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A Phonetic Study of West African Languages (Second Edition) by Peter Ladefoged

By Peter Ladefoged

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19 to show that the transformation (−) of CFGs preserves the strings but not the set of terms if applied also to unary rules. The rule d has the form T → B. It is converted into the string function I( f d )(x) = x, in other words the identity function. This function is iterable, while the rule is not. Thus the term f d f d f g would evaluate in G Q to /0/. 67) However, there is no derivation with term f d f d f g . Try to start with the symbol T, for example: T B x0 fd x0 ? 68) Similarly if we start with /B/.

Sometimes we can successfully perform such a substitution, as certain nouns accept two plural endings: we have /formulas/ next to /formulae/. Most of the time the substitution will fail though. In P1 on the other hand the substitution of the plural morph is illicit for a different reason: it is not a constituent. The form /cats/ is the value of p f cat , so the only constituent substitution we can perform is to replace f cat by f mouse and in this case the result is /mice/. In P3 string substitution of the plural morph by something else is sometimes licit sometimes not.

A derivation of the third string is as follows. 52) o Let us now look at a bottom up version of CFGs. Obviously, to get such a grammar we simply turn the rules around. Rather than assuming a rule, say, ρ = A → BC, we define a string function f ρ of arity 2 such that f ρ is interpreted as concatenation, which is to say I( f ρ )(x, y) = x y. However, this function is only defined if x is a B-string, that is, if we can derive x from B in the grammar and if y is a C-string. In this way we guarantee that x y is an A-string.

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