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<?xml version="1.0" standalone="yes"?> <Paper uid="C90-3017"> <Title>A Symmetrical Approach to Parsing and Generation</Title> <Section position="2" start_page="0" end_page="0" type="metho"> <SectionTitle> 2 Al~o <'ailed meh' r.h'x I11781. </SectionTitle> <Paragraph position="0"> Hypotheses on compositionaHity. The parsing and generalion problems can be rendered tractable only if certain hypmheses are made concerning the composition of linguistic structures. Thus generation can be arduous if the semantics associated with the composition of two structures is the nm'estricted lambda-application 3 of tile first structure's semantics on the second structure's semantics: this is because knowledge of the mother's semantics does not constrain in a usable way the semantics of the daughters. 4 On the contrary, parsing is greatly simplified if the string associated with the composition of two strqctures is the concatenation of tile strings associated with each st,ucture: one can then use string indexing to orient and control tl'e progression of the parsing process, as is done in DCG under tile guise of &quot;dil'ferential lisls&quot;.</Paragraph> <Paragraph position="1"> l,exical Granlmar. The formalism of Lexical Grammar (LG) makes explicit certain compositionality hypotheses which ensure the existence of guides for parsing as well as for generation.</Paragraph> <Paragraph position="2"> A Lexical Grammar has two parts: a (variable) lexicon and a (fixed) rule component. The rule component, a definhe clause specification, spells out basic linguistic compositionality rules: (i) how a well-formed linguistic structure A is composed from well-formed structures B and (27: (it) what .:ire the respective statuses of B and C (left constituent vs ri,,,ht constituent, syntactic head vs syntactic dependenl, semantic f-wad vs semantic depemlent): and (iii) how the string (,'esp. semantics, subcategorization list .... ) associated with A is related to the strinoA (resp.</Paragraph> <Paragraph position="3"> semantics, subcategorization lists .... ) associated with /3 and C (see sectioi, 2).</Paragraph> <Paragraph position="4"> The ability to define a guide for parsing is a (simple) consequence of the fact that the string associated with A is the concatenation of the strings associated with B and (.,5. The ability to define a guide for generation is a (less simple) consequence of LG's hypotheses on subcategorization (see sections 2 and 4).</Paragraph> <Paragraph position="5"> &quot;~ By tmrestricted lambda-application, we mean functional application lbtlowed by, ivwriting to a ilOl'tlla\] lollll, 4 In theories favoring such an approach (such as GPSG IGKPS871), parsing may be computatiollally tractable, but generation does not seem to be. These theories can be questioned as plausible computational models, for they should be judged on Iheir ability to account for production behavior (generation) as well as for understanding behavior {parsing).</Paragraph> </Section> <Section position="3" start_page="0" end_page="0" type="metho"> <SectionTitle> 5 A fairly standard assumption, ll: empty string lealizalions are allowed, then </SectionTitle> <Paragraph position="0"> extraposifion call still be handled, as '~ketched in section 5.</Paragraph> <Paragraph position="1"> 90 1 (P0) Lexical Grammar rules /N conse Kvat J ve addit i on conserva t J ve add:i t i on of parsing guide o\[ gent.ration guide ./ \ guided parsing guided generation generation: paper overview Parsing and Generation with l,exical Grammar. Fig. I gives an overview of our approach to parsing and generation. Let us briefly review the niain points: -- (P0) is a definite clause specification of the original LG rules. It contains a purely declarative definition of linguistic compositionality, but is unsuitable for direct implementation (see section 2).</Paragraph> <Paragraph position="2"> ..... (Pip) (resp (Plg)) is a guided conservative extension of (P0) for parsing (resp. for generation); that is, (Plp) (resp (Plg)) is a specification which describes the same linguistic structures as (P0), hut adds a certain redundancy (guiding) to help constrain the imrsing (resp. generation) process, ttowever, these definite clause programs are not yct adequate for direct top-down implementation, since they are left-recursive (see section 3). -- (Plp) and (Pig) can be seen as symmetrical instantiations of a common program schema (P1); (Pl) can be transformed into (P2), an equivalent non-leftorecursive program schema (see section 3).</Paragraph> <Paragraph position="3"> -- (P2p) (resp (P2g)) is the non-left-recursive version of (Plp) (resp. (Pig)). Under the guide-consumption condition, it is guaranteed to terminate in top-down interpretation, and to enumerate all solutions to the parsing (resp. generation) problem (see section 4).</Paragraph> <Paragraph position="4"> For lack o/' space, theorems are stated here without proofs'; these, and more details, can be \]bund in \[D9Ob\].</Paragraph> </Section> <Section position="4" start_page="0" end_page="0" type="metho"> <SectionTitle> 2. Lexical Grammar </SectionTitle> <Paragraph position="0"> Rule component The fixed rule component of LG (see Fig. 3) describes in a generic way the combination of constituents. A constituent A is either lexically specified (second clause in the phrase definition), or is a combination of two constituents /3 and C (first clause in the phrase definition). B and C play complementary roles along the following three dimensions: -- combine .strings : B is to the hift of C in the surface order, or conversely to the right of C.</Paragraph> <Paragraph position="1"> This information is attached to each constituent through the string order feature.</Paragraph> <Paragraph position="2"> -- combine syns : B is the syntactic-head and C the syntactic-dependent, or conversely (syn order feature).</Paragraph> <Paragraph position="3"> .... combine seres : B is the semantic-head and C the semantic-dependent, or conversely (sere_order feature).</Paragraph> <Paragraph position="4"> Because B and C play symlnetrical roles (' , these seemingly eight combinations actually redttce to four different cases. To avoid duplicating cases, in the definition o1' the phrase predicate, the symmetry has been &quot;broketf' by arbitrarily imposing that B be the left constituent. 7 Fig. 2 gives an example of a derivation tree in LG, using the lexicon of Fig. 4.</Paragraph> <Paragraph position="6"> Our notion of semantic-head is a variant of that given in \[SNMP89\], where a daughter is said to be a semantic-head if it shares the semantics of its mother.</Paragraph> <Paragraph position="7"> The combine seres predicate is responsible for assigning sere -I-wad status (versus sem dep status) to a phrase, and for-imposing the following constraints: i. the semantic-head shares its semantics with its mother, it. the semantic-head always subeategorizes its sister ((b) in Fig. 3), iii. the mother's subeategorization list is the concatenation of the semantic-dependent list and of the semantic-head list minas the element just incorporated ((c) in Fig. 3). 8 The subcategorization list attached to a constituent X corresponds to constituents higher in the derivation tree which are expected to fill semamic roles inside X. Subcalegorization lists are percolated flom the lexical entries up the deriw~tion tree according to iii.</Paragraph> <Paragraph position="8"> 6 Remark: the rules are m)t DCG rules, bul simply d<finite (orl\]o!C/ 0 (tau.sc.~ 7 If line (a) in the definitioll of phrase were omitled, the same ~('l el lingtListic strUCtLIFeS Wollld result, but some strLlcltlres ',A'otl\[d be described twice, Line (a) is simply onc means of clinlinating these spurious ambiguities. '\[he S~llllC el'lEcl would be produced by rephlcing (a) by fi.sem enter = sere \]wad or by</Paragraph> <Paragraph position="10"> % complement ; C.sem order = sere_head, C.subcat = \[_ \]). % modifier (b) (c) Semantic-heads need not correspond to syntacticheads. In the case of a mod~fi'er like often, in paris, or hidden by john, the modifier phrase, which is the syntactic-dependent, is the semantic-head and semantically subcategorizes its sister: thus, in the example of Fig. 2, the modifier phrase D semantically subcategorizes its sister E; combine sen:s has then the effect of unifying tile semantics of E (visit(ntary,nd)) to the substructure X in the semaatics (often(X)) attached ) -e to D (see the lexical enty for ~jten in Fig, 4). This is reminiscent of work done in c'ttegorial gramnmr (see for instance IZKC~ ~l), where a n'odifier is seen as having a category of the fornl A/A, aud acts ;.Is a functor on the group it modifies.</Paragraph> <Paragraph position="11"> The combine syms predicate is responsible for assigning swz_head status (verstls syndcp status) to a phrase, and for ensuring the following constraints: i. Tile category cat of the ssntactic-head is transmitted to the mother. The category of a phrase is lherefore always a projection of the category (n.vpa ..) of some lexical item.</Paragraph> <Paragraph position="12"> ii. When the syntactic-dependent is the same as tile semamic-dependent, then the syntactic-dependent is semantically saturated (its subcat is empty). This is the case when the syntactic-dependent plays the syntactic role of a complement to its syntactic-head.</Paragraph> <Paragraph position="13"> iii. When the syntactic-dependent is tile same as the semantic-head, then tile syntacticdependent's subcat contains only one element m. This is the case when the syntactic-dependent plays the syntactic role of a rood(fief to its syntactic-head.</Paragraph> <Paragraph position="14"> The lexicon in LG Because LGs have a fixed rule component, all specific linguistic knowledge 9 Here, as in the sequel, we have made use of a &quot;dot notation&quot; for functional access to the different featttros of a linguistic structure A: for instance, A.cat represen%; the content of tile ('at feature ill A. l0 The &quot;external argument&quot; of the modifier, identified with the ~;emanticdependent by tile semantic combhmtkm rule.</Paragraph> <Paragraph position="16"> Consider a typical entry, for instance the cntry for in. This entry specifies a possible leaf T of a derivation tree. T has the following properties: i. T has string \[in\], and is of category p (preposition).</Paragraph> <Paragraph position="17"> ii. T semantically subcalegorizes two phrases: O (the object of the preposition), of category n. and S (the &quot;implicit subject&quot; of the preposition), of category v. By the general constraints associated with combine seres, this means that S and O will both have semantic-dependent status.</Paragraph> <Paragraph position="18"> iii. In the surface order, S is to the left of its semantic-head, while O is to the right of its semantic-head.</Paragraph> <Paragraph position="19"> iv. The semantics in(S.sem,O,sem) of 7 is obtained by unification from the semantics of its subcategorized constituents S and O.</Paragraph> <Paragraph position="20"> v. S is constrained to having syntacticqmad status, and O to having syntactic-dependent status.</Paragraph> <Paragraph position="21"> Because of the constraints imposed by combine syns, this means that O will be a syntactic complement of the preposition, and that the prepositional phrase will be a modifier of its &quot;subject&quot; S.</Paragraph> <Paragraph position="22"> Idioms. The lexical apparatus allows for a direct account of certain types of idiomatic constructions. For instance, if the lexical entries of Fig. 5 are added to the For eas ~ is f ex msilion, tile c )tltlib itioll of he tense to the semantics of verbs is ignored here.</Paragraph> <Paragraph position="23"> 92 3 lexicon, then the expression &quot;X kicked the bucket&quot; will he assigned the semantics die(X). Entry (a) expresses the fact that (in its idiomatic use), the verb form kicked subcategorizes for a subject S and an object 0 whose semantics is thebucket, and is itself assigned the semantics dietS.sere).</Paragraph> <Paragraph position="25"> 3. Guides and lefl-recursion elimination Guide,i. Consider a finite string l t, and let 12 be a proper suffix of ll, l 3 be a proper suffix of 12, and so on. This operation call only be iterated a finite number of times. The notion of guide-structure generalizes this ~,;ituation.</Paragraph> <Paragraph position="26"> DEFINITION 3.1. A guide-structure is a partially ordered set G which respects the descending chain condition, i.e the condition that in G all strictly decreasing ordered chains 11 > 12 > ... > l i > ... are ,finite.</Paragraph> <Paragraph position="27"> Consider now the following elementary definite clause program (P0')t2: a(A) :- a(B), ~(B.A). (P0) a(A) :- ttA).</Paragraph> <Paragraph position="28"> We assume here that g) is an abbreviation which ,,;lands for a disjunction (C:,'-...'('k) of conjunctions Q of goals of the form a(A), t(A), or {T=S} (unification ::oals) where the T, S are variables or partially iustantiated terms. Among the variables appearing inside 'i), only the &quot;interface&quot; variables A, B are explicitly mentioned. We further assume that the defining clauses (not shown) for the t predicate have right-.hand sides which are conjunctions of term unification goals {T=S}. We call t the lexicon predicate, and a the generie nonterminal predicate. Consider now the following program (Pl), called a guided extension of (P0):</Paragraph> <Paragraph position="30"> (Pl) is obtained from (P0) in the following way: (i) guide variables (Lin, Linte r, Lout)have been threaded throughout (P0), and (it) the l-predicate t has been rcphtced by a 3-predicate t'which is assumed to be a r<finement of t, ie, Jbr all A, Li,, Lot ., t'(A,Lip~,Lour) imp.lies t(A).</Paragraph> <Paragraph position="31"> Program (Pl) is a more constrained version of program (P0): t' can be seen as a version of t which is able to &quot;consult&quot; Liv ~, thus coostraining lexical access at each step. We will be interested in programs (Pl) which respect two conditions: (i) the guide-consumption I! Only programs of the (P0) form are discussed here, but the subsequent discussion of guides generalizes easily to arbitrary definite clause programs. condition, and (it) the conservative extension condition.</Paragraph> <Paragraph position="32"> I)~iFlNrrlOY 3.2. Program (PI) is said to satisfy the guide-consumption condition if/&quot; (i) the guide variables take their values in some guide-structure G, and (it) any call to t'(A,Lin,Lout) with Lin fully instantiated returns with Lou t ./idly instantiated and strictly smaller in G.</Paragraph> <Paragraph position="33"> DEFINITION 3.3. Program (P1) is said to be a conservative extension of (PO) iff: a(A) is provable in (PO) e:> there exist Lin,Lou t such that a'(A,Lin,Lout) is provable in (P1).</Paragraph> <Paragraph position="34"> The ~ part of the previous definition is automatically satisfied by any program (P1) defined as above. The ~ part, on the other hand, is not, hut depends on further conditions on the refinement t' of t. Saying that (PI) is a conservative extension of (P0) is tantamount to saying that (P1) adds some redundancy to (P0), which can be computationally exploited to constrain processing.</Paragraph> <Paragraph position="35"> Left-recursion elimination 13. Program (PI) is left-recursive: in a top-down interpretation, a call to a' will result in another immediate call to a', and therefore will loop. On the other hand the following program (P2) is not left-recursive, and Theorem 3.4 shows fllat it is equivalent to (Pl):</Paragraph> <Paragraph position="37"> Here, ,.to' and t' are the same as in (P1), and a new predicate aux, called the auxiliary nonterminal predicate has been introduced.~4 THFORFM 3.4. Programs (P\] ) and (P2) are equivalent in predicate a'.l 5 The fact tMt (p2) is not left-recursive does not alone guarantee termination of top-down interpretation. However, if (PI) respects the guide-consumption condition and a further condition, the no-ehain condition, then (P2) does indeed terminate. 16 DEFINrrIoN 3.5, Program (P1) is said to re,v~ect the no-chain condition llf each goal conjunction Ci' appearing in (c)' contains at least one call to a' or to t'. THEOREM 3.6. Suppose (PI) satisfies both the guide-consumption condition attd the no-chain condition. Then relative to top-down, depth-first, interpretation of (P2), the query a(A,L0,Ln), with L 0 completely instantiated, has a finite SLD search tree \] 7 associated with it (in other words, all its solutions will be enumerated through backtracking, and the program will terminate).</Paragraph> <Paragraph position="38"> 4. Parsing and generation in Lexical</Paragraph> <Section position="1" start_page="0" end_page="0" type="sub_section"> <SectionTitle> Grammar </SectionTitle> <Paragraph position="0"> The rules of Fig. 3 are completely symmetrical in their specification of syntactic compositionality, 13 The general problem of left-recm'sion elimination m I)CGs (including chain rules and mall rules \[H78\]) is studied in \[D90al; the existence of a Generali=ed Greibaeh Normal Form is proven, and certain decidability results are givcll.</Paragraph> <Paragraph position="1"> 14 The (PI) ~ (I)2) translbrmation is closely related to lej?-eorner parsing \[MTIIMY83\], which can in fact be recovered fronl this transformation through a certain encoding t)rocedurc (see ID90b\]),</Paragraph> <Paragraph position="3"> Orienting the rules. The phrase predicate can be rewritten in either one of the two forms: phrase j), where emphasis is put on the relative linear order of constituents (h, ft vs. right), and phrase_g, where emphasis is put on the relative semantic status (semantic head vs. semantic dependent) of constituents.</Paragraph> <Paragraph position="5"> combine(B,C,A).</Paragraph> <Paragraph position="6"> LEMMA 4.1. phrase_p and phrase g are both equivalent to phrase.</Paragraph> <Paragraph position="7"> The phrase j) (resp. phraseg) programs are now each in the format of the (P0) program of section 3, where a has been renamed: phrase p (resp. phrase_g), and 09: P(resp. G).</Paragraph> <Paragraph position="8"> These programs can be extended into guided programs (Plp) and (Plg), as was done in section 3: phrasej/(A,Lin,Lou t) :- (Plp) phrase p'(B,Lin,Linter), P'(B,A,Linter,Lout). phrase_p'(A,Lin,Lout) :- term~o'(A,Lin,Lout). where: and In these programs, term p' and term_g' are the refinements of term (corresponding to t' in program (P1) of section 3) used for parsing and generation respectively. Their definitions, which contain the substance of the guiding technique, are given below. N.B. Programs (Plp) and (Pig) respect the no-chain condition:phrase_p' is called inside 'P', and phrase_g' is called inside G'.</Paragraph> <Paragraph position="9"> A conserv'ltive guide for parsing. Let us define term_p' in the following way: term I/(A,Lin,Lou t) :- term(A), append(A.string,Lo,,.Li,~).</Paragraph> <Paragraph position="10"> (Gp) It is obvious that term p' is a refinement of term. Using the definition of combinestrings&quot; in section 2, one can easily show that program (PIp) is a conservative extension of program (POp). The guide-structure Gp is the set of character strings, ordered in the following way: st\] <_ st2 iff stl is a suffix of st2. If the lexicon is such that for an 5 ' entry term(A), A.string is instantiated and is different from the empty list, then it can easily be shown that (PIp) respects the guide-consumption condimm. The guide just introduced for parsing is simply a restatement in terms of guides of the usual differential lists used in the Prolog translation of DCG rules. A conservative guide for generation. Let us define term g&quot; in the following way (using the auxiliary predicate extract sems): term_g'(A,Lin.Lo, t) .'- term(A), L m=\[A.sem/Lmter\], extract sems(A.subcat,SubcatSems), append(SubcatSems,Li,te!.,Lont).</Paragraph> <Paragraph position="11"> extract_sems( \[\],/ \] ).</Paragraph> <Paragraph position="12"> extract_sems(\[X/Rest\],\[X.sem/RestSems\]).'extract sems(Rest.RestSems). (Gg) The guide structure L used for generation is a list of semantic structures, initially instantiated to IS.semi, where S is the linguistic structure to be generated, of which the semantics S.sem is known. When a call term g'(A,Lin,Lo,a) to the lexicon is made, with Lin instantiated to a list of semantic structures, the lexical structure A selected is constrained to be such that its semantics A.sem is the first item on the Lin list. The A.sem element is &quot;popped&quot; from the guide, and is replaced by the list of the semantics of the phrases subcategorized by A. (Fig. 7 illustrates the evolution of the guide in generation.) 18 This symmetry should not be obscured by tile fact that, in order to avoid duplicating clauses with the same logical content, the presentation of tile rules appears otherwise (see above the discussion of &quot;broken symmetry&quot;). It is&quot; obvious that term_g' is then a refinement of term, and furthermore, using the definition of eombine sems in section 2, one can prove: Lt&quot;,MMA 4.2. Progranl (Plg) is a conservative extension of program (POg).</Paragraph> <Paragraph position="13"> 7'he guide.consumption eonditio~ in generation. Let us define recursively the size of an LG semantic representation as the function fi'om terms to natural numbers such that: size\]atom\] = 1 size\[atom(T I ..... T,)\] = 1 + sizelTl\] + ... + sizelT,J Assume now that, for any entry term(A), the lexicon respects the following condition: If A.se,n is fully instantiated, then the A.subcat list is instantiated sufficiently so that, for any element X of this list, (i) X.sem is J'ully instantiated, and (ii) X.sem has a strictly smaller size than A.sem.</Paragraph> <Paragraph position="14"> Under these conditions, one can define a guide-structure Gg (see \[D90b\]), and one can prove: LEMMA 4.3. Program (Plg) satL@'es the guide-consumption condition.</Paragraph> <Paragraph position="15"> The resulting programs for parsing and generation. After the left-recursion elimination transforrnation of section 3 is performed, the parsing and generation programs take the following forms: convenience interface predicates parse and generale arc provided.</Paragraph> <Paragraph position="16"> Under the conditions on the lexicon given above -- which are satisfied by the lexicon of Fig. 4 - , programs (Plp) and (Pig) both respect the guide-consumption condition; they also respect the no-chain condition (see remark following the description of (Pip) and (Plg)); Theorem 3.6 applies, and we have the following result: /f parse(A.string,A.sem) (resp.</Paragraph> <Paragraph position="17"> gencrate(A.string,A.sem)) is called with A.string instantiated (re,v). A.sem inslantialed), then all solutions will be enumerated on baeklracking, and the query will terminate.</Paragraph> </Section> </Section> <Section position="5" start_page="0" end_page="0" type="metho"> <SectionTitle> 5. Further research </SectionTitle> <Paragraph position="0"> Handling extrapositinn with guides. The specific guides defined above for parsing and generation are not the only possible ones. If for some reason certain conditions on the lexicon are to be relaxed, then more sophisticated guides must and can be defined.</Paragraph> <Paragraph position="1"> Thus, the guide introduced above for parsing essentially assumes that no lexical entry has an empty string realization. This condition may be too strict for certain purposes, such as handling traces.</Paragraph> <Paragraph position="2"> Interestingly, however, the guide consumption condition can still be imposed in these cases, if one takes care to suitably enrich the notion of guide.</Paragraph> <Paragraph position="3"> I,et us assume, fl)r instance, that there be a general syntactic constraint to the effect that two empty lexical 6 95 items cannot immediately follow each other 19. Let us then posit as a guide structure, instead of a list L of words, a couple <L,B>, where B is a variable restricted to taking values 0 or 1. Suppose further that these couples are ordered &quot;lexicographically&quot;, ie that:</Paragraph> <Paragraph position="5"> It is easy to see that the set of guides is then a partially ordered set which respects the descending chain condition.</Paragraph> <Paragraph position="6"> Let us finally assume that term_p' is redefined in the following manner: It can be shown that this definition of guide_parse is sufficient to ensure the guide-consumption condition, and therefore guarantees the termination of the parsing process.</Paragraph> <Paragraph position="7"> Variations on this idea are possible: for instance, one could define the guide as a couple <L,X> where X is a list of left-extraposed constituents (see \[P81\]). Any time a constituent is added to the extraposition list X, this operation is required to consume some words from L, and any time a trace is encountered, it is required to &quot;cancel&quot; an element of X. Because the lexicographical order defined on such guides in the following way:</Paragraph> <Paragraph position="9"> respects the descending chain condition, the parsing process will be guaranteed to terminate.</Paragraph> </Section> class="xml-element"></Paper>