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Finite State Processing of Tone Systems FINITE STATE PROCESSING OF TONE SYSTEMS Dafydd Gibbon (U Bielefeld) ABSTRACT as floating tones and compound tones. Floating tones are not associated with syllables, but are po- It is suggested in this paper that two-level stulated to explain appparent irregularities in pho- morphology theory (Kay, Koskenniemi) can be ex- netic patterning in terms of regular tone sandhi tended to include morphological tone. This exten- properties. sion treats phonological features as I/O tapes for Finite State Transducers in a parallel sequential The tone sandhi rules define how tones affect incrementation (PSI) architecture; phonological their neighbours. The example to be treated here is processes (e.g. assimilation) are seen as variants of a kind of tonal assimilation known as tonal sprea- an elementary unification operation over feature ding in which low tones are phonetically raised tapes (linear unification phonology, LUP). The following a high tone or, more frequently, high phenomena analysed are tone terracing with tones are lowered after a low tone, either to the tone-spreading (horizontal assimilation), down- level of the low tone (total downstep) or to a mid step, upstep, downdrift, upsweep in two West Afri- level (partial downstep). The newly defined tone is can languages, Tem (Togo) and Baule (C6te then the reference point for following tones. d'Ivoire). It is shown that an FST acccount leads to more insightful definitions of the basic pheno- The latter kind of assimilation produces a cha- mena than other approaches (e.g. phonological racteristic perceptual, and experimentally measu- rules or metrical systems). rable, effect known as tone terracing. Tone se- quences are realized at a fairly high level at the beginning of a sequence, and at certain well- 1. Descriptive context defined points the whole pitch register appears "to be downstepped to a new level. The process may The topic of this paper is tone sandhi in two be iterated several times. It is often represented in West African tone languages and suitable formal the literature in the following way (partial down- models for it. The languages investigated are Tern step); it can be seen that a later high tone may be (Gur/Voltaic family, Togo) and Baule (Akan fami- as high as or lower than an earlier low tone: ly, C6te d'Ivoire). Tone languages of other types, in particular the Sino-Tibetan languages, will not be discussed. The specific concern of this paper is with the way in which certain quite well-known morpho- phonological (lexical) tone patterns are realized in hhhllhhllhh sequence in terms of phonetic pitch patterns. There are three interacting factors involved: i. tone-text In particular, it will be seen that the two ter- association rules; ii. tone-sandhi rules; iii. phone- raced tone languages, Tem and Baule, involve si- tic interpretation rules. milar processes in detail and have similar basic FST architectures, but differ systematically at cer- Tone-text association rules are concerned with tain well-defined points involving sandhi generali- the association of tones with syllables (primary ty, and scope of sandhi context. associations and a form of tone spreading) as well 291 Detailed phonetic interpretation involves pitch mappings between abstract and concrete phonolo- patterns between neighbouring tones of the same gical and phonetic levels of representation. FST type within terraces. These are processses of systems are conceptually bidirectional; they may downdrift (neighbouring tones fall) or upsweep easily be processed in either direction with the (neighbouring tones, usually high tones, rise). same finite state mechanism; the problem of the They will not be dealt with here. recoverability of underlying structure (short of am- biguity through genuine neutralization) loses its importance. 2. Theoretical context The idea of formulating prosodic patterns in The view is developing, based on work by Kay English intonation in FS terms was originated and and Kaplan, Koskenniemi, Church, and others, developed by Pierrehumbert (1980), though FS that in phonology it is sufficient to use finite state intonation models had been developed much ear- transducers which are not allowed to apply to their lier by 't Hart and others for DutcL intonation. own output. Kay and Kaplan have shown that it is These existing FS intonation descriptions are possible to reduce conventional, so-called straightforward finite state automata (FSAs; for "context-sensitive" phonological rules to finite- Dutch, probabilistic FSAs). The problem of map- state relations, and to apply the FSTs thus pro- ping such patterns at one level on to patterns at duced in sequential order (Kay 1986). another, the traditional problem in descriptive lin- guistics as well as in computational parsing and Koskenniemi developed a somewhat different translation, has not been formulated in finite state concept for Finnish morphology, in which the terms for this domain. This mapping question is a FSTs operate as parallel filters over the input: they different one from the question of recognition, and must all agree in their output. A careful analysis the finite state devices required for an answer to also shows that Church's allophonic parser, in his the question are different. Additionally, the tone actual implementation using matrix operations to language application constitutes a different domain. simulate bottom up chart parsing, can also be seen as a system of parallel finite state filters. The PSI The input and output languages for FSTs are (Parallel Sequential Incrementation) system of pro- both regular sets (Type 3 languages). FSTs have sodic analysis being developed by myself in the various interesting properties which are in part DFG Forschergruppe "Koh~renz" in Bielefeid in- similar to those of FSAs. The reversibility property corporates a similar concept of FSTs used as a pa- shown in the simulations is one of the most inter- rallel filter bank (Gibbon & al. 1986). esting. Any FST which is deterministic in one di- rection is not necessarily deterministic in the other, The context within descriptive phonology is as the neutralization facts in Tern and Baule show. that of theories which postulate interreelated but Furthermore, it is not true for FSTs, as it is for structurally autonomous parallel levels of organi- FSAs, that for any non--deterministic FST there is zation in phonology. The four major classical di- a deterministic one which is weakly equivalent re- rections in this area are traditional intonation ana- lative to the input language. This only holds if the lysis (surveyed and developed in Gibbon 1976), paired input and output symbols are interpreted Firthian "prosodic phonology", Pike's simul- as compound (relational) input symbols, and the taneous hierarchies, and the non-linear (autoseg- input and output tapes are seen as a single tape of mental and metrical) phonologies of the last thir- pairs. This is an abstraction which formally redu- teen years. ces FSTs to FSAs. Kay has suggested this perspec- tive on FSTs as an explication for relations be- Parallel FST systems are used in order to ex- tween linguistic levels, where FSTs define relations plicate both traditional phonological rules, so long between linguistic levels of representation in an as they do not apply to their own output, and also, essentially declarative fashion, though with a pro- with appropriate synchronization measures, the cedural interpretation. For a slightly different FST parallel tiers which figure in autosegmental phono- definition cf. Aho & Ullman (1972). In current logy, the mappings between these tiers, and the computational theories of language (FUG, GPSG, 292 LFG), the standard treatment for concord restric- Reverse: tion, to which phonological assimilation and neu- tralization may be compared, is in terms of a class INs (LC LC LC LC) of operations related to unification. The situation OUTs t (L L L L) in autosegmental phonology is simpler than in syn- IN: (HC H H) tax, in that each feature or tier can be modelled by OUTt 1 (H H H) 2 (H H L) a finite state device. The elementary unification operator required is, correspondingly, restricted to INJ (LC !H H) OUT1 % (L H H) non-recursive, adjacent feature specification on a 2 (L H L) given tier, as in the present analysis. In a INs (LC!HHLC) non--parallel architecture, the operation would be OUTs 1 (LHHeL) 2 (LHLL) embedded in a more complex, perhaps context-free-style, context. IN= (LC !H LC} OUTs t (L H ~L) INs (LC LC LC !H) OUT: 1 (L L L H) 3.The Tern and Baule data IN= (LC fH H !H) OUT: 1 (L H L H) The essential tonal properties of Tern are: IN~ (LC ~H H LC !H) downstep, downdrift, phonetically constant OUT: t (L H L L H) (non-terraced) low tone, high tone spreading over IN= (LC !H H !H H) a following low; only terracing and sandhi are OUT: 1 (LHLHH} dealt with here. The Tern data and the inter-level 2 (LHLHL) relations are taken from Tchagbale (1984). The INI (LC 'H H LC !H H LC) following shows a simulation using a bidirectional OUT - l (L H L L H H =L) 2 (L H L L H L L) FST interpreter, with runs in each direction. INs (LC !H H !H H H) 0UT: 1 (LHLHHH) Forward: 2 (LHLHHL) INi (L L L L) [NI (HC H !H H LC) OUT: 1 (LC LC LC LC) OUT: 1 (H L H H ~L) 2 (H L H L L} INs (H H H} OUTt 1 (HC H H) INi (L H H) OUTI 1 (LC !H H) IN: (L H L L) OUTs I (LC !H H LC} The essential tonal properties of Baule are: INt (L H ~L} partial or total downstep (style-determined), up- 0UT2 1 (LC !H LC) step, upsweep, downdrift, tone spreading of both IN= (L L L H} low and high over the first tone of an appositely OUT= X (LC LC LC !H) specified sequence, compound tone.
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