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Edmund Grimley-Evans; George Anton Kiraz; Stephen G. Pulman
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lion. II,S(? (right conl;cxt) (rN+l,..., 1. Sm in t)racticc all the left conl;(;xts start Definition of the Formalism with all the right contexts end with L*, 2.1 Formal Definition we omit wril;ing it and assume it by default. The We use tapes, where tim first tapes are operators are: for CII. s, for S(] rules and ]exical and the remaining are surface, -- for coInposite rules. M. In practi(:e, :: We write Ei prot)osed morphologit:at analysis is an for the alphabet of sylnbols used on tape i, and tuI)le of strings, and rules are intert)reted as :: (Er {el) {c}), so that E* is applying section of this analysis in conl;ext: 455 ~o ,~- 1. 4> *{= ?'i I.i "e~N 7£ de.-. Cl ?" 1.n~ ix '1"~,. be, 1, ix .s' a') tO =- tO be, ot: re= 1~1 H. i rule. V = B b}, * C - a i E + a < E a ] B - aft;re' pro._ = tit(; B ..., X - B = E n • = B A * C19, - (;' P (1, a - a C x A 1 a = (2 B a e, e P E = (b, B E B R~=) A P,. 1 E A r - (R=>, - a B G b c. * v a ~ V ¢ tit(; = ...(.(I, w a a is E v a x c,., u P1 j = + P A A j a R~=) a E a i a a G X : = P,. i E j d E b i c 0 d a (b, j ¢ E c i * A b O b ¢> l}l~,t~ (n-way concatenation of left con- R3: text, centre, aim right context). Formally: Defiinition 2.3 rule c, r) contextually R1 and R2 illustrate the iterative application of allows (1}, Pc, P,.) iff l, and rules on strings: they sanction the lexical-surface [] strings (VBBB,Vbbb), where the second (B,b) pair serves as the centre of the first application Definition 2.4 An SC rule (l, cl, r) coer- of R2 and as the left context of the second ap- cively disallows (Pt, P~,Pr) iff l, r, plication of the same rule. is an cpenthetic P,. Ecl and [] rule which also demonstrates centres of unequal Definition 2.5 N:M two-level grammar is length. (We assume that rule (l, c,r) ERa, we can make this representa- tuitive for the user when insertion rules are used. tion unique by defining canonical way of convert- For example, the rule (E* (g, g), E~, E~ v, E*) ing each such possible centre into same-length ('change to g') would not disallow string-tuple 6'. simple way of doing this is to string-tuple partitioned as g), (e, c), (u, u)... pad with 0s the right making each string as long assmning some CR rule allows (e, e). as the longest string in C: if (Pl, ...,pn), Earlier versions of the partition fbrmalism could (>0", ...,p,,0*) z*(0, 0) (1) not (in practice) cope with multiple lexical char- actors in SC rules, see (Carter, 1995, §4.1). This However, since we know set of possible is not case here. titions it is U{c ~l,r(l,(-,'r} 1{:,}- we can Th