Frank, Robert

Hunter, Tim

English

ScholarWorks@UMass Amherst

Proceedings of the Society for Computation in Linguistics Volume 4 Article 36 2021 Comparing methods of tree-construction across mildly context-sensitive formalisms Tim Hunter University of California, Los Angeles, timhunter@ucla.edu Robert Frank Yale University, bob.frank@yale.edu Follow this and additional works at: https://scholarworks.umass.edu/scil  Part of the Computational Linguistics Commons Recommended Citation Hunter, Tim and Frank, Robert (2021) "Comparing methods of tree-construction across mildly context-sensitive formalisms," Proceedings of the Society for Computation in Linguistics: Vol. 4 , Article 36. DOI: https://doi.org/10.7275/2yek-w380 Available at: https://scholarworks.umass.edu/scil/vol4/iss1/36 This Paper is brought to you for free and open access by ScholarWorks@UMass Amherst. It has been accepted for inclusion in Proceedings of the Society for Computation in Linguistics by an authorized editor of ScholarWorks@UMass Amherst. For more information, please contact scholarworks@library.umass.edu. Comparing methods of tree-construction across mildly context-sensitiveformalismsTim HunterDepartment of LinguisticsUniversity of California, Los Angelestimhunter@ucla.eduRobert FrankDepartment of LinguisticsYale Universitybob.frank@yale.eduA central constraint on minimalist derivations iscyclicity, as instantiated in the extension condition(Ext), which permits trees to grow only at (or near)the root. A second key idea concerns the notion ofderivational state: how much information about thederivational past can the applicability of a certainoperation be contingent on? Conditions along thelines of Phase Impenetrability and Shortest Move,for example, can sometimes limit the amount ofinformation that conditions subsequent derivationalsteps; some versions of such conditions result in afinite bound (Fin).Interestingly, Ext and Fin define points of vari-ation across mildly context-senstive grammar for-malisms, systems that have been proposed to char-acterize the computational structure of syntacticderivations. On the one hand, Minimalist Gram-mars (MGs; Stabler, 2011) abide by Ext, mak-ing use of the standard minimalist operations ofMerge and Move, as do Combinatory CategorialGrammars (CCGs; Steedman, 1996), whose deriva-tions involve bottom-up concatenation of lexicalitems, and the closely related Linear Indexed Gram-mars (LIGs; Gazdar, 1988). In contrast, the ad-joining operation of Tree Adjoining Grammars(TAGs; Joshi and Schabes, 1997) allows trees togrow “in the middle”, contra Ext. Turning to Fin,both MG and TAG operate with bounded deriva-tional state, whereas CCG, with its unboundedlylarge categories, and LIG, with its stack-valuednon-terminals, permit unbounded state. These rela-tionships are summarized in the table in (1).(1) Ext ¬ExtFin MG TAG¬Fin LIG, CCGOur goal here is to use a pattern of extractions inlanguages like Bulgarian, which lack the wh-islandconstraint, to argue against the conjunction of Extand Fin, and therefore against the viability of thestandard version of the MG formalism. Adequatelycapturing this pattern requires abandoning eitherExt (as in TAG) or Fin (as in CCG and LIG). Theability of TAG/LIG/CCG to capture this structuralpattern is striking, given that they are strictly lesspowerful than MGs in weak generative capacity.1 The relevant empirical patternOur empirical starting point is Bulgarian sentenceslike (2) and (3) (Rudin, 1988; Richards, 1997). Thesignificant point here is that these sentences exem-plify the abstract structure shown in (4).(2) Kojawhichkniga1bookteyoupopitaaskedučiteljateacher[ kogo2who[ubediconvincedIvanIvant2 [ datopublikivapublisht1]]]“Which book did the teacher ask you whoIvan convinced to publish?”(3) Kojwhichkontinent1continentteyoupopitaaskedučiteljateacher[ koj2who[t2 ehasotkrildiscoveredt1]]?“Which continent did the teacher ask youwho discovered?”(4) [wh . . . [wh [. . . t . . . t . . . ]]]We assume that the pattern can be extended with-out bound as indicated in Figure 1, modulo perfor-mance complications (Miller and Chomsky 1963,but cf. Joshi et al. 2000). To be clear, the pointhere is independent of the linear order of the wordsin the sentence, and relates only to the structuralconfiguration we wish to assign to (2) and (3): (4)describes a tree in which some subtree (correspond-ing to the innermost square brackets) contains twotraces but neither of the corresponding wh-phrases.The key point is also independent of whether thewh-phrases and traces are organized in nested orcrossing configurations (Pesetsky, 1982); note thatno subscripts are shown in Figure 1.355Proceedings of the Society for Computation in Linguistics (SCiL) 2021, pages 355-358.Held on-line February 14-19, 20212 wh-phrases: [wh . . . [wh [. . . t . . . t . . . ]]]3 wh-phrases: [wh . . . [wh . . . [wh [. . . t . . . t . . . t . . . ]]]]4 wh-phrases: [wh . . . [wh . . . [wh . . . [wh [. . . t . . . t . . . t . . . t . . . ]]]]]...Figure 1(a) discovered which-continent unchecked: 1(b) who discovered which-continent unchecked: 2(c) [CP who [TP t discovered which-continent ]] unchecked: 1(d) teacher ask you [CP who [TP t discovered which-continent ] unchecked: 1(e) [CP which-continent teacher ask you [CP who [TP t discovered t]]] unchecked: 0Figure 2A natural minimalist-style bottom-up (Ext-satisfying) strategy for deriving (3) is indicatedinformally in Figure 2, where highlighting in-dicates phrases with unchecked featural require-ments. The number of highlighted elements istherefore one thing that contributes to the deriva-tional state that conditions subsequent grammaticaloperations. The important point is that in step (b),all of the derivation’s wh-phrases (here, two) haveunchecked featural requirements. Assuming thatthe relevant pattern extends without bound as in-dicated in Figure 1, there will be no bound on thenumber of highlighted elements that a derivationmight need to track.Notice that imposing the Phase ImpenetrabilityCondition (PIC) on a derivation like Figure 2 andrequiring successive cyclic movement (with multi-ple specifiers allowed) does not change the fact thatthere will be a point at which all of the derivation’swh-phrases will need to be “highlighted”. The PICconstrains where the highlighted elements are al-lowed to be (roughly, it says they are not allowed tobe too far away from the root of the tree), but doesnot impose any upper limit on how many there areallowed to be at a given time.Consequently, as the crucial pattern is extended,this familiar Ext-satisfying strategy (with or with-out the PIC) will require unbounded derivationalstate (i.e. ¬Fin).2 Two sufficient derivational strategiesWe will consider two derivational strategies forgenerating the structural pattern in Figure 1, corre-sponding to two strategies for generating the famil-iar anbn string language. First, the strategy implicitin a CFG: a rule like ‘S → a S b’ introduces an aalong with its corresponding b, and this a-b paircan be “forgotten” for the purposes of subsequentrewrites because those rewrites occur in the middleof the string. The second strategy is exemplified bya pushdown automaton (PDA): being restricted toreading through a string from one end to the other,a PDA must use its unbounded stack to maintaina count of unmatched occurrences of a, and thiscount can grow without bound.TAG, being relevantly similar to a certain kindof context-free tree grammar (Kepser and Rogers,2011), can generate the pattern in Figure 1 usinga form of the first strategy. Elementary trees in-troduce matched pairs of a wh-phrase and trace,as shown in Figure 3 for (2), like the a-b pairs in-troduced by the CFG rule ‘S → a S b’. The factthat the trees are not constrained to grow only atone end (¬Ext) allows the tree-building system tooperate with a finite amount of memory (Fin).LIG, like its close relative CCG, generates thepattern in Figure 1 using a version of the secondstrategy. What LIG adds to CFGs is the ability tostore information in an unbounded stack at eachnode of a tree, and this information can be propa-gated upwards/downwards in order to control non-local dependencies, such as the dependency be-tween a wh-phrase and its trace. While LIG deriva-tions construct trees in the same end-to-end (Ext)(whether bottom-up or top-down) manner as CFGderivations, LIG has an unbounded (¬Fin) amount356CPTPVPCPaskteacherCCPCPTPVPCPt2convincedIvanCwho2CPCPTPVPt1publishPROCwhich book1Figure 3CP[]CP[t1]TP[t1]VP[t1]CP[t1]CP[t2 t1]TP[t2 t1]VP[t2 t1]CP[t1]TP[t1]VP[t1]t1publishPROCt2convincedIvanCwho2askteacherCwhich book1Figure 4of memory available to ensure that wh-phrases andtraces are appropriately paired up — just as a PDAuses its stack to pair as with bs when generatinganbn. An LIG derivation for (2) is shown in Fig-ure 4, where each node’s stack is written in squarebrackets.CCG is closely analogous to LIG in the relevantrespects: CCG derivations construct trees bottom-up, and allow unboundedly complex categories tobe derived through function composition.3 Minimalist GrammarsA common assumption is that in the abstract con-figuration in (5), WH1 prevents WH2 from mov-ing. Beyond this, however, versions of “ShortestMove” differ. MGs implement a simple conceptionof Shortest Move, according to which this con-figuration dooms the derivation, since WH2 hasbeen prevented from moving to its closest poten-tial attractor. This constraint prevents uncheckedfeatural requirements from accumulating (as theydid in Figure 2), and places a bound on the storedinformation that can condition derivational oper-ations (Fin). Therefore after a certain number oftraces have been generated (or, after a certain num-ber of wh-phrases have been introduced into theirbase positions) it becomes impossible to retain thecorresponding requirements for wh-phrase surfacepositions.(5)WH2-whWH1-whC+whAlternative versions of Shortest Move say thatWH1 can move, which frees up WH2 for subse-quent attractors (e.g. Richards 1997). This involvesunbounded storage (¬Fin), because there is nolimit to how many elements might be waiting tobe “freed up” in this manner; the situation remainsequivalent in relevant respects to Figure 2. Thisapproach to generating the pattern in Figure 1 istherefore more analogous to LIG than to MG.MGs can produce a certain variant of the pat-tern of interest (Gärtner and Michaelis, 2010),namely one where the number of wh-phrases isunbounded but the number of contiguous clustersof wh-phrases (i.e. wh-phrases that surface togetherat the edge of a single clause) remains bounded, byusing one of the boundedly many units of deriva-tional state to store each cluster. But in the crucialpattern in Figure 1, where each wh-phrase con-stitutes its own cluster, there is no bound on thenumber of clusters. Note also that no operation ex-corporating a wh-phrase from a cluster is possible:this would require the recovery of information thathad been abandoned when the cluster was formed357in order to satisfy Fin.Non-standard variants of MGs that are not re-stricted in this way include Graf (2012) (which re-jects Ext) and Gärtner and Michaelis (2005) (whichrejects Fin). Kobele and Michaelis (2005) showedthat the latter has the power of a Turing machine.In contrast, LIG rejects Fin in a restricted way:the stack-structured memory generates wh-tracedependencies that are structurally nested, in accor-dance with the empirically-motivated Path Con-tainment Condition (Pesetsky, 1982). The PDA–CFG equivalence demonstrates a trade-off betweenstack-based storage (¬Fin) and non-edge string-rewriting (a string version of ¬Ext); LIG andTAG’s differing methods of tree-construction standin the same relationship (Joshi et al., 1990), soTAG also predicts structurally nested wh-trace de-pendencies. The position shared by LIG and TAGis the first step on a hierarchy that can be definedeither via different relaxations of Fin (Weir, 1992)or different relaxations of Ext (Rogers, 2003). Thedifferent points on this hierarchy will make distinctpredictions about the possible patterns of wh-traceconfigurations in trees, investigation of which weleave for future work.4 ConclusionOur main claim here is that a pattern of extractionsin languages like Bulgarian — if it extends withoutbound as indicated in Figure 1, as we have assumed— is incompatible with the conjunction of Ext andFin, and therefore incompatible with (standard ver-sions of) the MG formalism. Adequately capturingthe relevant pattern requires abandoning either Ext(as in TAG) or Fin (as in LIG and CCG). In pre-senting this argument we aim to highlight waysof comparing mildly context-sensitive formalismsthat are not based on weak generative capacity.ReferencesHans-Martin Gärtner and Jens Michaelis. 2005. A noteon the complexity of constraint interaction: Local-ity conditions and Minimalist Grammars. In Log-ical Aspects of Computational Linguistics, volume3492 of LNCS, pages 114–130, Berlin Heidelberg.Springer.Hans-Martin Gärtner and Jens Michaelis. 2010. Onthe Treatment of Multiple-Wh Interrogatives in Min-imalist Grammars. In Thomas Hanneforth and Gis-bert Fanselow, editors, Language and Logos, pages339–366. Akademie Verlag, Berlin.Gerald Gazdar. 1988. Applicability of indexed gram-mars to natural languages. In Uwe Reyle and Chris-tian Rohrer, editors, Natural Language Parsing andLinguistic Theories, pages 69–94. Springer.Thomas Graf. 2012. Movement-generalized Minimal-ist grammars. In LACL 2012, volume 7351 of Lec-ture Notes in Computer Science, pages 58–73.Aravind K. Joshi, Tilman Becker, and Owen Rambow.2000. Complexity of scrambling: a new twist tothe competence-performance distinction. In AnneAbeillé and Owen Rambow, editors, Tree Adjoin-ing Grammars, pages 167–181. CSLI Publications,Stanford, CA.Aravind K. Joshi and Yves Schabes. 1997. Tree-adjoining grammars. In Grzegorz Rozenberg andArto Salomaa, editors, Handbook of Formal Lan-guages, volume 3, pages 69–124. Springer, NewYork, NY.Aravind K. Joshi, K. Vijay Shanker, and David Weir.1990. The convergence of mildly context-sensitivegrammar formalisms. University of PennsylvaniaDepartment of Computer and Information ScienceTechnical Report No. MS-CIS-90-01.Stephan Kepser and Jim Rogers. 2011. The Equiva-lence of TAGs and Monadic Linear CF Tree Gram-mars. Journal of Logic, Language and Information,20(3):361–384.Gregory M. Kobele and Jens Michaelis. 2005. TwoType-0 Variants of Minimalist Grammars. In JamesRogers, editor, Proceedings of FG-MoL 2005.George A. Miller and Noam Chomsky. 1963. Finitarymodels of language users. In Robert Duncan Luce,Robert R. Bush, and Eugene Galanter, editors, Hand-book of Mathematical Psychology, volume 2. Wileyand Sons, New York.David Pesetsky. 1982. Paths and categories. Ph.D. the-sis, MIT.Norvin Richards. 1997. What moves where when inwhich language? Ph.D. thesis, MIT.James Rogers. 2003. Syntactic structures as multi-dimensional trees. Research on Language and Com-putation, 1:265–305.Catherine Rudin. 1988. On multiple questions and mul-tiple wh-fronting. Natural Language and LinguisticTheory, 6:445–501.Edward P. Stabler. 2011. Computational perspectiveson minimalism. In Cedric Boeckx, editor, The Ox-ford Handbook of Linguistic Minimalism. OxfordUniversity Press, Oxford.Mark Steedman. 1996. Surface Structure and Interpre-tation. MIT Press, Cambridge, MA.David Weir. 1992. A geometric hierarchy beyondcontext-free languages. Theoretical Computer Sci-ence, 104(2):235–261.358

Comparing methods of tree-construction across mildly context-sensitive formalisms

https://scholarworks.umass.edu/cgi/viewcontent.cgi?article=1225&amp;context=scil

Comparing methods of tree-construction across mildly context-sensitive formalisms

Abstract

Similar works

Full text

Available Versions

ScholarWorks@UMass Amherst