ACL-OCL / Base_JSON /prefixC /json /C94 /C94-1029.json
Benjamin Aw
Add updated pkl file v3
6fa4bc9
{
"paper_id": "C94-1029",
"header": {
"generated_with": "S2ORC 1.0.0",
"date_generated": "2023-01-19T12:48:48.010113Z"
},
"title": "MULTI-TAPE TWO-LEVEL MORPHOLOGY: A Case Study in Semitic Non-linear Morphology",
"authors": [
{
"first": "George",
"middle": [
"Anton"
],
"last": "Kiraz",
"suffix": "",
"affiliation": {
"laboratory": "",
"institution": "RIDCI,; (St John's Colh!ge) E-mail. George. Kiraz~cl. cam. ac",
"location": {
"country": "uk"
}
},
"email": ""
}
],
"year": "",
"venue": null,
"identifiers": {},
"abstract": "This I)aper presents an implemented multi-tal)e twolevel model capable of describing Semitie non-linear morphology. The computational fl'arnework behind the ettrrcnt work is motivated by [Kay 1987]; the fimnalism presented here is an extension to the formalism reported by [Puhnan art(1 Hepl)le. 1993]. The objectives of the current work are: to stay as close as possible, in spirit, to standard two-level morl)hology, to stay close to the linguistic description of Semitic stems, and to present a model which can be used with ease by the Semitist. The. Imper illustrates that if finite-state transducers (FSTs) in a standard two-level morphology model are replaced with multi-tape attxiliary versions (AFSTs), one can account for Semitic root-andq)attern morphology using high level notation.",
"pdf_parse": {
"paper_id": "C94-1029",
"_pdf_hash": "",
"abstract": [
{
"text": "This I)aper presents an implemented multi-tal)e twolevel model capable of describing Semitie non-linear morphology. The computational fl'arnework behind the ettrrcnt work is motivated by [Kay 1987]; the fimnalism presented here is an extension to the formalism reported by [Puhnan art(1 Hepl)le. 1993]. The objectives of the current work are: to stay as close as possible, in spirit, to standard two-level morl)hology, to stay close to the linguistic description of Semitic stems, and to present a model which can be used with ease by the Semitist. The. Imper illustrates that if finite-state transducers (FSTs) in a standard two-level morphology model are replaced with multi-tape attxiliary versions (AFSTs), one can account for Semitic root-andq)attern morphology using high level notation.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Abstract",
"sec_num": null
}
],
"body_text": [
{
"text": "This paper aims at presenting a computational morphology model which can handle the non-linear phenomenon of Semitic morphology.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "INTRODUCTION",
"sec_num": null
},
{
"text": "The approach presented here builds on two-level mori)hology [Koskennienfi 1983] , extending it to achieve the desired objective. Tit('. contril)ution of this l)almr tnay ])e Slllllmarised as follows:",
"cite_spans": [
{
"start": 60,
"end": 79,
"text": "[Koskennienfi 1983]",
"ref_id": null
}
],
"ref_spans": [],
"eq_spans": [],
"section": "INTRODUCTION",
"sec_num": null
},
{
"text": "With regards to the two-level model, we extend this model by allowing it to have multiI)le tapes on the lexical level and retaining the one tape on the surface level; hence, 'multi-tape two-level morphology'. Feasible pairs in the standard two-level model become 'feasible tuple pairs' in our multi-tape model.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "INTRODUCTION",
"sec_num": null
},
{
"text": "With regards to the formalism, we have. chosen a twodevel formalism and extended it to be al)le to write multi-tape two-level grammars which involve non-linear operations. To achieve this, we made all lexieal expressions n-tuple regular expressions. In addition, we introduced the notion of 'ellipsis', which in-*Supported by a Benefitctor Studentship from SI+ Jolm's College. q~llis research was done tllld(!r the SUlmrvision <ff I)r Steph(!n G. Pulman whom I thank fro' guidance, support and feedback. q'hanks to 13r ,Iohn Carroll for editm'ial comments, Arturo 'lh'ujillo for useful 'chats' ;rod Tanya Bow(h!n for Prolog tips, dicates the (optional) omission from left-context lexical e\u00d7I)ressions of tui)les; this accounts for spr(~a(ling.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "INTRODUCTION",
"sec_num": null
},
{
"text": "Two-level implementations either work directly on rules or compile rules into FSTs. For the latte.r cats(:, we propose, an au\u00d7iliary finite-state transduce.r into which multi-tape two-level rules can be co)replied. Tit(.' machine scans %Ulfle imirs ' instead of pairs of symbols.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "INTRODUCTION",
"sec_num": null
},
{
"text": "'Fhe outline of the paper is as follows: Sect;ion 2 introduces the root-and-pattern nature of Semitic roof phology. Section 3 provides a review of the previous prol)osals iBr han(lling Semitie morphology. Section 4 t)resents our proposal, extending two-level morphology anti l)roposing a formalism which is adequate, for writing non-linear grammars using high level notation. Sex> tion 5 al)i)lies our model on the Arabic verb. Section 6 I)resents an auxiliary automaton into which multi-tape two-level rules can/)e compiled. Finally, section 7 giw;s eonchtding remarks.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "INTRODUCTION",
"sec_num": null
},
{
"text": "Non-linear root-and-pattern morphology is best il+ lustrated in Semitic. A Setnitic stem (:onsists of a root and a vowel tnelody, ;u'rattged according to a canonic.al i)atte.rn. For examph~, Arahic/Iv'uttib/ 'caused t.o write' is composed front the root murphenm {ktb} 'notion of wril.inp;' and the vowel melody morpheme {ui} 'pertlwt lmssive'; the two are arr:mged act:ording to the pattern morpheme {CVCCVC} 'causative'. shown'~ llh+ttly sl, etns t!xperhmce l~holxcd()gicaJ l)roc,~!ssitlg t.<) give am'face forms, (!.~i. /nkatab/ -+ /?inkatab/ (ffn'm 7); the root, morphemes .shown ar,'+ iwd; +fit++d lit tlm litm+ature in all forms, e.g. Lhere is llo such verb as */tal~attab/ (form 5), but there is /takassab/ from the root morpheme {ksb}; the qua.lity of the Sl!COlld VOWel ill forth I iS ([iflerent, frm+t ()lie roo\u00a3 t() tl+tlOI,hol'+ 1!.+~, /qalal/ %o kill',/qabil/ %0 accept', /kabur/ 'to become I)i~,', front the met morphemes {qtl}, {qbl} and {kbr}, reSlmctiv(dy. Some ['orNflS do llol. ()(:cut' ill the passive. ",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "1~10 ()T-A ND-PATTI,;I)~N MORPItOL-OGY",
"sec_num": "2"
},
{
"text": "L I C V C C V C patter'a I \">/ I k t l) ~'ool,",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "1~10 ()T-A ND-PATTI,;I)~N MORPItOL-OGY",
"sec_num": "2"
},
{
"text": "Similarly, one can describe nonfinals such as /kitaab/ 'l)ook', /kutub/ 'books', /kaatib/ 'writer', /kitaaba/ 'writing' and /katiiba/ 'squadron' etc.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "1~10 ()T-A ND-PATTI,;I)~N MORPItOL-OGY",
"sec_num": "2"
},
{
"text": "2The analysis of Arabic here is I)ased tm CV theory [McCarthy 1981] . Morale [Mc('arthy The process can He deseriHed l)y the rules:",
"cite_spans": [
{
"start": 52,
"end": 67,
"text": "[McCarthy 1981]",
"ref_id": null
},
{
"start": 77,
"end": 87,
"text": "[Mc('arthy",
"ref_id": null
}
],
"ref_spans": [],
"eq_spans": [],
"section": "1~10 ()T-A ND-PATTI,;I)~N MORPItOL-OGY",
"sec_num": "2"
},
{
"text": "x: x -> ..... (l) I :l) _> ...... (2) (::0 :> v:v .... -t:0 (3)",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "1~10 ()T-A ND-PATTI,;I)~N MORPItOL-OGY",
"sec_num": "2"
},
{
"text": "liule I is t.he default rule., where a lexi(:;d charac. ter al)l)ears oil the mlrfat:e. ]~.llle 2 is the I)oml(lary rule, where l;he lexieal morph(mm boundary symbol is deleted on the surface (i.e. surfaces as '0'). l{ule 3 sl:at.es the deletion of lexical [e] in {re(we} in the. cont;ext shown.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "1~10 ()T-A ND-PATTI,;I)~N MORPItOL-OGY",
"sec_num": "2"
},
{
"text": "One can see t.hat two-level morl)hology is highly inlhmneed by co[icatellative morphology: the first requirement for at sm'faee form to be related t:o a lexical tbrm, given by [/{.itchie 1992] , states that \"the lexical t;alm is the eont:atcnatimz of the lexieal forms in qul!sl.ion...\" (italics mine). This makes it extremely ditlieult, if not imlmssil)le , to apply the mttonomous Inorl)helues o[ ,qemil,ic Lo l~lainst, remll two-level IIOI,3~~ (ion.",
"cite_spans": [
{
"start": 176,
"end": 192,
"text": "[/{.itchie 1992]",
"ref_id": null
}
],
"ref_spans": [],
"eq_spans": [],
"section": "1~10 ()T-A ND-PATTI,;I)~N MORPItOL-OGY",
"sec_num": "2"
},
{
"text": "Working within standard two-level morphology, [Kataja and Koskenniemi 1988] went around the problem. Nominal forms, such as /kitaab/ 'book', were entered in the lexicon. Vert)al forms were derived by a 'lexicon component'. A verb, such as /nkutib/ (form 7), has the lexical entries",
"cite_spans": [
{
"start": 46,
"end": 75,
"text": "[Kataja and Koskenniemi 1988]",
"ref_id": "BIBREF5"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Previous Proposals",
"sec_num": null
},
{
"text": "n E1 u El i El",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Previous Proposals",
"sec_num": null
},
{
"text": "where El is the alphabet of the root and E~ the alphabet of the vocalism/affixes. Tim lexicon compovent takes the intersection of these two expressions and produces/nkutib/. Now/nkutib/is fed on the lcxical tape of a standard two-level system wtfich takes care of conditional phonetic dmnges (assimilation, deletion, etc.) and produces/'einkutib/, a A similar approach was used by [Lavie et al. 1988] for IIehrew using a 'pre-h!xical compiler'.",
"cite_spans": [
{
"start": 381,
"end": 400,
"text": "[Lavie et al. 1988]",
"ref_id": "BIBREF9"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Previous Proposals",
"sec_num": null
},
{
"text": "[Kay 1987] proposed a finite-state aplnoacl~ using fimr tapes for root, CV-skeleton, vowel melody and surface, each having an indel)endent head, i.e. the machine can scan from one lexical tape without moving the head on other lexieal tapes. The absence of motion is indicated by ad hoc notation coded in the lexical strings.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Previous Proposals",
"sec_num": null
},
{
"text": "[Beesley 1991], working on Arabic, impleme,ited a two-level system with 'detours', where, according to [Sproat 1992, p. 163-64] , detouring involves nmltiple dictionaries being open at a time, one for roots and one for templates with vowels pre-compiled (as in iIarris' description).",
"cite_spans": [
{
"start": 103,
"end": 127,
"text": "[Sproat 1992, p. 163-64]",
"ref_id": null
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Previous Proposals",
"sec_num": null
},
{
"text": "Other non two-level models were proposed (there is no place here for a review of ttmse works): [Kornai 1991] proposed a model for autosegmental l/honology using FSTs, where non-linear autosegmental representations are coded as linear strings. [llird and Ellison 1992] proposed a model llased on one-level phonology using FSA to model representations and rules. [Wiel)e 1992] pr(llmsed I,l(Jdellii,g autosegmental phonology using multi-tal/e FSTs, where mitosegmental representations m'e coded in arrays.",
"cite_spans": [
{
"start": 95,
"end": 108,
"text": "[Kornai 1991]",
"ref_id": null
},
{
"start": 243,
"end": 267,
"text": "[llird and Ellison 1992]",
"ref_id": null
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Previous Proposals",
"sec_num": null
},
{
"text": "[Puhnan and Hepi)le 1993] prol)osed a formalism for bidirectional segmental phonological processing, and i)roposed using it for Arabic. The next subsection presents the develoi)ment of this formalism. xt The special symbol * indicates an empty context, which is always satisfied. The operator ~ states that lw, x 'tttay sur[itc.e, as StJIIF ill the given context, while the operator \u00a25 adds the condition that when LEx appears in the given context, then the surface description must satisfy S1HII.'. 'Phe later caters for obligatory rules.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Previous Proposals",
"sec_num": null
},
{
"text": "The advantage of this Rn'malism over others is that it allows inter alia mappings between lexical and surface strings of uneqmd lengths/! Rules 1-3 can be expressed in this formalism as follows: a",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Previous Formalisms",
"sec_num": "3.3"
},
{
"text": "EQUATION",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [
{
"start": 0,
"end": 8,
"text": "EQUATION",
"ref_id": "EQREF",
"raw_str": "\u2022 -X-* => *-X-* (,l) \u2022 --* ~ *-+-* (5) \u2022 --* <~ v-e-+",
"eq_num": "(6)"
}
],
"section": "Previous Formalisms",
"sec_num": "3.3"
},
{
"text": "Pulman and llepi)le proposed using the formalism for Arabic in the following manner: surface /k'utti5/ call be expressed with the r/lle: 4This allows two-level i~rallllll~l,y.tl Lo handle C,V, lIior0,1c &lid infixrd,ional im~tlyses which we shMI present in a future work. s0 in rules 1-3 is indicated here by blank.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Previous Formalisms",
"sec_num": "3.3"
},
{
"text": "\u2022 --Ct'tt.U2C2iC:l --* -> -}---CIC2Ca --+ WIH!I'I! (',,, l'l!pl'l!S",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Previous Formalisms",
"sec_num": "3.3"
},
{
"text": "This work follows [Kay 1987 ] in using I;hree I, apes l))l\" the lexical level: pattern tape (PT), root tal)e (liT) and voeallsm tape (VT), and <m<: sm'face, tape (ST). Ill syntliesis, the lexical tapes are in read mode and the surface l;aI)e is in write mode; in recognil;ion, the opposite state of affairs holds. One of the lexieal tapes is called the prhnary lexieal tape (PILF) through wtfieh all lexical morphentes which fall out of the donlain of rool;-and-pattern morl>hology are passed (e.g. pretixes, sutlixes, I~artic:les, prepositi<ms). Since char: acters in P'.I' correspond to those on ST, P'F was chosen as PLT.",
"cite_spans": [
{
"start": 18,
"end": 27,
"text": "[Kay 1987",
"ref_id": null
}
],
"ref_spans": [],
"eq_spans": [],
"section": "A Multi-Tape Two-Level Model",
"sec_num": "4.1"
},
{
"text": "There is linguisti<: SUl)pnrt for n lexical l.apes maI)l)ing to <)ne surface tape.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "A Multi-Tape Two-Level Model",
"sec_num": "4.1"
},
{
"text": "As described })y [McCarthy 1986] , when a word is uttered, it is pronounced in a linear string of segmmits (eorrespondinf,; to the linear ST in this model), i.e. the multi-tier representatioll is linearised. McCarthy ealls this process tier eonllation.",
"cite_spans": [
{
"start": 17,
"end": 32,
"text": "[McCarthy 1986]",
"ref_id": null
}
],
"ref_spans": [],
"eq_spans": [],
"section": "A Multi-Tape Two-Level Model",
"sec_num": "4.1"
},
{
"text": "The l'ulnuul-Ih;pl)le/lhmssink/lllaek ct aL fornialisnl is adopted here with l;wo extensions. The first extension is that all expressions in the lexical side of (.he rules (i.e. LLC, LBX and RLC) are n-tuple regular expressions of the form: If a regular expression ignores all tapes lint Pl;I?, the parentheses can 1)e ignored; hence, (x) is the sanlt! ;ts :.): where x is on PIfF. llaving n-tuI)le lexical exI)r(!ssions and 1-tuple surface expression corresponds to having n-tapes on the lexieal level and one ()it the surface. The second extension is giving LI,C the ability to contain ellipsis, ... , which indicates the (ol)tional) omission li'om LLC of tvples, provided that the t. Now that we have presented otir prol)osal , we are ready to aplily it, to the Aral)ic data of '1'ahh! I.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Fornmlism",
"sec_num": null
},
{
"text": "ANAI,YSIS OF 'I?IIE ARABIC VEIt.B",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "5",
"sec_num": null
},
{
"text": "~ection 5. l presents l;he default and I)oundary rules for Arabic. in the twoqevel fortnalisni. ,qec.I;ion 5.2 gives rules which handle vocalised-, non-voealised-, and l)arlially voealised tex(;s. I,'inally, we shall see the use of ellipsis to m:connt for gelllingd;ion and spreading in section 5.3.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "5",
"sec_num": null
},
{
"text": "The default and boundary rules for Arabic in the mull,i-I.ape fornlalisnl are: G * ---((,<,X, ) Rule 7 is equiwdent to Rule 1. llule 8 states that any (} on t.he pal,l*q'n i.al)e and X on l;he root tal)e with lie I,ralisitioll (lti I;he. vocalisni tape c.orrespolld (,o X (ill the Sllrfac(! tape. Rule 9 sl, al;es that ally V oil the l)attern l;al)e and X {)n vocalisltl tal m with I1o transition on I;]ie root tape ('.orresl)ond to X on tile. sln'face tape. Rule 10 is the bomMary rule for morl)henw.s which lie out of the doniain of rool,-andqml.1;ern niorphology. Rule 11 is I,he })OllIiditry rille for sl,enis.",
"cite_spans": [],
"ref_spans": [
{
"start": 81,
"end": 95,
"text": "* ---((,<,X, )",
"ref_id": null
}
],
"eq_spans": [],
"section": "Defimlt and Boundary I{ules",
"sec_num": "5.1"
},
{
"text": "EQUATION",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [
{
"start": 0,
"end": 8,
"text": "EQUATION",
"ref_id": "EQREF",
"raw_str": "--* *-X-* -> *--(V,,A')-* V < {,,,,'.~ }",
"eq_num": "("
}
],
"section": "*-X--* -> *-X--* (7) *-X--* =~",
"sec_num": null
},
{
"text": "llere is the derivation of Idri,,,,,',.ij,d (r<) ,-,n Q3)f=,>tn the three morphemes {e,c.2v,nc:,v2c4}, 7 {<ilt,'i) and {ui}, and the sutlix {at} '3M pers(m' which falls oul, of l,he dOillahl el rllol,-alld-.liat;tern Inort)holo/ry all(i> hence, I, akes its place on PI'I'. The numl)ers between Srl ' and the lexical tapes indicate l:he rules which sanction the moves. We find l,hat default and l)oundary rules represent :t wide range of Seniti,it stenls. ",
"cite_spans": [
{
"start": 27,
"end": 48,
"text": "Idri,,,,,',.ij,d (r<)",
"ref_id": null
}
],
"ref_spans": [],
"eq_spans": [],
"section": "*-X--* -> *-X--* (7) *-X--* =~",
"sec_num": null
},
{
"text": "Orthographically, Semitic texts appear in three forms: eonsonantal texts do not incorporate any w~wels but mattes lectionis ~, e.g. ktb for/katab/ (forln 1, active), /kutib/(form 1, passive) and/kutub/'books', but kaatb for/kaatab/(form 3, active) and/kaatib/'writer'; partially voeallsed texts incorporate some vowels to clarify ambiguity, e.g. kufl> for /kutib/ (form 1, passive) to distinguish it fi'om / katab/ (form 1, active) ; and voeallsed texts incorporate flfll vocalisation, e.g. st&tab (form 10, active) .",
"cite_spans": [],
"ref_spans": [
{
"start": 408,
"end": 431,
"text": "katab/ (form 1, active)",
"ref_id": null
},
{
"start": 491,
"end": 515,
"text": "st&tab (form 10, active)",
"ref_id": null
}
],
"eq_spans": [],
"section": "Vocalisation",
"sec_num": "5.2"
},
{
"text": "This phenomenon is taken care of by the following rules:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Vocalisation",
"sec_num": "5.2"
},
{
"text": "EQUATION",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [
{
"start": 0,
"end": 8,
"text": "EQUATION",
"ref_id": "EQREF",
"raw_str": "*- -* a (x0-(v)-(x=,) X I , X2 -\u00a2 vowel",
"eq_num": "(12)"
}
],
"section": "Vocalisation",
"sec_num": "5.2"
},
{
"text": ", --, ~ (I',, x,, ) -(p, , x) One additional rule is required t<> allow the omission of vowels which experience spreading (see Rule 17 below).",
"cite_spans": [],
"ref_spans": [
{
"start": 8,
"end": 29,
"text": "(I',, x,, ) -(p, , x)",
"ref_id": null
}
],
"eq_spans": [],
"section": "Vocalisation",
"sec_num": "5.2"
},
{
"text": "The only two phonological <:hanges ill the Arabic sl.em are gemination and spreading, e.g. /tukuttib/ (form 5) fi'om the morphemes {tvlct vl c~c~v2<:a }, {ktb} and {ui}. The gemination of the second radical [t] and the spreading of the first vowel [u] can be expressed by Rule 14 and Rule 15, respectively: e.2,X, ) -o2-,",
"cite_spans": [],
"ref_spans": [
{
"start": 307,
"end": 315,
"text": "e.2,X, )",
"ref_id": "FIGREF2"
}
],
"eq_spans": [],
"section": "Gemination and Spreading",
"sec_num": "5.3"
},
{
"text": "*-X-* ~ (",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Gemination and Spreading",
"sec_num": "5.3"
},
{
"text": "* --X --* ~ (111, , X) ....",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Gemination and Spreading",
"sec_num": "5.3"
},
{
"text": "8'Mothers of readlng', these are consonantal h!tters which play the role of vowels, all{[ are represented ill t.he p3.ttel'll l/iol'|)helill~ by VV (e.g. /aa/, /uu/, /ii/). Mattes lectionis cannot be omitted fi'om the orthographic string.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "V I --* (15)",
"sec_num": null
},
{
"text": "Note. the use of ellipsis to indicate, t;hat there are elemenl;s separal;ing tile two [u]s. Form 5 is illustrated below (without boundary symbols). In fact, gemination can be considered as a case <>f spreading; llnle 14 lmcomes,",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "V I --* (15)",
"sec_num": null
},
{
"text": "EQUATION",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [
{
"start": 0,
"end": 8,
"text": "EQUATION",
"ref_id": "EQREF",
"raw_str": "\u2022 -x-, -~ (<,,x,) .... ~,~-,",
"eq_num": "(|6)"
}
],
"section": "V I --* (15)",
"sec_num": null
},
{
"text": "This allows fin/tuk'ul, l, ib/(form 5)and/l,:tawtab/(form \\,Ve also need to allow a vowel which originally surfaces hy spreading t:o be onfil.ted in the Slll'face ill llllvocalised words. This ix accomplished l)y l;he. [bllowing rule:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "V I --* (15)",
"sec_num": null
},
{
"text": "('U[, ,X)..-(Pl,Xl, )-v I -([~,X2, ) X = vowel, P1,1~ C { el, <,, c:~, c4 },",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "V I --* (15)",
"sec_num": null
},
{
"text": "Not:e thai, the segments in SIJItF iIl the above rules do not appear in LI.;X, rather in L[,C. This means [;hat, if rllles are to })e eoml>ile<l ill{;() alltolllata, the alll;Omata }lave t;o rcmember i;he segments from LLC. 9 This leads us on thinking about what sorl; of allI;Olllal;a are needed to describe a mull,i-tape two-level grammar.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Xt,X) = radical (I7)",
"sec_num": null
},
{
"text": "We define the following antomat, ou iul;o which rules can he cmnpiled: A multLtape f-register auxiliary finite-state automaton (AFSA) with n-tapes consists of: n read tapes and heads, a linite state control, and a readwrite storage tape of length g, where f < w, and w is the length of the inlml; strings (of. APDA in [I]opcrofl. and Ulhmm 1979] ). The auLomal;on is illustrated iu Fig. 5 (next page) . I\u00b0",
"cite_spans": [
{
"start": 318,
"end": 345,
"text": "[I]opcrofl. and Ulhmm 1979]",
"ref_id": null
}
],
"ref_spans": [
{
"start": 382,
"end": 400,
"text": "Fig. 5 (next page)",
"ref_id": null
}
],
"eq_spans": [],
"section": "C, OMPlI,ATION INTO AUTOMATA",
"sec_num": "6"
},
{
"text": "In cme mow~, depending on the state of the finite control, along with the symbols scanned by the input aml storage heads, the AFSA may do any (n' all of the following: \u2022 mow~ its ~t input heads independently c,n,:~ l)osil.iou to the right;",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "C, OMPlI,ATION INTO AUTOMATA",
"sec_num": "6"
},
{
"text": "\u2022 print a symbol on the coil scanned by the sLot'age head and (optionally) move that; head ont, l)osition to the right or loft.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "C, OMPlI,ATION INTO AUTOMATA",
"sec_num": "6"
},
{
"text": "More fern, ally iLI/ AFSA is a se.xtui)lo of tim fOl'lli (Q,);, F, 6, q0, F'), whore:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "C, OMPlI,ATION INTO AUTOMATA",
"sec_num": "6"
},
{
"text": "\u2022 Q is a finite sot; of states;",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "C, OMPlI,ATION INTO AUTOMATA",
"sec_num": "6"
},
{
"text": "\u2022 E is the machine's alphabet;",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "C, OMPlI,ATION INTO AUTOMATA",
"sec_num": "6"
},
{
"text": "\u2022 it' C )] is the storage alphahot;",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "C, OMPlI,ATION INTO AUTOMATA",
"sec_num": "6"
},
{
"text": "\u2022 ~$ is the transition function, a map from Q \u00d7 a x F t,o Q x I' x {L,/{}, where o\" is (al, ..., o,,) and a i C Y;;",
"cite_spans": [
{
"start": 87,
"end": 101,
"text": "(al, ..., o,,)",
"ref_id": null
}
],
"ref_spans": [],
"eq_spans": [],
"section": "C, OMPlI,ATION INTO AUTOMATA",
"sec_num": "6"
},
{
"text": "\u2022 qll El Q is t.h,', initial sl.~tl.e;",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "C, OMPlI,ATION INTO AUTOMATA",
"sec_num": "6"
},
{
"text": "\u2022 1,' C Q is the. sot of final st;ares.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "C, OMPlI,ATION INTO AUTOMATA",
"sec_num": "6"
},
{
"text": "The transil;ion function a(l,, ~, r) -= (q, ,,., .,) iff t.he machine emt move from state p to state q wlfile s(:antfin Z the n-tuplo cr from the input tapes and r from the current storage cell, and upon ente.ring state q, writes the symbol w onto the. cllrrent sl, or;Lg(1 cell ;m(I moves the storage head according to m E { L, l~}.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "C, OMPlI,ATION INTO AUTOMATA",
"sec_num": "6"
},
{
"text": "A multi-t:ape ,t?-reglstm' auxiliary finite-state transducm' (AFST) wit;ll n inlmt tapes and k outlntt tapes is ml AFSA with (t+ + k)-tapos. AFSTs lw.httvo like AFSAs, but scan t.uple pairs.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "C, OMPlI,ATION INTO AUTOMATA",
"sec_num": "6"
},
{
"text": "Note that an AFST with n = k -= I and ~? =: 0 is equivalent to a. FST.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "C, OMPlI,ATION INTO AUTOMATA",
"sec_num": "6"
},
{
"text": "The rules are comIfiled into AFSTs in the same lines of standm'd two-level morphology. We shall ttso. a special ease of AFSTs: We hypothosise that, in lilms with tie.r confl:+A:ion, for all tnortJtcJogical processes, k=l (i.o. on('. surface tape); further, wo .:msmno l,hat, m> less one proves otherwise, all morphological processes require that f < 1 (hence, we shall ignore m in a). l,'or Semitic, n=3. The AFST for Rub 15 is illus-Ix;tted bolc~w. Transitions m;u'ked with l)ef (for default) take phu'.o wh(!n a is a ft!:mibh! i.uI)le pair, oLhor dm, n l.hoso explicidy shown. The onq)t.y st.rhlg is rot)resented I)y 0. The transil.ions are:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "C, OMPlI,ATION INTO AUTOMATA",
"sec_num": "6"
},
{
"text": "\u2022 @so, l)cf, 0) = (so, 0) allows strings not related to l.his rub to be accepted;",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "C, OMPlI,ATION INTO AUTOMATA",
"sec_num": "6"
},
{
"text": "\u2022 @s0,0, ,O,X) : X,O) -. (sl,X) enters the rule writ.inp; X in t.he storage coil;",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "C, OMPlI,ATION INTO AUTOMATA",
"sec_num": "6"
},
{
"text": "\u2022 ,S (.~,,(',,,,O,X) :",
"cite_spans": [
{
"start": 5,
"end": 20,
"text": "(.~,,(',,,,O,X)",
"ref_id": null
}
],
"ref_spans": [],
"eq_spans": [],
"section": "C, OMPlI,ATION INTO AUTOMATA",
"sec_num": "6"
},
{
"text": "X,0) = (.~t,X) at,d",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "C, OMPlI,ATION INTO AUTOMATA",
"sec_num": "6"
},
{
"text": ",S(s.,, ('vl, 0, X) : X,(]) = (st, X)ensure. badda'acking;",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "C, OMPlI,ATION INTO AUTOMATA",
"sec_num": "6"
},
{
"text": "\u2022 ~(,'1, De f, O) = (sl, O) t'Oln'Osents ellipsis;",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "C, OMPlI,ATION INTO AUTOMATA",
"sec_num": "6"
},
{
"text": "\u2022 (S(sl, (v1,0,0): X, X) == (.,'2,0)retrieves the ('otx-t~mt.s of the storage cell;",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "C, OMPlI,ATION INTO AUTOMATA",
"sec_num": "6"
},
{
"text": "\u2022 ,S(.~.,, (',.,,, 0, 0) : .V, .V) =: (<,, {I) ;dl,,ws ,:,,,,s,,,:,,Uv,, ,,,.di,,r; op,.'at.i,) ns, e.g. This lmpor has shown that a. muld-t:apo I;wo-lovol approach using t:he Puhnan-I [eplflO/ILuessinl\u00a2/Bhtcl~ et al. formalism with the. extensions mentioned is capable of do.scribing the whole range of Arabic stems. Why do we need storage in the automata? It is known that ml automaton with linito storage can bo rOl)laeed with a larger (me without storage (:t simt)le sohd.i(m is i.o dui)licato l.he ma(:hino for each case); hence, 18.q using finite storage (especially with g _< 1 and a small finite set of I') does not give the machine extra l)ower. The reason for using storage is to minimise the munher of machines and states.",
"cite_spans": [
{
"start": 11,
"end": 24,
"text": "(',.,,, 0, 0)",
"ref_id": null
},
{
"start": 38,
"end": 95,
"text": "(<,, {I) ;dl,,ws ,:,,,,s,,,:,,Uv,, ,,,.di,,r; op,.'at.i,)",
"ref_id": null
}
],
"ref_spans": [],
"eq_spans": [],
"section": "C, OMPlI,ATION INTO AUTOMATA",
"sec_num": "6"
},
{
"text": "With regards to the implementation, first we implemented a small system in order to test the usage of AFSTs in our model. Once this was estat)lished, we made a second implementation based on the work of [Pulman and Hepple 1993] . This iml)lementation differs fi'om theirs as follows: Lexical expressions are ntuples, i.e. implemented as lists-of-lists instead of listsof-characters. A facility to check ellipsis in rules was added. The lexicon consists of multii)le trees, one tree per tape. Finally, a morphosyntactic pro:set was added.",
"cite_spans": [
{
"start": 203,
"end": 227,
"text": "[Pulman and Hepple 1993]",
"ref_id": null
}
],
"ref_spans": [],
"eq_spans": [],
"section": "C, OMPlI,ATION INTO AUTOMATA",
"sec_num": "6"
},
{
"text": "Wc conclude this paper by looking at the possil)ility of using our model for toiml hmguages.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "C, OMPlI,ATION INTO AUTOMATA",
"sec_num": "6"
},
{
"text": "This approach may be capable of des(:rit)ing other types of non-linear morphology, though we have not yet looked at a whole range, of examples. The following may form a theoretical franmwork for a number of non-linear phenomena.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Beyond Semitic",
"sec_num": "7.1"
},
{
"text": "Consider sui)rasegmental morphology in tonal languages. Tense in Ngbal~% a language of Zaire, is indicated l)y tone, e.g. {kpolo} 'return' gives Ikpat,)/ (Low),/kpSls/(Mid),/kpbl6/(Low-Iligh), and/kp61S/ (Iiigh) [Nida 1949] . This can be expressed with the stem nlorpheme. {lq)olo} on one tape and the tonal morphemes {L}, {M}, {LH} and {tI} on a second tape with the lbllowing rules: where C is a consonant, V is a vowel and T is a tonal segment (these rules are for the al)ove data only). The transitions for /kpald/are shown below: For all other cases one needs to add a rule for spreading the tonal morpheme.",
"cite_spans": [
{
"start": 212,
"end": 223,
"text": "[Nida 1949]",
"ref_id": null
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Beyond Semitic",
"sec_num": "7.1"
},
{
"text": "EQUATION",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [
{
"start": 0,
"end": 8,
"text": "EQUATION",
"ref_id": "EQREF",
"raw_str": "*-C-* => *-C-*",
"eq_num": "("
}
],
"section": "Beyond Semitic",
"sec_num": "7.1"
},
{
"text": "Cmrently, we are looking at descrihing tl,e Semitic stem using morak: [McCarthy and Prince 1990a] and affixational [McCarthy 1992] analyses of Semitic sLems. Another area of interest is to look at the formal properties of the formalism and of the AFSM.",
"cite_spans": [
{
"start": 70,
"end": 97,
"text": "[McCarthy and Prince 1990a]",
"ref_id": null
},
{
"start": 115,
"end": 130,
"text": "[McCarthy 1992]",
"ref_id": null
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Future Work",
"sec_num": "7.2"
},
{
"text": "'qlf the h'aph!mental, ion works dh'e(%ly on ru[es~ this can he achieved by unification. lI)~ ::: A ill LhO dla,P;rRHL",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "",
"sec_num": null
}
],
"back_matter": [],
"bib_entries": {
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"ref_entries": {
"FIGREF0": {
"text": "ing of e()nSollatlts att(l pattern morphemes consisting of vowels and affixes. Morphemes which fall old: of the domain of the root-an(l-l)attern system, such as particles and preposil,ions, are. (:lassitied as belonging to a third (:lass consisting of successions of consonants and vowels. The analysis of /kuttib/ i)roduces: the root {ktb} 'notion of writing' and the pattern {_.u_:i } 'causative -perfect passive' (wh(!re _ indicates a cons()nan( slot, and : indicates gemination). [McCarthy 1981] provided a deel)er analysis raider the fl:amework of autoseglnental 1)honology [Goldsmith 1976]. IIere, morphemes are elassiIied into: root morphemes CO[lSiStillt~ of COIIS()llalltS, vo('alism nlorl)henms consisting of vowels, and pattern morphemes wlfieh are. CV-skelet:{. 2 Each sits on a separate tier in the alttosegmental model, and they m'e (:oordinated with association liims according to 0m I)rineipies of autosegmental phonology; when universal l)rin -(:il)les fail, language specific rules al)l)ly. '12he analysis of/kuttib/produces three inori)hemes , linked as illustrated below.",
"num": null,
"type_str": "figure",
"uris": null
},
"FIGREF1": {
"text": "Fig. 1 Autosegmental analysis of/kuttib/ n i voealism",
"num": null,
"type_str": "figure",
"uris": null
},
"FIGREF2": {
"text": "Two-level description of moved [ -m o ~v e-F e d lexical",
"num": null,
"type_str": "figure",
"uris": null
},
"FIGREF3": {
"text": "Black et al. 1987] pointed out ttmt previous two-level rules (cf. ,~a.1) affect one character at a time and proposed a formalism wtfich maps tletween (equal ram> bered) sequences of surface and lexical characters of the form, SURF ~ LEX alnidal consonant clusters, CC, take a prosthetic /Pi/.A lexical string maps l;o a sllrfaee sLring iff they can be partitioned into pairs of lexical-sm'fi~ce, subsequences, wtmre each pair is licenced I)y a rule.[l].uessink 1989] added explicit contexts and allowed unequal sequences. [Puhnan and IIepple 19931 (leveloiled the l'ormalism further, allowing feature-based representations interpreted via unification.The developed formalism is llased on the existence of only two levels of rel)resentation: sm'face and lexical. Two types of rules are provided: LSC -SuI~,\" -I1.SC --> LLC -LF:x -B.LC LSC -Sm~v -RSC c> LLC -LEX -",
"num": null,
"type_str": "figure",
"uris": null
},
"FIGREF5": {
"text": "uples to tlt(: left of... are the first to apl>ear Oil {;h(! ]ell. of l,[~X. For examf)le , (;It(: LI,C (:xl)ression (<0 \"\" (~') matcltes al), axtl), axlx2t), axlx.2...1), where xi 7 / (at. In standard two-lew~l morphology we talk of feasilfle pairs. Ilere we talk of feasible tulile pairs el the forlrl (.\",, :\"':,..., :':,,) : (:'D For example, ll.ule 8 (see. I)elow) gives rise 1.o four feasible tul)le l)airs (C/, X, ):(X), 1 < i 5-4 4. The set of feasible tuple pairs is determined the same way as the set of feasible pairs in standard two-level gramniars.",
"num": null,
"type_str": "figure",
"uris": null
},
"FIGREF7": {
"text": "Fig. 3a Form Q3 -i-{a} u \" i I-VT ........ J ........ ], ......",
"num": null,
"type_str": "figure",
"uris": null
},
"FIGREF8": {
"text": "6Varialih!s are indicated by Ilplier-i':ase leti,ers and {t|,OllliC (!]-(!lll(!llI,s Iiy lllwi!r ('itSl!-If!lJAws, 7Nnte that assm:iat.lon lines are indicated hnplicltly by IliIlllbering the (~V element;; in the pattern Inorpheliie,",
"num": null,
"type_str": "figure",
"uris": null
},
"FIGREF9": {
"text": "-(i~, x~, ) P (~ {vl,v2}, X = vowel, 1\",,1~ E {cl,c2,ea,c4}, XI, X2 = radical (13) R.ule 12 allows the omission of non-stmn vowels (i.e.. prefixes and suffixes). Rule 13 allows the omission of stern vowels. Note that the lexical contexts, LI,C and RLC, ensure that mattes lectionis are not omitted in the surface. Here is form Q3 with partial vocalisation on the surface.",
"num": null,
"type_str": "figure",
"uris": null
},
"FIGREF10": {
"text": "Fig. 3b Form Q3 -I-{a} partially vocalised ~ u i + VT",
"num": null,
"type_str": "figure",
"uris": null
},
"FIGREF11": {
"text": "Fig. 4 Form 5 --q i VT",
"num": null,
"type_str": "figure",
"uris": null
},
"FIGREF12": {
"text": "Fig. 5 input tapes AFST",
"num": null,
"type_str": "figure",
"uris": null
},
"FIGREF13": {
"text": "Fig. 6 AFST for Rule 15 Def, 0 ; 0 (v1,0,X):X, 0 ; X",
"num": null,
"type_str": "figure",
"uris": null
},
"FIGREF14": {
"text": "[aa] in/~.t..,~.t,/ (form 6st,0) allows noll-(:OllSectttive reading operations, e.g. the three [a]s in /I.akatt.b/ (form ~).",
"num": null,
"type_str": "figure",
"uris": null
},
"FIGREF17": {
"text": "Fig. 7 {kpolo) -I-{LII}",
"num": null,
"type_str": "figure",
"uris": null
},
"TABREF0": {
"type_str": "table",
"content": "<table><tr><td>(next page) gives the Arabic perfeetive vet-</td></tr><tr><td>hal forms (from [McCarthy 1981]). l</td></tr><tr><td>t As indicated by [McCarthy 1981], the datain q'a|fle 1 pro-</td></tr><tr><td>vi(les stems [n urtdtwlyhlg morphl)h)i;i(:al forms. Ilence, it, should</td></tr><tr><td>he noted that: tlICTCld~ C3+S(++ l,~tHt[t(}r gLrld lllli+111)t!l ' Hl3.t'k[llg. i,q IU2)~</td></tr></table>",
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