into account. If the g oal o f the a rticle is to g ive a formal pres entation of IG which focuses o n the sy nt actic level o f natur al languages, the formalism is designed in such a w ay that v arious formalizations of semantics can b e plugged into IG. The rea der ca n ﬁnd a ﬁrst prop osal in [35]. An imp or tant conc e r n with IG is to provide a realistic for malism, whic h c an be expe rimented parsing actual corp o r a. In order to combine the theoretical developmen t of the fo rmalism with ex pe r imentation, we have designed a pa rser, Leop ar , ba sed on IG [5 ]. If a relatively eﬃcient parser is a ﬁrst co ndition to get a rea listic for malism, a second condition is to b e able to build lar ge c overage grammar s and lexico ns. With a n appr opriate to ol, XMG [14 ], we hav e built a F r ench interaction grammar with a relatively larg e coverage [36]. This g rammar is designed in such a way tha t it can b e linked with a lexicon indep endent of any for malism. Since our purp ose in this article is to present the formal asp ects of IG, we will not dwell on the exp er iment al side. The layout o f the pap er is as follows:  Section 1 gives an intu itive view of the main IG features (pola rities, su- per p osition a nd under sp eciﬁcation) thr ough sig niﬁcant examples.  Section 2 prese nt s the syntax of the langua ge used to represent p olarized tree descr iptions, the basic ob jects of the formalism.  Section 3 explains how s y nt actic pa rse trees a re rela ted to p olar ized tree descriptions with the notion of minimal and saturated mode l.  In section 4, w e illustra te the express ivity of IG with v arious linguistic phenomena.  In s e ction 5, we compare IG with the mo s t closely related formalisms. 1 As no standard term exists, we use the term “sup erp osition” to name the op eration where t wo trees are combined by merging some no des of the ﬁr st one with no des of the second one. INRIA Inter action Gr ammars 5  Section 6 brieﬂy presents the computational asp ects of IG thro ugh their implemen tation in the Leop ar par ser, which works with a rela tively la rge F r ench in teraction gr ammar. 1 T he main features of In teraction Grammars The aim of this section is to give informally , through examples, an ov erview of the key features of IG. 1.1 A basic examp le 1.1.1 Syn tactic tree In IG, the parsing output of a sentence is an o r dered tree wher e no des represent syntactic constituents describ ed b y feature structures . An example of syntactic tree for sentence (1) is shown in Figure 1 2 . (1) Je an John la it voit. sees. ‘John see s it.’ Each leaf of the tree car ries a phonological form whic h is a str ing that can be empt y (written ǫ ): in our example, “J e an ” in no de [C], “la” in [E], “voit” in [F], ǫ in [G] a nd “ .” in [H]). The phonolo gic al pr oje ction of a tr ee is the left to right rea ding of the phonological for ms of its leav es ( “Je an ” · “la” · “voit” · ǫ · “.” = “J e an la voit.” in the example). [C] /Jean/ cat = np funct = subj [B] cat = np funct = subj [D] cat = v [F] /voit/ cat = v [E] /la/ cat = clit funct = obj [G] cat = np funct = obj [H] /./ cat = punct [A] cat = s Figure 1 : Syntactic tree for the sentence “Je an la voit.” 1.1.2 Initial tree descriptions The elemen tary sy ntactic structur es a r e initial p olarize d t re e descriptions (writ- ten IPTDs in the following). Figure 2 shows the four IPTDs used to build the syntactic tree in Figure 1. A syntactic tree is sa id to be a mo del of a set of IPTDs if each node of the syntactic tree in terprets some no des of the IPTDs and this tree satisﬁes sa turation and minimality constraints. F or our exa mple, the interpretation function is also given in Figure 2 . 2 T o i ncrease readability , only a part of the f eature structures i s shown in the ﬁgures; many other features (gender, num ber, moo d, . . . ) are used in practice. In the f ollowing, we only sho w r elev ant features in ﬁgures. RR n ° 6621 6 B. Guil laume & G. Perrier [C1] /Jean/ cat = np funct = ? [B1] cat -> np funct <- ? [D2] cat ~ v [F2] cat ~ aux | v [E2] /la/ cat = clit funct = obj [G2] cat -> np funct <- obj [A2] cat ~ s [G3] cat <- np funct -> obj [A3] cat -> s [D3] cat = v [B3] cat <- np funct -> subj [F3] /voit/ cat = v [H4] /./ cat = punct [A4] cat <- s { A2, A3, A4 } − → A { B1, B3 } − → B { C1 } − → C { D2, D3 } − → D { E2 } − → E { F2, F3 } − → F { G2, G3 } − → G { H4 } − → H Figure 2 : IPTDs and in terpre ta tion function for the sentence “Je an la voit.” IPTDs a r e undersp eciﬁed trees: for ins ta nce, in Fig ure 2, the pr ecedence relation b etw een no des [D2] and [G2 ] is large: [D2] m ust b e to the left o f [G2] but a ny num b er of in termediate no des b etw een [D2] and [G2] are allowed in the ﬁnal tree mo del. Moreov er, IPTDs contain features with p olar ities a cting as constr aints. A po sitive (written -> ) po larity must be asso ciated with a compatible negative (written <- ) o ne: in the example, when building the mo del, the po sitive fea ture cat -> s of node [A3 ] is asso ciated with the ne g ative feature c at <- s of node [A4]. 1.1.3 T ree descriptions A more g eneral notion of tree description is not s trictly needed in the for malism deﬁnition, how ever this notion is useful to represent partia l par ses of sentence and to co nsider ato mic steps in parsing proces s. These pola r ized tr ee descrip- tions (PTDs) a re formally describ ed in the next section. 1.2 Polarized features to control syntactic c omp osition The no tion of p olar ity represents the cor e of the IG formalis m. 1.2.1 P ositive and negative pol arities Like in categor ia l grammar s, resour ces can b e iden tiﬁed as av ailable (p ositive po larity) or needed (negative po larity). E ach po sitive or negative feature m ust be neutralized by a dual p ola r ity when the mo del is built. A p olar ity which is either po sitive or nega tive is said to b e active . This mechanism is int ensively use d. It is used similarly as in CG, for in- stance, to control the in teractio ns of:  a determiner with a noun;  a prep o sition with a no un phr ase; INRIA Inter action Gr ammars 7  a v erb, a predica te no un or adjective with its arg uments deﬁned in the sub c ategoriza tion frame. But p ola rities are also used in a mor e s pe c iﬁc manner in IG to deal with other kinds of int era ctions. F or instance:  to handle pair s of gr ammatical words lik e ne/p as , . . . (see b e low subsec- tion 4.1);  to manage interaction o f punctua tio n with o ther co nstructions in the sen- tence;  to link a reﬂexive pr onoun s e with the reﬂexive c onstruction of verbs;  to manag e interaction b etw ee n auxilia ries and past par ticiples. 1.2.2 Virtual p olarities Recently , a third kind o f p ola rity was a dded whic h is called virtual (wr itten ∼ ). A feature with a virtual po la rity must b e com bined with some other compatible feature which has a p ola rity diﬀerent from ∼ . It gives mo re ﬂexibility to expres s constraints o n the context in which a node can app ear . Virtual p ola rities are used, for instance:  to descr ib e in terac tion b etw een a mo diﬁer a nd the mo diﬁed co nstituent (adverb, adjectiv e, . . . ), see subsection 4.3 for an example;  to express context constra in ts on no des around the active part of a descrip- tion; it allows for a co ntrol on the sup erp osition mechanism: in Figure 2, the three no des [A2], [D2] and [F2] with virtual cat p olarities describe the context in whic h the clitic “la” must b e used; this IP TD requir es that three other non-virtual no des co mpatible with [A2 ], [D2] and [F2] exis t in some other IPTDs; in our example, non-virtual no des [A3], [D3] and [F3] are given b y the v erb. This mechanism handles the cons traint o n the F r ench clitic “la” . It comes b efore the v erb (no de [E2] b e fore node [F2]) but contributes with an o b ject function (no de [G2] after no de [F2 ] b ecaus e the canonical positio n o f F r ench direct ob ject in on the r ight of the verb). 1.2.3 P olarities at the feature lev el A diﬀere nc e with resp ect to other fo rmalisms using p olarities is that, in IG, po larities ar e attac hed to features rather than to no des. It is then p o s sible to use p ola r ities for sev eral diﬀerent fea tures to co nt ro l diﬀerent t yp es of po s i- tive/negativ e pairing (for instance in our g rammar, the feature mood is po larized in the a uxiliaries/ past participles in teraction; the feature neg is p olarize d in the int era c tio n of the tw o pieces of negation). Hence with polar ities at the feature level, the same syntactic constituent can int era c t more tha n once with its en vironment through several feature neutral- izations. One of the typical usag e of suc h int era ctions, that implies mo r e than tw o no des is sub ject inv ersio n. In F rench, in some sp ec iﬁc ca s es the sub ject can b e put after the verb (sentences (2) , (3) and (4)). Ho wev er, unco ntrolled sub ject RR n ° 6621 8 B. Guil laume & G. Perrier inv e r sion would lea d to o ver-generatio n. A solution is to us e t wo diﬀere nt inter- actions: betw een the sub ject and the verb on one ha nd; a nd on the other hand betw een the sub ject and some other word which is s pec iﬁc to the cons truction where the sub ject can b e p ostp oned. (2) Je an John qu’aime that Marie lov es vient. Mary comes. ‘John that Mary lov es comes.’ (3) Aujour d’hui T o day c ommenc e beg ins le the printemps. spring. ‘T o day begins the s pring.’ (4) Que What does mange eat Je an ? John? ‘What do e s John eat?’ In the sentence (2), the sub ject “Marie” o f the verb “aime” can be p ostp oned bec ause it is in a r elative clause introduced by the o b ject re lative pro no un “que” . Hence, in the noun phrase “Je an qu’aime Marie” (see ﬁgure 3), the prop er no un “Marie” in teracts bo th with the verb “aime” (neutralization of the features cat -> np in [A] and c at <- np in [B]) and with the rela tive pronoun “ qu’ ” (neutralization of the features f unct <- ? in [A] and funct -> subj in [C]). Figure 4 gives the PTD after sup erp os ition. /qu’/ cat = cpl cat ~ v [C] cat ~ np funct -> subj cat ~ n | np cat <- s cpl = que cat -> np funct <- obj cat ~ np cat <- np funct -> obj cat = v /aime/ cat = v [B] cat <- np funct = subj cat -> s /Marie/ cat = np [A] cat -> np funct <- ? Figure 3: IPTDs for the seq uence of words “qu ’aime Marie” b efor e s upe r p osi- tion 1.3 T ree sup erp osition as a ﬂexible w a y of realizing syn- tactic c omp osition F o r the grammatical formalisms tha t a r e ba sed on tr ees (the most s imple for - malism of this type is Context F r ee Grammar), the mec hanism of s yntactic comp osition often reduces to substitution: a leaf L of a ﬁrst tree merges with the ro ot R o f a second tree. In this w ay , constraints on the comp os ition of b oth trees are lo calized at the no des R and L . They canno t say a nything ab out the environmen t of both nodes. INRIA Inter action Gr ammars 9 /qu’/ cat = cpl cat = v [A-B-C] cat = np funct = subj /aime/ cat = v /Marie/ cat = np cat = np funct = obj cat ~ n | np cat = s cpl = que cat ~ np Figure 4 : PTD for the sequence of w ords “ qu’aime Marie” after super p osition The T AG formalism oﬀers a more sophisticated opera tion, adjunction , but this op eration is also limited in expr e s sing constr aints o n syntactic comp osition: instead of merg ing tw o no des , we merge tw o pairs of no des. A no de N splits into an up no de N up and down no de N dow n , which resp ectively merge with the ro ot R a nd the fo o t F o f the aux iliary tree. Constraints on syntactic co mpo sition is now loca lized on three no des N , R and F . In IG, the syn tactic comp osition is mu ch more ﬂexible: w e can merge any t wo no des (in the sa me P TD or in tw o diﬀeren t o nes). Then, the propaga tion of the constraints related to each PTD en tails a pa r tial sup erp ositio n of the t wo tree structures around the tw o nodes. In this wa y , we can expr ess constraints on the environmen t of a no de. (5) Je an John en of it c onna ˆ ıt knows l’auteur. the author. ‘John knows the author o f it.’ Let us co nsider the sentence (5). The clitic pr onoun “en ” provides the o b ject “auteur” of the v erb “c onna ˆ ıt” with a noun co mplemen t. O ur F rench lexicon gives the IPTD of Fig ure 5 to repr esent the syntax of this usage o f the clitic pronoun “en ” . In this IPTD, the no de [N] with feature prep -> de represents the tra ce of the prep osition phrase r epresented by the clitic “en ” as a sub- constituent of the ob ject of the verb. Figure 6 shows a PTD resulting from the (pa r tial) parsing of “c onna ˆ ıt l’auteur” . In this PTD, the no de [M] with feature prep <- de repr e sents the noun co mplement that is exp ected by the noun “auteur” . Now, when we comp os e “en ” with “ c onn a ˆ ıt l’auteur” (i.e. tree descriptions of Figures 5 and 6), no des [N] and [M] ha ve to b e merge d in o rder to neutralize their features cat , fu nct and p rep . B y pro pa gating tr e e w ell-formedness and po larity constra int s, the merging o f [N] a nd [M] entails the par tial sup er po sition (Figure 7) of the tw o P TDs. Note that there are 9 atomic op er ations of no de merging during this comp ositio n. RR n ° 6621 10 B. Guil laume & G. Perrier cat ~ v cat ~ aux | v /en/ cat = clit cat ~ np funct = obj cat ~ n cat ~ n [N] cat -> pp funct <- deobj prep -> de cat = np | s cat = prep prep = de cat ~ s Figure 5 : IPTD representing the syntax of the clitic “en ” cat = np funct = obj cat = n funct = obj /l’/ cat = det [M] cat <- pp funct -> deobj prep <- de /auteur/ cat = n funct = obj /connaît/ cat = v cat = v cat -> s cat <- np funct -> subj cat ~ prep prep = de cat = np funct = deobj Figure 6 : PTD repre s enting the syntax of the phrase “c onna ˆ ıt l’auteu r” 1.4 Undersp eciﬁed structures With IG, bo th dominance and precedence relations can be undersp e ciﬁed: an IPTD can constra in a rela tion betw een tw o nodes witho ut restricting the dis- tance betw een the no des in the mo del. Underspe ciﬁed relations, combin ed with tree sup er po sition, incr ease the ﬂexibilit y o f the formalism: it is possible to give more g eneral cons tr aints o n the context of a no de. INRIA Inter action Gr ammars 11 cat = v /connaît/ cat = v /en/ cat = clit cat = np funct = obj cat = n funct = obj /l’/ cat = det /auteur/ cat = n funct = obj [M-N] cat = pp funct = deobj prep = de cat = np funct = deobj cat = prep prep = de cat -> s cat <- np funct -> subj Figure 7 : PTD representing the syntax of the phrase “en c onna ˆ ıt l’auteur” Undersp eciﬁcation o n dominance relation makes it poss ible to express gen- eral pr op erties on unbounded dep endencies. F or instance, the relative pronoun “que” can intro duce an unbounded dependency b e t ween its anteceden t and a verb which has this a nteceden t as o b ject of a djectiv al co mplemen t: sentences (6) and (7) 3 . (6) Je an John que that Marie Mary aime lov es  dort. sleeps (7) Je an John que that Pierr e Peter cr oit thinks que that Marie Mary aime lov es  dort. sleeps Figure 8 provides an IP TD to model this use of “que” . An empty no de [E ] represents the trace of an ob ject o r an adjectiv al phrase; [N] represe nt s the c la use in which the trace is a direct constituent and [M] repr esents the r elative clause int ro duced b y the relative pronoun “que” . [N] can be embedded a t any depth in [M], whic h is expressed by an under sp eciﬁed dominance relation. Figur e 9 shows a mo del for the sentence (6) in which the relation is re a lized by merging [M] and [N], wher eas Figure 10 s hows a model for the sentence (7) in which the relation is rea liz e d by an immediate dominance relation. In order to deal with island constra int s, large dominances need to b e con- trolled. In IG, this is po ssible with the no tion of ﬁltering feature structures. A ﬁltering fea ture structure is a p o la rized feature structure where all p olarities are neutral. A la r ge do minance M > ∗ N labelled with a ﬁlter ing feature structure 3 The symbol  i ndicates the origi nal pl ace of the extracted argumen t. RR n ° 6621 12 B. Guil laume & G. Perrier cat ~ v funct ~ subj /que/ cat = cpl [M] cat <- s cpl = que [N] cat ~ s cat = s funct = obj | void cat ~ n | np cat ~ np [E] cat -> np funct <- attr | obj Figure 8 : IPTD for the r elative pr onoun qu e ψ means that no de M must domina te N in the mo de l and that each no de alo ng the path fro m M to N in this mo del m ust b e compatible with ψ . F or instance, in Figure 8 , s uch a ﬁlter is used to avoid extra ction through no des that a re not of c ategory s . /Jean/ cat = np funct = subj [M-N] cat = s cpl = que cat = v cat = np funct = obj cat = np funct = subj /que/ cat = cpl cat = np funct = subj cat = v /dort/ cat = v /./ cat = punct /aime/ cat = v /Marie/ cat = np funct = subj cat = s Figure 9 : Syn tactic tree for the sentence (6) INRIA Inter action Gr ammars 13 /Jean/ cat = np funct = subj [M] cat = s cpl = que cat = v [N] cat = s cpl = que funct = obj cat = np funct = subj /que/ cat = cpl cat = np funct = subj cat = v /dort/ cat = v /./ cat = punct /croit/ cat = v cat = np funct = obj cat = v /que/ cat = cpl cat = np funct = subj /Pierre/ cat = np funct = subj /aime/ cat = v /Marie/ cat = np funct = subj cat = s Figure 1 0: Syntactic tree for the s e nt ence (7) With underspec iﬁcation on precedence rela tion, it is possible to describ e a free order ing of so me arg uments. F or insta nc e , bo th sentences (8) a nd (9) can be par sed using the same IPTD (Figure 11) for the word “demande” . (8) Je an John demande asks une an invitation invitation ` a to Marie. Mary . ‘John a s ks an invitation to Mary .’ (9) Je an John demande asks ` a Ma rie Mary une an invitation. invitation ‘John a s ks Mary an invitation.’ 2 F ormal deﬁnitions This section is dedicated to formal deﬁnitions of IG. W e deﬁne in turn:  syntactic tr e es : the ﬁnal syntactic structures in the pa rsing pro c ess;  initial p olarize d t r e e descriptions (IPTDs): the initial syntactic str uctures that are asso c iated to words at the b eginning of the pa rsing pr o cess; PTDs are also deﬁned as a genera lization of IP TDs; RR n ° 6621 14 B. Guil laume & G. Perrier cat ~ prep prep = a cat ~ n | np funct = dat cat <- np funct -> obj demande cat = v cat = v cat <- pp funct -> dat prep <- a cat -> s cat <- np funct -> subj Figure 1 1: IP TD for the verb “ demande”  the no tio n of mo del which links IP TDs and syntactic trees. 2.1 Syn tactic trees 2.1.1 F eatures F ea tures ar e built relatively to a feature sig nature. A fe atur e signatu r e is deﬁned by:  a ﬁnite set F of constants called fe atur e names ;  for each feature name in F a ﬁnite set D f of constants called atomic values . A fe atur e is a co uple ( f , v ) where f ∈ F and v ∈ D f and a fe atur e structur e is a set of featur es with diﬀerent feature na mes. 2.1.2 Syn tactic trees A synt actic tr e e is a totally order e d tree wher e:  each node carr ie s a featur e str uc tur e,  each lea f carries a string (which can b e the empt y string written ǫ ) ca lled phonolo gic al form . In syntactic tr ees, pare nt ho o d relatio n is written M ≫ N (this means that M is the mother node of N ), immediate precedence b etw een s isters is written M ≺ ≺ N (this means that M and N hav e the same mother and that M is just befo re N in the sisters ordering) 4 . W e also use the notatio n M ≫ [ N 1 , . . . , N k ] when the set of da ughters of M is the order ed list [ N 1 , . . . , N k ]. Let ≫ ∗ denote the reﬂexive and transitive c losure of ≫ . If M ≫ ∗ M ′ then we call path ( M , M ′ ) the list of no des fro m M to M ′ : 4 W e use double symbols to a void confusion with relations that are deﬁned later f or IPTDs. INRIA Inter action Gr ammars 15 path ( M , M ′ ) = { N i } 1 ≤ i ≤ n such that    N 1 = M N i ≫ N i +1 for 1 ≤ i < n N n = M W e deﬁne the phonolo gic al pr oje ction P P ( M ) of a no de M to b e the list of non-empty str ings built with the left to r ight re a ding of the phonolo gical forms in the subtree ro oted b y M :  if M ≫ [] (i.e. M is a le a f ) and the phonological form o f M is ǫ then P P ( M ) = [],  if M ≫ [] and the pho nological for m of M is the non-empty string p hon then P P ( M ) = [ phon ],  if M ≫ [ N 1 , . . . , N k ] then P P ( M ) = P P ( N 1 ) ◦ . . . ◦ P P ( N k ) (where ◦ is the co ncatenation of lists). The phonolog ic a l pr o jection of a syntactic tree is the phono logical pro jection of its ro ot. W e conclude here with a rema r k. The fa ct that s y nt actic tr ees ar e completely ordered trees ca n sometimes pro duce unw anted eﬀects. F or instance, when a no de has several empty daughters, it may be not relev ant to consider the rela tive order of thes e no des. In sentences (8) and (9), the verb “ demander” with a direct o b ject and a dative do es not impo se a ny order b etw een arg ument s. When the tw o argument s are realized as clitics in s entence (10), the r elative o rder of clitics is ﬁxed but there are tw o mo dels with diﬀerent ordering on empty no des corres p o nding to the tw o arg uments. (10) Je an John la it lui to her demande. asks. ’John a s ks it to her .’ In order to a void this pr oblem, it is p o ssible to deﬁne an eq uiv alence rela tion that identiﬁes the t wo models of the s e n tence (1 0). W e will not deta il this relation in this article. 2.2 P olarized tree descriptions 2.2.1 P olarities Polarities are heavily used in IG to tak e into account the reso urce sensitivity of na tural la nguages. F urthermore, the par sing pr o cess stro ngly relies on these po larities. The curr e nt IG forma lism uses four p ola rities:  p ositive (written -> ): a feature with a p o sitive p olar it y descr ib e s an av ail- able re s ource;  ne gative (written < - ): a fea ture with a neg ative pola rity de s crib es a needed resource ; RR n ° 6621 16 B. Guil laume & G. Perrier  virtual (written ∼ ): a featur e with a vir tual p ola rity is waiting for uniﬁca- tion with another non-virtual one; v irtual p olar ities are used for expres sing constraints on the context in which an IPTD can b e inserted;  neutr al (written = ): a feature with a neutral po larity is not concerned by the reso ur ce management: it ac ts like a ﬁlter in case of uniﬁcatio n; but uniﬁcation is not required. A multiset of po larities is s a id to be glob al ly satur ate d :  if it contains exactly one p ositive and one negative p o larity;  or if it contains no p ositive, no negative and a least one neutra l p olar it y . 2.2.2 P olarized features Whereas features in ﬁnal syntactic trees are deﬁned by a couple name v alue, in the tr ee descr iption a polar ity is attached to ea ch featur e and the feature v alues can be unders p eciﬁe d (with a disjunction of atomic v alues). Hence, p olarize d fe atur es are now deﬁned by triples of:  a feature name f taken from F ,  a p ola r ity ,  a fea ture v alue whic h is a disjunction of atomic v alues tak en from D f ; a feature v alue is written as a list o f atomic v alues separa ted by the pip e symbol | ; the question mar k symbol ? denotes the disjunction o f all v alues in D f . A p olar ized feature is wr itten as the conc a tenation of these three comp onents (for instance ca t -> np|pp , fun ct <- ? ar e po larized features). It is a lso p ossible to give a dditional constra int s on feature v alues with co- references. A co-r e fer ence is noted with < i > ; fo r instance mood = <2 > ind|subj is a co-r eferenced feature. 2.2.3 P olarized feature structures A p olarize d fe atur e structu r e is a set o f p ola rized features with diﬀerent feature names. 2.2.4 Filtering feature structures Filtering fe atur e structur es are used to represent constraints on underspe ciﬁed dominances. A ﬁltering fe atur e stru ctur e is a p o la rized feature structure where all po larities ar e neutral. The constr a ints o n undersp eciﬁed dominances are stated in ter ms of c om- p atibility . A feature structure ϕ is sa id to be c omp atible with a ﬁlter ing feature structure Ψ (notatio n ϕ ⊳ Ψ) if, fo r e a ch feature name f deﬁned in b oth struc- tures, the atomic v alue as so ciated with f in ϕ is included in the disjunction asso ciated with f in Ψ . INRIA Inter action Gr ammars 17 2.2.5 P olarized no des A p olarize d no de is des crib ed b y:  a p ola r ized feature structure;  a no de t yp e. No de types express constraints on the phonological pr o jection o f no des in the mo del. Each node has one o f these four types:  anc ho r with an asso ciated phonologica l for m (a non-empt y string): the image of an anchor must b e a leaf of the tree mo del (anchors are drawn with a double b or der in ﬁgure s);  full : a full no de m ust have a n image with a non-e mpt y phonolo g ical pro- jection;  empt y : an empty no de must hav e a n image with an empty phonolo gical pro jection (empty no des are dr awn with white background in ﬁgures );  default : a default no de has no co nstraint on its phonological pr o jection. 2.2.6 P olarized tree descriptions W e conside r four t yp es of r elation b etw een no des in our tr e e descriptio ns: dominance The relation M > N co nstrains the ima ge of M to b e the mother o f the image of N . In such a r elation it ca n als o be imp osed that N is the leftmost (resp. rightmost) da ug hter of M : we write M > • N (resp. M > N • ). Finally , an a rity constra int can be expressed on the set of da ughters of a no de: M > { N 1 , . . . , N k } imp oses tha t the imag e of M in the mo de l has exactly k daughters that ar e images of the N i (this ar it y constra int do es not imp ose any order o n the k daugh ters of the no de M ). large dominance M > ∗ N constrains the image o f N to be in the subtree ro oted at the imag e of M 5 . A large dominance ca n also carr y an additional co nstraint on the no des that a re o n the pa th fro m M to N in the mo del: M > ∗ Ψ N (where Ψ is a ﬁltering feature structure) constrains that the image of N is in the subtr ee ro oted a t the image of M and that ea ch node along the path betw een the t wo images ca rries a feature structure whic h is compa tible with Ψ . precedence M ≺ N constrains the ima ges of the tw o no des to b e daugh ters of the same no de in the mo del a nd the imag e of M to be the immediate left sister o f the image o f N ; 5 Note that the symbol > ∗ is another relation whic h is not deﬁned as the reﬂexiv e and transitive closur e of the relation > . The same r emark applies to relations ≺ + and ≺ deﬁned below. RR n ° 6621 18 B. Guil laume & G. Perrier large precedence M ≺ + N c o nstrains the images o f the tw o nodes to b e daughters of the same node in the mo del and the image of M to precede the image of N in the ordered tree; this precedence is strict, hence the tw o images ha ve to b e diﬀerent. A p olarize d tr e e description (PTD) is deﬁned by:  a set of p o larized no des ;  a set of relations on these no des which veriﬁes the co ndition: if N 1 ≺ N 2 or N 1 ≺ + N 2 then there is a no de M suc h that M > N 1 and M > N 2 . Note that this co ndition imp ose s that N 1 and N 2 hav e the sa me mother in the IPTD and no t only in the mo del. 2.2.7 Initial p olarized tree descriptions IPTDs ar e elementary structures that are linked with words in the grammar; an IPT D is a PTD which veriﬁes the additional constr aint: the rela tio n > ∪ > ∗ deﬁnes a tr ee structure o n the no des, this implies connexity and the fac t that except the r o ot no de, all other no des N ha ve exa ctly either one mother no de M ( M > N ) or one a ncestor no de M ( M > ∗ N or M > ∗ Ψ N ). 3 S y nta ctic trees as mo dels of IPT Ds The aim of this section is to des crib e precisely the link betw een IPTDs a nd syntactic trees. 3.1 Syn tactic trees as mo dels of set of IPTDs Let G b e an interaction gramma r . A syntactic tree T is a mo del of a multiset of IPTDs P = { P i } 1 ≤ i ≤ k if ther e is an interpr etation function I from the no des N P of the multiset P to no des N T of the syntactic tree T s uch that: Dominance adequacy  if M , N ∈ N P and M > N then I ( M ) ≫ I ( N ). Large dominance adequacy  if M , N ∈ N P and M > ∗ N then I ( M ) ≫ ∗ I ( N ).  if M , N ∈ N P and M > ∗ Ψ N then I ( M ) ≫ ∗ I ( N ) and for each no de P in path ( I ( M ) , I ( N )), ϕ ( P ) ⊳ Ψ. Precedence adequacy  if M , N ∈ N P and M ≺ N then I ( M ) ≺ ≺I ( N ). Large precedence adequacy  if M , N ∈ N P and M ≺ + N then I ( M ) ≺ ≺ + I ( N ). F eature adequacy INRIA Inter action Gr ammars 19  if M ∈ N T and f = v is a feature of M then, for each no de N in I − 1 ( M ), either v is an admissible v alue for the featur e f in N or N do es not contain the feature name f ;  if M , N ∈ N P b oth contain a feature f with the sa me co-re ference, then the v a lues asso ciated with f in I ( M ) a nd I ( N ) are identical. No de t yp e adequacy  if M ∈ N P is an anchor with phonological form phon , then P P ( I ( M )) = [ phon ];  if M ∈ N P is e mpt y then P P ( I ( M )) = [];  if M ∈ N P is full then P P ( I ( M )) 6 = []. Saturation  the m ultiset of pola rities asso ciated to a feature na me f in the set of no des in I − 1 ( M ) which contains the feature f is globally s aturated. Minimali t y  I is surjective;  if M , N ∈ N T and M ≫ N then there is M ′ ∈ I − 1 ( M ) and N ′ ∈ I − 1 ( N ) such that M ′ > N ′ ;  if M ∈ N T and f = v is a feature of M then at leas t one node in I − 1 ( M ) contains a feature with name f ;  if M ∈ N P is a leaf node with a non-empt y phonological form phon , then I − 1 ( M ) contains exactly one anchor node with phono logical form phon . The four p o ints deﬁning minimalit y co ntrol the fact that “no thing ” is added when the mo del is built. They resp ectively control the absence of no de creatio n, parenthoo d relation crea tion, feature creation, and phono logical for m creatio n. Note that there can b e mor e than one interpretation function for a given tree mo del. 3.2 P olarized grammars An inter action gr ammar G is deﬁned as a set of IPTDs. The tree language deﬁned by the g r ammar G is the set o f sy n tactic trees which a re the mo dels of a multiset of I P TDs from G . The str ing language deﬁned by a grammar is the set of phonolog ical pro jections o f the trees in the tree languag e. W e said that a syntactic tree T is a p arse tr e e of a s e nt ence S , that is a list of words S = w 1 , . . . w n if:  T is a mo del of some multiset of IPTDs fro m G ,  P P ( T ) = [ w 1 , . . . , w n ]. An interaction gr ammar is said to b e lexic alize d if each IPTD cont ains at least one anchor (an a nchor is a leaf with a non-empty phonologica l form). An int era ction grammar is said to b e strictly lexic alize d if ea ch IPTD co n tains exactly one anchor. In this case , the link with the words o f the languag e can be seen as a function which maps a w ord to the subset o f IPTDs whic h have this word as the phonologica l form of its anchor. The grammar written so far for F r ench is stric tly lexicalized. RR n ° 6621 20 B. Guil laume & G. Perrier 4 T he expressivit y of In teraction Grammars W e pr esent four asp ects of IG that highlight their expressivity . W e illustrate these aspec ts with ex amples ta ken fro m our F rench IG because it is the o nly IG which is fully implemented at the moment, but there is no essential obstacle to use IG with other languages (an English IG is b eing written). 4.1 The use of p olarit ies for pairing grammatical words In F rench, there are some grammatica l words that are used in pairs :  comparative, “plus . . . qu e” (more . . . than), “moins . . . qu e” (less . . . than), “ s i . . . qu e” (so . . . that), “aussi . . . qu e” (as . . . as );  negation, “ne . . . p as” (not), “ ne . . . rien ” (nothing), “ne . . . aucun ” (no), “ne . . . p ersonne” (nob o dy), . . . ;  co ordinating words lik e “soit . . . soit . . . ” (either . . . or), “n i . . . n i . . . ” (neither . . . nor), “ou . . . ou bien . . . ” (either . . . or). The diﬃculty of mo delling them is that their rela tive po sition in the sentence is mo re or less free. F o r instance , her e a re exa mples that illustr ate v arious po sitions o f the determiner “aucun ” used with the particle “ n e” : (11) [A ucun] No c ol l` e gue colleague [ne] p arle talks ` a to la the femme wife de of Je an. John. ‘No collea gue talk s to J ohn’s wife.’ (12) Je an John [ne] p arle talks ` a to la the femme wife d’ of [aucun] no c ol l` e gue. colleague. ‘John talk s to no co lleague’s wife.’ (13) L e The dir e cteur director dans in [aucune] no entr eprise compagny [ne] d´ ecid e decides seul. alone. ‘The dir ector in no co mpagny decides alo ne.’ (14) Je an John [n ’] est is ` a at la the tˆ ete head d’ of [aucune] no entr eprise. compagny . ‘John is at the hea d of no co mpagny .’ (15) ∗ Je an John qui who dirige heads [aucune] no entr eprise, compagny , [n]’est isn’t satisfait. satisﬁed. The IPTDs from Figure 12, asso cia ted with the words “ ne” and “aucun ” , allow all these sen tences to b e correctly parsed. The w ord “ne” put a positive feature neg -> true on the ma ximal pro jectio n of the verb that it mo diﬁes and this feature is neutr a lized b y a dual feature n eg <- true provided by “ aucun ” . In its IPTD, there is a constr aint in the undersp eciﬁed dominance relation that forbids the acceptatio n of the sent ence (15). INRIA Inter action Gr ammars 21 cat ~ s cat ~ v neg -> true cat ~ aux | v /ne/ cat = clit cat <- n funct -> ? /aucun/ cat = det cat ~ v neg <- true cat ~ s cat ~ np | pp cat -> np funct <- ? cat = np | pp Figure 12 : IPTDs a s so ciated with the par ticle “ne” and the determiner “aucun ” 4.2 Constrained domina nce relations mo delling long-distance dep endencies Undersp eciﬁed dominance r e lations are used to repr esent unbounded dependen- cies and the feature s tr uctures that lab el these relations allow for the expr ession of c onstraints on these dep endencies, such as barr iers to extraction. Relative prono uns , such as “qui” o r “ le quel” , give rise to un b ounded dep en- dencies in series, a phenomenon that is called pie d piping . Sen tence (16) is an example o f pied piping. (16) Je an John [dans in l’ the entr eprise compagny de of qui ] whom Marie Mary sait knows que that l’ the ing ´ enieur engineer tr avail le works  est is malade. sick. ‘John, in the compa gny of whom Mary knows the enginee r works, is sick.’ (17) ∗ Je an John [dans in l’ the entr eprise compagny de of qui ] whom Marie Mary qui who tr avail le works  le knows c onna ˆ ıt it est is malade. sick. (18) ∗ Je an John [dans in l’ the entr eprise compagny qui which app artient belo ngs ` a to qui ] whom Marie Mary tr avail le works  est is malade. sick. In ex a mple (1 6), there is a ﬁr st unbo unded dependenc y b etw een the v erb “tr avail le” a nd its extracted complement “dans l’entr eprise de qui” . The trace of the extracted co mplement is denoted by the sym b ol  . This dep endency is RR n ° 6621 22 B. Guil laume & G. Perrier represented with an undersp eciﬁed dominance rela tion in the IPTD describing the synt actic b ehaviour of the relative prono un “qui” on ﬁgure 13. The dom- inance relation links the no de [RelCl] representing the relative clause “[dans l’entr eprise de qui ] Marie sait que l’ing ´ enieur tr avail le  ” and the no de [Cl] representing the clause “que l’ing ´ enieur tra vail le  ” , in which the extracted prep ositional phr ase “dans l’entr eprise de qui ” plays the role of a n oblique com- plement . T he ﬁltering fea tur e structure lab elling the rela tion expresse s that the path from [RelCl] to [Cl] can only c r oss a sequence of ob ject clauses. This way , the sen tence (17) is rejected b eca use the dep endency cr osses a noun phr ase, which violates the constra int. Inside the extra cted pr epo sitional phr a se, there is a second unbounded de- pendenc y be t ween the head of the phrase and the r elative pro noun “ qui” , whic h can b e embedded more or less deeply in the phrase. This dep endency is also represented on ﬁgure 13 with an undersp eciﬁed dominance r elation. This dom- inance r elation links the [Extr PP] no de and the node representing the rela tive pronoun “qui” and the ass o ciated ﬁlter ing feature s tr ucture expresses that the embedded cons tituen ts are o nly common no uns , noun phrases or prepo sitional phrases. Finally , the sentence (18) is rejected. [Cl] cat ~ s [TracePP] cat -> pp funct <- <4>? prep -> <5>? cat = np cat = prep [RelCl] cat <- s mood = cond | ind | inf typ = decl cat = s [ExtrPP] cat <- pp funct -> <4>? prep <- <5>? /qui/ cat -> np funct <- adj | aobj | dat | deobj | obl gen = <1>f | m num = <2>pl | sg pers = <3>3 cat = n | np | pp [ModN] cat ~ np gen = <1>f | m num = <2>pl | sg pers = <3>3 [Ant] cat ~ n | np Figure 13: IP TD asso ciated with the rela tive pro noun “qui” used in an oblique complement INRIA Inter action Gr ammars 23 4.3 Adjunction of modiﬁers wit h virt ual polarities In F rench, the p ositio n of adv erbial complemen ts in a sentence is relatively free, as the following examples s how: (19) L e soir , A t night, Je an John va r endr e visite ` a visits Marie. Mary . ‘A t night, John visits Mary .’ (20) Je an, John, le soi r , at night , va r endr e visite ` a visits Marie. Mary . ‘A t night, John visits Mary .’ (21) Je an John va r endr e visite visits le soi r at night ` a Marie. Mary . ‘John vis its Mary at night.’ (22) Je an John va r endr e visite ` a visits Marie Mary le soi r . at night . ‘John vis its Mary at night.’ These v ariants express diﬀeren t communicativ e in tentions but the adv erbia l complement “le soir” is a sentence mo diﬁer in a ll cases . The vir tual po larity ∼ was absent from the previous version of IG [35]. Mo diﬁer adjunction was pe rformed in the same way as in several formalisms (CG, T A G) b y adding a new level in the syntactic tree including the mo diﬁed constituent: ins tead of a no de with a categ ory X, we inserted a tree with a ro o t and tw o daug hters;  the ro ot represents the constituent with the categ ory X after mo diﬁer adjunction;  the ﬁrst daughter represents the co nstituent with the category X b efor e mo diﬁer adjunction;  the se c ond daughter represents the mo diﬁer itself. Sometimes, this introduction of an additional level is justiﬁed, but mos t of the time it brings additional artiﬁcia l complexity and ambiguit y . Borr owing an idea from the system o f black and white p olar ities of A. Nasr [31], we have int ro duced the virtual p ola rity ∼ . This p olarity allows for the intro duction of a mo diﬁer as a n additional da ug hter of the no de that it mo diﬁes without changing anything in the rest o f the tree including the mo diﬁed no de. Figure 13 g ives an example of an IPTD mo delling a mo diﬁer: the rela tive pronoun “qu i” , after combining with the relative clause that it in tro duces, provides a mo diﬁer of a noun phrase. The noun phra se to b e mo diﬁed is the antecedent of the re la tive pronoun, repr esented by no de [Ant] and the no un phrase , after mo diﬁcatio n, is the r o ot [Mo dN] of the IPTD. RR n ° 6621 24 B. Guil laume & G. Perrier 4.4 The c hallenge of coor dination Even if we r estrict our selves to syntax, mo delling co o rdination is a c hallenge . First, there is no consensus abo ut the ana lysis of the phenomenon in thslae communaut y of ling uists [10, 1 8]. Then, whatever the c hosen a pproach is, for- malization enco un ters serious obstacles . In particular, both Phrase Grammars and Dependenc y Grammar s ha ve diﬃculties for mo de lling co ordination of non- constituents. J. Le Roux and G. Perrier prop o se to mo del c o ordination in IG with the notion of p ola rity [25, 2 4]. F rom this notio n, they deﬁne the interface o f a PTD as the no des that car ry p ositive, negative or virtual p ola rities. The interface characterizes the ability of a phrase to interact with other phras es. Tw o phrases can be coor dinated if the P TDs r epresenting their syntactic structure oﬀer the same interface. Then, co ordination co nsists in mer ging the in terfaces of the tw o PTDs. This mer g ing needs to sup erp ose se veral p ositive or negative p olarities and it als o requires parse structure to be D AGs rather than trees . Hence, the merge of t wo interfaces cannot b e mo delled directly in IG and it is sim ulated in the PTD asso ciated with a co or dina tion conjunction: this is divided in to three parts; t wo low er parts a re used to satur ate the interfaces of the co njuncts and a higher part presents the co mmo n interface to the o utside. With this principle, it is p o s sible to par se the following sen tences, which illustrate diﬀerent kinds of non-constituent co or dination: (23) Je an John [b oit drinks du vin] wine et and [mange eats du p ain]. bread. ‘John dr ink s wine and ea ts brea d.’ (24) [Je an John aime] likes mais but [Marie Mary d ´ eteste] dislikes la c omp ´ etition. comp etition. ‘John likes but Mary dislikes compe titio n.’ (25) Je an John donne gives [des ﬂeurs ﬂow ers ` a to Marie] Mary et and [des b onb ons candies ` a to Pierr e]. Peter. ‘John g ives ﬂow ers to Mary a nd ca ndies to Peter.’ (26) L a The destruction destruction [de of la the gar e r outi` er e bus station p ar by les b omb es] bo mbs et and [de of la the gar e ferr oviair e railwa y station p ar by les tanks] tanks r end makes l’ ac c ` es access ` a to la the vil le city diﬃcile. diﬃcult. ‘The des truction o f the bus statio n by b ombs and of the railwa y station by tanks makes access to the city diﬃcult.’ (27) Je an John voit sees [sa its so eur sister lundi] on monday et and [son its fr ` er e brother mar di]. on tuesday. ‘John see s its sister on monday and its br other o n tuesday .’ INRIA Inter action Gr ammars 25 (28) [Je an John aime likes le ski] skiing et and [Marie Mary  la swimming. natation]. ‘John likes skiing and Ma ry likes swimming.’ Sent ences (23) and (23 ) resp ectively illustra te left and rig ht no de raising. Sent ences (25) and (26) illustrate coo rdination o f argument cluster s. Sen tence (27) coo rdinates clusters mixing arguments and adjuncts. Sentence (28) illus- trates the co o rdination of sen tences with gaps. Here, the gap, which is repre- sented b y the  symbol, corresp onds to the elided verb “aime” . 5 Comparison with other formalisms Currently , there exists no linguistic formalisms that prev ails over the others. This means that the doma in of natural lang uage mo delling is still in an em- bryonic s tate and the congestion o f the market is not a go o d reas o n for not examining a ny new pr op osal. On the contrary , the market is o p en. But any new formalism has to show s ome adv antages with respect to the established ones in or der to survive. The challenge is to approximate linguistic gener alities as muc h as p ossible while re maining tractable. Remaining tractable means b e- ing a ble to build la rge sc a le gra mmars and eﬃcien t parsers. Under this angle, the num b er of re le v ant formalisms is not that impo rtant: among the most well known and larg ely use d, there are LFG, HPSG, T AG or CCG. The compa r ison of IG with o ther for malisms will highlight some of its strong features. 5.1 Categorial Grammar The list of linguistic formalisms above mentions CCG (Combinatory Ca tegorial Grammars) [4 5]. CCG ar e pa rt of the CG family and since IG stems fro m CG, it is natura l to beg in the compara tive study with CG. IG shares with CG the fac t that syntactic compos ition is based on the re- source sensitivity of natura l langua ges, a prop erty which is built-in in b oth kinds of formalisms. How ever, they diﬀer in the framework that they use. F or this, w e refer ag ain to the distinction betw een tw o appr oaches for syntax in- tro duced by G. Pullum and B. Scholtz [3 7] and w e can claim that CG uses a generative-enumerativ e syn tactic (GES) framework wherea s IG uses a mo del- theoretic syntactic (MTS) fr amework. In o ther words, CG der ives all a cceptable sentences of a language from a ﬁnite s e t of axioms, the lexicon, using a ﬁnite set of r e writing rules. IG asso ciates sen tences w ith a set of cons traints, which are s olved to pr o duce their syntactic structures. [34] prop oses a metho d for tra nsp o sing grammar s from the GES to the MTS framework under some conditions . This metho d applies to CG and can b e used to compare IG with CG by putting them in the same MTS fra mework. The precise description of suc h a tr anslation go es b eyond the g oal of this ar ticle but we giv e a n outline of its output. T o be more precis e, let us fo c us on a particularly interesting member of the CG family: CCG. The fo r malism of CCG is a v ery g o o d c o mpromise b etw een expressivity , simplicity and eﬃciency . A t the same time, it is able to model diﬃcult linguistic phenomena, the most famous b eing co or dination [44 ], and it is used for par sing large cor p ora with e ﬃcient p o ly nomial algo rithms and lar ge scale g rammars [19, 11]. RR n ° 6621 26 B. Guil laume & G. Perrier If we use the metho d prop osed in [3 4] to tr anslate a particular CCG in the MTS fr amework, we obtain a very sp eciﬁc IG with the following features as output:  Each syntactic type is tra nslated in to an IPTD with a pa r ticular shap e. No des ar e lab elled w ith feature structures which c ontains only the cat feature. The v a lues of this feature a re the atomic type s of the CCG. Im- mediate dominanc e relations a lwa ys go fro m no des with a po s itive featur e to no des with a negative feature (po ssibly with intermediate no des without lab els). F or large do minance re la tions, this is the co ntrary .  In the output IPTD, there ar e no precedence rela tio ns. W or d or de r is con- trolled by a sp ecial featur e phon , which g ives the phonologica l form of each no de. This feature is neutral and takes its v alues fro m the monoid of the words of the lang uage. W e need to extend the sys tem of IG feature v alues to allow the prese nce of v ar ia bles inside terms representing pho n v alues. These v ar iables are used to mo del the sharing of unknown substrings o f words b y ph on v a lues of diﬀerent no des.  Successful CC G deriv a tions ar e tr anslated into cons tr uctions of IPTD mo dels. How ever, all v alid IPTD mo dels do no t corre s po nd to suc c essful deriv a tio ns, becaus e the particula r form of the co mbinatory r ules imposes constraints to sup erp osition. Conv ersely , in very rare cases, CCG deriv a- tions cannot b e tra ns lated in to co nstructions of IPTD mo dels b eca us e of t wo rules: backward and forward cr ossed compos itions. By allowing word per mutation, these rules c ontradict the monoto ny of the MTS framew or k . A simple solution consists in discarding the tw o proble ma tic rules and considering o nly a restriction of C CG. Even if the transla tion of a CCG in to an IG is no t p erfect, this highlight s the diﬀerence b etw een the tw o forma lisms. CCG ca n be viewed as IG with addi- tional co nstraints o n the form of IPTDs and sup er po sitions. What is imp or tant, is that no de merging is restricted to pairs o f no des with dual cat features. This has tw o imp or tant consequences:  It is not p o ssible to expr ess passive constraints on the environment of a syntactic ob ject, a s we do in IG using no de s with v irtual and neutra l features.  The internal structure of an IPTD, that is its saturated no des, is ignored by C C G. The only thing that matters is its in terface, that is its unsatu- rated no des . The abstra ction power that is ex pressed by this last remark is a so urce of ov er- generation for CCG. T o limit ov er-gene r ation, [3] hav e intro duced mo da lities to control the applicabilit y of com binators rules. These mo da lities are sp eciﬁed in the lexicon, so that the syntactic b ehaviour of a word can b e more o r less constrained. The problem is tha t w e cannot relativize these constraints with resp ect to the environment in which the word can be situa ted. F or instance, consider the following sentence: (29) Mary whom John met yesterday is my wife. INRIA Inter action Gr ammars 27 In CCG, the relative pro noun “whom” provides an ob ject for the clause tha t it int ro duces on the right p eriphery of this clause, but the transitive verb “met” exp ects its ob ject immediately on its right. The w ay to s olve this contradiction is to assign a modality to the lexical en tries of “met” and “yester day” , which allow the p e rmutation of the ob ject of “ m et” with “ yester day” . But, do ing this, we mak e the following sentence acceptable: (30) * John met yesterday Mary . IG does not present such an drawbac k, b ecause “yester day” is taken a s a sen- tence mo diﬁer and it is mo delled a ccording to the metho d pr esented in subsec- tion 4 .3. T o summarize, multi-modal CCG limits ov er-g eneration but do es not elimi- nate it. 5.2 Dep endency Grammars Like CG, Dep endency Gra mmar (DG) [32] does not denote a unique formalism but rather a family o f fo r malisms. At the ro ot of this family , ther e is the concept of dep endency . A dep endency links tw o words in an asymmetrica l manner: one word is the r´ egi ssant and the second word is the sub or donn´ e , according to the terminology intro duced b y L . T esni` ere, the pioneer of DG [47]. Even if there is no explicit notion o f po larity in DG, this under lie s the notio n of dep endency . The p otentialit y of tw o words to establish a dep endency b etw een themselves can b e expressed b y equipping the r´ eg issant with a negative feature and the sub or donn´ e with a positive feature, the tw o features having the same v alue, t he P OS (part-of-sp eech) of the sub or donn ´ e for instanc e . This is the general idea, which m ust b e made more precise by examining the diﬀerent DG formalisms. A key feature which diﬀerentiates DG v ariants is the r elationship betw een dep endency structure and word order . Pro jective DG forbid cro ss-dep endencies. They hav e interesting computa- tional prop erties and they can b e easily tr anslated into phrase s tr ucture gr am- mars, esp ecially Adjukiewicz- Bar-Hillel (AB) grammar s [4]. Since AB grammar s can be viewed as CCG with only tw o com binator y rules , forw ard a nd bac kward applications, the consequence is that pr o jective DG can b e translated in to IG following the method presented a b ove. This translation highlights the limits of pr o jective DG. In fa c t, these a r e not expressive enough to represe nt cross- depe ndencie s or lo ng -distance dep endencies. If we lo ok at non pro jectiv e DG, there is no formalism tha t has reached suﬃcient maturity to be used for developing rea l grammar s. Nev ertheless some works a re pr omising and we pr op ose to fo cus on Generalized Categorial Dep en- dency Gra mmar (GCDG) [13], which co nstitute a go od c o mpromise b etw e en expressivity and co mplexity . GCDG include tw o kinds of dependencies , thus g iving bir th to tw o indep en- dent formal sy s tems:  pro jective dep endencies are r e pr esented by AB gr ammars, slightly ex - tended to b etter take modiﬁer s into acc o unt,  discontin uous dep endencies are represented with p ola rities that neutralize themselves in dual pairs. RR n ° 6621 28 B. Guil laume & G. Perrier A word that is a ble to gov ern another o ne in a disco nt inuous dependency is equipp e d with a negative p olar ity typed by the categ ory of the sub or donn´ e a nd the su b or donn´ e is equippe d with the dual p ola r ity . This r epresentation of disco ntin uous depe ndenc ie s mak es the c ompariso n with IG diﬃcult. It is not p ossible to translate it in the framework of IG b ecause it has no simple relationship with domina nce and precedence rela tions, which consider phrases and not words. In IG, disc o ntin uo us dep endencies ar e genera lly represented in the IPTD a sso ciated with o nly o ne of the word res po nsible fo r the depe ndency , by means of an undersp eciﬁed dominance relation (see section 4). Another r e ason that makes the comparison b etw een IG and GCDG diﬃ- cult is that there is no eﬀectiv e GCDG for any langua ge. Nevertheless, we can make some r emarks. In GCDG, the iteration o pe r ator ∗ allows to repr esent mo diﬁers by sister adjunction as in IG. On the o ther hand, the her metic sepa- ration b etw een the t wo kinds of dependencies do es not allo w to expr ess that the same words r equire a dep endency when it do es not matter if the dependency is pro jective or discontin uous. Because of the ﬁne depe ndenc y structure that they prop os e, GCDG can con- tribute to mak e clearer a contro versial is sue in DG, the analysis of grammatica l function words, but they will b e confronted to syntactic constructions, whic h remain pr oblematic for all DG: co ordination for instance. 5.3 Uniﬁcation Grammars The family of Uniﬁcation Grammars (UG) includes a ll formalisms for whic h the mechanism of uniﬁcation b etw een feature structures o ccupies a central p o sition. HPSG [41] is the member of this family for which the idea is integrated as completely as p ossible. The grammatical ob jects are t yp ed featur e structures (grammatical rules, lexica l entries and par tial analysis structures ) a nd the only comp osition o p eration is uniﬁcation. F r om some a ngle, HPSG feature structures can b e viewed a s DA Gs, in which edges a re la bele d with feature names and leaves with atomic feature v alues . In this wa y , uniﬁcation app ears as D AG sup erp o s ition. As in IG, sup erp osition gives ﬂexibility to HPSG and allows to repr esent sophisticated pa s sive contexts of s yntactic constructions. The main diﬀerence is that the notion of unsaturated structure is not built- in in the co mp o s ition mechanism such as for IG with the notion o f p o la rity . How ev er, this notion is pr e sent in so me gr ammatical principles such as the V alenc e Princip le . Moreov er, HPSG pre sents three imp or tant diﬀerences with resp ect to IG  D AG are more expressive than trees. In this way , so me phenomena are easier to mo del with H PSG than with IG. F or insta nce, factorization, which is sp eciﬁc to co or dination, is dire c tly represented in HPSG [29], whereas it must b e sim ulated in IG (see pa ragr aph 4.4 and [25]).  Undersp eciﬁcation is more r e s tricted in HPSG than in IG; it reduces to the undersp eciﬁcation a sso ciated with uniﬁcation. All dominance relations are completely sp eciﬁed, so that unbounded dep endencies a re represented with another mechanism: the slash fe atur e , the pr opaga tion of which allows to mimic unbounded dep endencies. INRIA Inter action Gr ammars 29  word or de r is not expressed by linea r order b etw een DA G no des but with a sp eciﬁc feature PHON. Lexical F unctional Gr ammar (LFG) [9] is ano ther well known member o f the UG family , but b eca use of their functional structures paired with cons tituency structures, they are diﬃcult to compar e with IG IPTDs. Nev ertheless , pre- senting functional structur e s a s path equations allows the expr ession o f a form of underspeciﬁca tion, w hich is not present in HPSG but which e x ists in IG: the concept of functional unc ert ainty is simila r to the IG notion of la rge dom- inance, with the same p os sibility of constraining the do minance path b etw een no des without determining its length. T r ee Adjoining Grammar (T A G) [1] is often ra nked in the UG family , ev en if they are rather tree grammars but their use of uniﬁcation is more limited: contrarily to previous formalisms, it cannot be used to superp o s e structures. Structures only combine by adjunction, which grea tly limits the expr essivity of the for malism. 6 Compu tational asp ects A que s tion that ar ises natura lly for a new formalism is its complexity . The the- oretical complexity is a n important point but the les s formal notion of “prac- tical” complexity is also crucial for applica tions. The pr actical complexity can be thought a s: “ how do es the formalism b ehav e with real g rammars and real sentences?”. It is clear that IG is no t as mature as the other formalisms presented in the previous section. Ho wev er, so me theore tica l and practical works pres e nt ed in this s ection give some insights ab out this question in the IG framework. The cur r ent w ork fo c uses o n strictly lexicalized IG: the methods and algo- rithms presented in this section apply to gra mmars whe r e each IPTD contains exactly one anchor. F or such a grammar, we call lexic on the function that maps each word to its corresp onding set of IPTDs. Ho wev er, it is e asy to transform any lexica lized gra mma r in to an eq uiv alent strictly lexicalized grammar with the mechanism used in section 4 .1. In the particula r case of strictly le xicalized grammar, the deﬁnition of sec- tion 3.2 can b e refomulated as follows. A sen tence S = w 1 , . . . w n has a par se tree T iﬀ there is an order ed list of IPTDs P = [ P 1 , . . . , P n ] s uch tha t:  for all 1 ≤ i ≤ n , w i is the phonolog ic al form o f the anchor of P i ;  T is a mo del of the multiset {P 1 , . . . , P n } ;  P P ( T ) = [ w 1 , . . . , w n ]. Hence, the pars ing pro ce ss can b e divided in tw o steps: ﬁrs t, select for each word of the sent ence o ne of the IPTDs giv en by the lexicon; then build a syntactic tree whic h is a mo del of the list of IPTDs chosen in the ﬁrst step. The choice of one IPTD for each word of the sentence is called a lexic al sele ction . 6.1 Complexit y The general par sing problem for IG is NP-complete, even if the gra mmar is strictly lexicalize d. It can be shown for instance with an enco ding o f a fra gment RR n ° 6621 30 B. Guil laume & G. Perrier of linear logic (In tuitionistic Implicative Linear Logic) in IG. In tuitively , the complexity has tw o so urces:  Lexical am big uit y . In a lexica lized IG, each w ord o f the lexico n can b e asso ciated to several IP T Ds. Hence , the num ber s o f lexical selectio ns for a given s ent ence gr ows exp onentially with the n umber of words it contains.  P arsing am biguity . When a lexica l selection is done, a mo del should b e built for the cor resp onding list of IPTDs. Building a mo del is equiv alent to ﬁnding a partition on the set of no des o f the IP TDs such that each no de obtained by the mergings of no de s that ar e in the same subset of the partition are saturated. Once ag ain, there is an expo nential nu mber of p ossible par titions. The next tw o subsections a ddress these tw o s o urces of a mbiguit y . As a lready men tion ab ov e, w e address the problem o f pra ctical complex ity . Hence, w e are lo oking fo r algor ithms which behave in a n in teresting way for r eal NLP grammar s. F o r instance, the forma lis m can b e used to deﬁne a gra mmar without any a ctive p olarity , but this is clearly out of the IG “spirit”. The metho ds describ ed b e low are desig ned for well-polariz ed grammar s. 6.2 Global ﬁltering of lexical selections In this section, w e descr ibe a metho d whic h is formalized in a previous pap er [6] and w e see how it applies to the IG formalism. The idea is close to tagging, but it relies on more precise syn tactic descriptions than POS-tagg ing. Such metho ds a r e sometimes called sup er-tag ging [8]: we consider a n abstrac tion of our syntactic structures for which parsing is very eﬃcient even if this abstractio n brings ov er-gener ation. The key p oint is that a lexical selection which is not parsed in the abstr act level cannot b e pa rsed in the for mer level and can b e safely r emov ed. In IG, we co nsider a s an a bstract vie w o f a n IP TD the multiset of active features presen t in the IPTD. Then, a lexical selection is v a lid in the a bstract level if the union of the multiset asso ciated to IPTDs is globally saturated. The pars ing at this abstr a ct level is eﬃcient because it can b e do ne using ﬁnite state automata (FSA). F or each co uple ( f , v ) of a feature name and a feature v alue, an acyclic automaton is build with IPTDs as edges and integers as state: the in teger in a state is the coun t of p ola rities (pos itive counts for 1 and negative for − 1) for the co uple ( f , v ) along ev ery paths from initial sta te to the curre nt state. Finally , o nly lexical se le ctions which end w ith a state la be lled with 0 sho uld b e kept. An automa to n is built for each p o ssible couple ( f , v ), then a FSA intersection of the set of automata describ es the set of lexical s e lections that are globally saturated. The fact that feature v alues ca n be dis junction o f atomic v alues in IP T Ds causes the automata to b e no n deterministic. W e turn them into deterministic ones using interv als o f integers instead of integers in states of the automato n. When a g rammar uses man y pola rized features, the metho d can b e very eﬃcient and remov e many ba d lexical selections b efore the deep pa r sing step. F o r ins ta nce, for the sentence (6.2) the num b er of lexical selections reduces from 578 34 0 to 1 15 (in 0.08 s). INRIA Inter action Gr ammars 31 (31) L’ The ing ´ enieur engineer le him pr ´ esente presents ` a to l’ the entr eprise. ent erpr ise. ‘The engineer presents him to the enterprise.’ The main drawbac k of the metho d is that the count of p olar ities is global and do es not de p end on word o rder: an y permutation of a saturated lexical selection is still satur a ted. Some r ecent or ongoing works try to apply so me ﬁner ﬁlters on automaton. In [7], a specialized ﬁlter is describ ed dealing with co ordination for instance. F or each IP TD for a symmetrical co ordina tion, this ﬁlter remov es the IPTD if it is no t possible to ﬁnd tw o s equences of IPTD on each side of the co ordination with the exp ected multiset o f p olar ities. 6.3 Deep parsing Deep pa r sing in IG is a constraint satisfaction pro ble m. Giv en a list of IPTDs, we hav e to ﬁnd the set of mo dels of the corresp onding m ultiset which r esp ects the word order of the input sentence. Three a lg orithms hav e b een developed for deep parsing in IG: Incremen tal This alg orithm scans the sentence word by word. An atomic step consists in chosing a couple of p ositive and negative features to sup er p o se. In others words, a n in terpre ta tion function is built step by step, guided by the saturation prop erty of mo dels. CKY-like The CKY-like alg orithm, a s the incremental o ne, tr ies to build the int erpre tation function step b y s tep. The diﬀerence with the previous one is the wa y the sen tence is scanned; it is done by ﬁlling a chart with pa r tial parsing co r resp onding to sequence [ i, j ] o f co nsecutive words. Earley-like This last alg orithm tries to build at the same time the tree mo del and the interpretation function. It pro ceeds with a top-down/left-right building of the tree. 6.3.1 No de merging The ﬁr st t wo alg o rithms use the same atomic op eration of no de merging. This op eration takes as input a PTD D a nd a couple of no des ( N 1 , N 2 ); it returns a new P TD D ′ which veriﬁes that each mo del of D ′ is a mo del of D . The mo del sea r ching can be deco mp o s ed in small no de merging steps b ecause of the following prop er ty: if the unsatura ted PTD D ha s a mo del T then ther e are t wo dua l no des N 1 and N 2 such that T is still a mo del of the P TD o btained by merging of N 1 and N 2 in D . T e chnically , when tw o no des are merged, some other cons traint pr opagatio n rules c a n b e applied to the output description without c hanging the set of mo d- els. F or instance, if M 1 > N 1 and M 2 > N 2 and N 1 is merged with N 2 then M 1 is necess a rily merge d with M 2 . 6.3.2 The incremen tal algorithm As alr e ady said, there is an exp o nent ial num b er o f possible choices of couples of no des to merg e. The incremental alg orithm tries to mimic the hum an reading of a sentence and uses a notion of bound inspired b y psycholinguistics motiv ations RR n ° 6621 32 B. Guil laume & G. Perrier to guide the par sing. This notion o f b ound is used in a very similar spirit in Morrill’s works [28]. The psycholinguistic hypo thesis is that the r eading uses only a small memory to represent the already r ead par t of the sentence. Hence, w e bo und the nu mber of unresolved depe ndencie s that can b e left op en while scanning the sentence. In our con text, w e b ound the num b er of active po larities. Then the algorithm uses a kind of shift/reduce mechanism: we start with an empt y PTD and then we used recur sively the tw o rules : REDUCE if the current PTD has a n umber o f active p olarities greater than the bo und o r if there is no more IPTD to add, then try the diﬀerent wa ys to neutraliz e tw o dual active features; SHIFT else, add the next IPTD to the curr ent P TD. In the Leop ar implemen tation, the search spa ce is co ntrolled in the RE- DUCE op era tion. Couples of activ e p olar ities are o rdered in such a way that m ultiple constructions of the same mo del which diﬀer o nly by a p ermutation on the neutra lizations order ar e avoided. 6.3.3 The CKY-lik e algorithm The well-known CKY pars ing algor ithm for CFG ca n b e adapted to IG. The basic idea is to fo cus on contiguous sequence of w ords and to use the following informal r ule: A PTD for a sequence [ i, j ] is o btained with a neutr alization of tw o dual features in tw o diﬀerent PT Ds for s equences [ i , k ] and [ k + 1 , j ]. This rule is used r ecursively to ﬁll a chart. In the end, w e consider the PTDs obtained fo r the who le sentence and se arch for mo dels: use the REDUCE rule of the previous algor ithm until there is no mor e active p ola rity and s econd, build a totally ordered tree which is a mo del of the saturated PTD obtained in the ﬁrst step. The adv antages of this algorithm is that it does not dep end on a b ound and that it is a ble to s hare more sub-pa rsing. The drawbac k is that it is designed to ﬁnd only mo dels that follow some contin uity conditions: for instance, it is not able to ﬁnd a mo del if neutralization arise s betw een w 1 and w 3 in a 3 words sentence. Ho wev er, in our F r ench grammar, this condition is most of the time resp ected. But this algor ithm sho uld be g eneralized in or der to deal with other languages . 6.3.4 The Earley-lik e algorithm Another algorithm inspired by the classical Earley pa rsing a lgorithm for CF G has b een develop e d for IG. The algorithm is describ ed in [24, 26]. It is b eing implemen ted in Leop ar and the curr ent version is not very e ﬃcient but we hop e to improv e it for the next releas e. There are t wo main diﬃculties to adapt this classical algo r ithm to IG. First, when trying to build the tree mo de l to p-down, we hav e to deal with large do m- inance r elations. If the no de M is used to build a no de in the tr ee mo del and if M > ∗ N , then the no de N must b e used a t any depth in the constructio n of the sub-tree r o oted in M . Our solution is to include in each item a set of INRIA Inter action Gr ammars 33 no des that must b e used in the s ubtree ro o ted a t the cur r ent no de. The other diﬃcult y is to deal with the fact that the daughters o f a no de are only pa rtially ordered in IPTDs a nd that w e ha ve to consider every total order ing co mpatible with the partia l order when building the tree str ucture of the mo del. 6.4 Implemen t ation The IG formalis m is implement ed in a par ser named Leop ar . This softw are contains several mo dules which ar e used in tur n for s entence parsing. T ok enizer a minimal tokenizer is included: it allows to deal with us ual tok- enization problems lik e co ntraction (for insta nce in F rench, the written word “au” should b e understo o d as the contraction of the tw o w ords “` a” and “le” ). The tok enizer r eturns an acyclic g raph to represent tokeniza- tion ambiguities. Lexer a ﬂexible system of linguistic r esources description is used in Leop ar . Several levels of desc ription ca n be used to describ ed v ar ious linguistic information: morphologic a l, syntactical,. . . . Unanchored IPTDs are read in an XML format pro duced by XMG [14] (a n external to ol which provides a hig h lev el la nguage to build larg e cov erag e grammars ). The anc horing mechanism is controlled by the no tio n of interface:  each descr iption tree o f the unanchored gr ammar is as so ciated with a feature struc tur e called int erfac e ;  each word is linked to a set of usages: a usage is a feature structure which describ es the mo rphologic a l and s yntactical prop erties of a word;  if an interface I ( T ) of a tree description T uniﬁes with a word usa ge U a sso ciated with a word w : then an IPTD T ′ is pr o duced from T with w as pho no logical form. The lexer outputs an acy c lic gra ph which edges a re la belle d by IPTDs. Filter this s ta ge implement s the global ﬁltering of lexical selections pr e sented ab ov e (subsection 6.2). It tak es as input the acyclic graph given b y the lexer a nd returns another acyclic graph which paths are the le x ical sele c- tions kept by the ﬁltering pro c ess. Deep parser the ﬁnal stage is the building of a set of mo dels for the acyclic graph g iven by the previous stag e. Implemented alg orithms are adapted to deal with the sharing given by the graph r epresentation of the ambiguit y in the output of the ﬁltering pro cess. The whole system ca n b e used either with c o mmands or through a n interface. In the interface, an in terac tive mo de is av ailable. The use r can choo se a path in the automato n given by the ﬁlter stage and then c ho ose couple o f no des to merge: this interactiv e mo de is very use ful in grammar testing/ debugging. RR n ° 6621 34 B. Guil laume & G. Perrier 7 Conclus ion In this pap er, we fo cused on a for mal pr esentation of IG, highlighting their or ig- inality with their a bility to expres s v a r ious and sophisticated ling uistic phenom- ena. W e left both Lang uage-Theo retic prop er ties and implementation asp ects of IG as ide , as they need to be studied for themselves. One of our fundamen tal ideas is to com bine theory and practice. The for - malism of IG is implemen ted in the Leop ar parser in the same form as it is describ ed in this pap er. In this wa y , it can b e v alidated exp er iment ally . T o use Leop ar on large co rp ora, we need r e sources. The r e exists a F rench IG with a relatively larg e coverage [36], which is usable with a lexico n independent of the IG formalism [17]. There exists a lexicon w ith a larg e cov erage av ail- able in the for mat required by the grammar: the Le ﬀf [42]. T he Le ﬀf con tains ab out 5 00 000 inﬂected forms corresp onding, among others, to 6 800 verb lem- mas, 37 600 nominal lemmas and 10 000 adjectiv al lemmas. With the Le ﬀ f and the F rench IG, Leo p ar is on the way of parsing r eal co rp ora. The formalism is not deﬁnitively ﬁxed a nd the forward and backw ard motio n betw een theory and practice is impor tant to improv e it step by step. Among the ques tions to b e studied in a deep er way , there are: the form of the syntactic structur e of a sentenc e: phenomena s uch as co- ordination or dislo cation show that the notion o f syntactic tr ee is to o limited to express the complexit y of the syntactic structure of sen tences; structures as direc ted acyclic graphs ﬁt in better with these phenomena; the enrichment of the fe atu r e dep endencies: dep endencies be t ween featur es are frequent in linguistic constr uctions but they canno t b e r epresented in a compact wa y in the cur r ent version of IG; all cases hav e to be enumer- ated, which is very co stly; it seems not to b e a diﬃcult problem to enrich the featur e system in o rder to integrate these dependencies . 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