«The statistical basis of an unnatural alternation Janet B. Pierrehumbert The /k/-/s/ alternation in word pairs such as electric, electricity is not ...»
The statistical basis of an unnatural alternation
Janet B. Pierrehumbert
The /k/-/s/ alternation in word pairs such as electric, electricity is not phonetically natural, and is learned by English speakers as a generalization over
morphological relatives. Data gathered in an open-response experimental
task show that it is productive before the sufﬁx -ity. Lesser productivity is
found for the same materials in a backformation task. Outcomes are analyzed as the result of a cognitive process of statistical inference.
descriptions make crucial use of phonological variables. Cognitive preferences for certainty and for robust, redundant descriptions are argued to jointly determine the universe over which operational statistics are estimated.
1. Introduction This paper presents an experimental study of the productivity of the /k/-/s/ alternation exhibited in derivational pairs such as electric, electricity. It is exempliﬁed in numerous word pairs in English involving various sufﬁxes, including -ity, -ism, and -ist. The Collins on-line English dictionary (distributed in 1990 through the ACL Data Collection Initiative) includes 108 clear examples of words ending in these sufﬁxes in which a stem-ﬁnal /k/ softens to /s/. The largest group, and the main topic of this paper, is words formed with -ity. The dictionary contains only twelve words with stems ending in /k/ which fail to soften before one of these three sufﬁxes (e.g. anarchy, anarchism, York, Yorkist). All involve afﬁxes other than -ity.
The productivity of the alternation is disputable. First, there are very few forms which would support extension of the alternation beyond an orthographic -ic followed by one of the triggering sufﬁxes. For the sufﬁxes just listed, the only common examples listed in the Collins are Greek/Grecism; opaque, opacity; reciprocal/reciprocate, reciprocity; and pharmacology, pharmacist. (A number of potentially relevant pairs, such as caducous, caducity; cecum, cecity; paucal, paucity; raucous, raucity would only be known to very erudite speakers.) Second, as Myers (1999) also notes, the 84 Janet B. Pierrehumbert /k/-/s/ alternation as presently found in English is not natural (in the sense of Anderson 1981).
Velar Softening is not phonetically natural because the evident phonetic pressures on a /k/ in the target position would not produce /s/. If the sufﬁx vowel is // (as transcribed in the dictionary) then coarticulation and lenition would yield an aspirated palatal approximant rather than the alveolar fricative /s/ (see Lavoie 2001). The alternative possibility for the vowel, //, provides still weaker phonetic motivation for /s/. /s/ differs from the phonetically expected outcome by its maximal vocal fold abduction and its precise tongue shaping, which directs a jet of air against the teeth. These are active adjustments which cannot be characterized asaccommodation to a following vowel. Thus, understanding the alternation of /k/ with /s/ requires recourse to some version of the concept of Structure Preservation in phonology (see Kiparsky 1985) which states that lexical alternations stay within a language’s system of phonological categories. Since an aspirated palatal approximant is not a contrastive category in the English lexicon, it cannot be the outcome of a morphophonological rule, either. The reanalysis involved in lexicalizing the phonetically expected approximant as the lexically contrastive segment /s/ reveals the role of abstract cognitive factors, over and beyond phonetic ones.
Velar Softening is also unnatural because it is phonologically opaque.
Though it originates historically in fronting and spirantization of the velar stop before a non-low front vowel, sufﬁxes with such vowels on the surface do not in general trigger the softening of /k/ to /s/ in the synchronic phonology. /k/ never softens to /s/ before -y, as smoke, smoky. On the other hand, -ize, beginning with a low vowel, does trigger softening, because -ize formerly had a nonlow front vowel. In Chomsky and Halle (1968), this historical ordering is recapitulated in the extrinsic ordering of rules in the synchronic phonology. The phonological opacity created by such orderings is precisely one reason that the psychological validity of the Chomsky-Halle model became a matter of widespread dispute. The ﬁnding that the vowel shift is only partially productive (c.f. Jaeger 1984; McCawley 1986) also calls into question the productivity of the rule of Velar Softening, which is ordered before it.
Understanding productivity is important because it provides a crucial line of evidence about cognitive abstractions. The failure of an alternation to generalize suggests that no abstract generalization over the forms exhibiting the alternation has been formed. If the alternation is aggressively and reliably extended, even to forms which differ substantially from attested The statistical basis of an unnatural alternation ones, it follows that a very broad abstraction has been formed. For example, the reliable and aggressive extension of the regular English plural pattern indicates that it abstracts away from many properties of the word. If the situation lies somewhere in the middle, then the exact pattern of productivity can yield insights about the exact character of the abstraction that is formed.
Phonotactics is the area in which most research has been done on the availability of lexical patterns for use in novel forms. Numerous studies, reviewed in Pierrehumbert (2003), indicate that the type frequency (frequency in the lexicon) of a phonological pattern affects the likelihood and perceived well-formedness of novel words containing that pattern. This dependence is gradient; frequent sequences readily extended to new words, rare sequences are avoided, and moderately frequent sequences fall in between. For example, Hay, Pierrehumbert, and Beckman (2004) found that the perceived well-formedness of novel words containing nasal-obstruent clusters (such as // and //) was a gradient function of the frequency of the cluster. The frequency for a tautomorphemic cluster was estimated as its frequency in trochaic monomorphemic words with a lax front vowel in the CELEX monomorphemes. (see Baayen, Piepenbrock and Gulikens 1995, regarding CELEX; Hay, Pierrehumbert and Beckman 2004, regarding monomorphemes).
This choice of universe for estimating frequencies was opportunistic, and obscures a central issue in understanding the relation of lexical frequencies to pattern productivity. This issue is taken up with Figure 1. Figure 1 shows a partial lattice of heterosyllabic N.O clusters. The atoms on the bottom are individual heterosyllabic phoneme clusters. The nodes above the atoms are some of the various available natural classes of such clusters. As is wellknown, natural classes can be formed using partial descriptions of phonological patterns. For example, the sequence /nt/ is an element of the set of clusters of /n/ followed by any stop; it is also an element of the set of clusters containing a homorganic nasal and stop. The cluster /np/ belongs to the former set but not the latter; the cluster /mp/ belongs to the latter set but not the former. The lattice is organized from speciﬁc (on the bottom) to general (at the top). Each node is labeled with the probability of the indicated descriptor with respect to the universe of N.O clusters, as estimated from counts in the CELEX monomorphemes. Clearly, the less speciﬁc the description, the more cases it encompasses and the larger the natural class it describes. Thus, the probabilities go up as we follow the lines up the lattice, but the exact way they go up depends on exactly what is lumped together in each class.
86 Janet B. Pierrehumbert The topmost case, any nasal followed by any obstruent, is taken to deﬁne the universe for the probabilities which are indicated below each node. If the universe were larger, the probabilities shown on the ﬁgure would all be smaller, but their rankings would remain the same.
Figure 1. Partial lattice of probabilities for the universe of heterosyllabic nasal-obstruent clusters in monomorphemic words of English.
Counts are established with respect to the Celex monomorphemes, as discussed in Hay et al. (2004).
Atoms at the bottom of the lattice represent speciﬁc nasal-obstruent sequences. For the sake of legibility, only eight atoms with a total P = 0.54 are shown. The remaining sequences, with a total P = 0.46, have been omitted. Superordinate nodes represent classes of nasal-obstruent sequences. Italic indices are used for convenience to indicate homorganicity or nonhomorganicity. (Actual phonological structures for homorganic consonants have feature sharing.) Capital N denotes any nasal. Probabilities of superordinate categories include frequencies of atoms which are not shown at the bottom, but which are properly described by the superordinate note. Superordinate nodes /Stop/ and /Fric/ are not shown.
The question raised by Figure 1 is: Of all the probabilities which may be deﬁned using partial phonological descriptions of a pattern, which are relevant to productivity and perceived well-formedness? For example, if the The statistical basis of an unnatural alternation description NiOi (p =.88) versus NiOj (p =.12) were the relevant level of abstraction then the feature [+/– continuant] would have no importance for the evaluation and productivity of these clusters, and inhomorganic nasal-fricative clusters would seem every bit as bad as inhomorganic nasal-stop clusters.
However, results in Hay et al. (2004) clearly show differential outcomes for nasal-stop and nasal-fricative clusters, indicating that this degree of generalization is too great. The next level down shows two alternative ways to break out the cases. One ﬁxes the nasal consonant and generalizes over the following the obstruent. The other generalizes over place. It separates homorganic from inhomorganic clusters regardless of place, but it maintains information about the continuance of the obstruent. If the ﬁrst alternative were the cognitively relevant description, then /np/ would be as acceptable as /nt/. This is false. The second alternative also groups /nt/ in a class with other clusters, namely /mp/ and // but not /np/. It is closer to the true state of affairs, since it captures both a strong effect of homorganicity on nasal-stop clusters and a weaker effect on nasal-fricative clusters. However, the lattice structure does not in itself say that one line of generalization is more relevant than the other.
Although any phonologist would sensibly prefer one line of generalization to the other, there is no explicit formal account of what this “sensibleness” consists of. Still less is there an explanation of why subjects operated at a detailed level of description, rather than applying a simple overarching generalization about all N.O clusters.
The same issue arises in a different guise in dealing with morphophonological alternations. When such alternations are language particular, they must be learned from examples. There is by now abundant evidence that the productivity of an alternation depends on its type frequency (as well as on other factors). Alternations found in extremely few types, such as irregular conjugations for auxiliaries, are not productive no matter how frequently the irregular forms may be used. However, the universe of examples relevant for any given alternation, and the types of formal generalizations which are made over these examples, is not well understood.
In comparison to phonotactics, morphophonology provides both challenges and opportunities in addressing this issue. It is challenging because many morphophonological alternations are generalizations over word pairs rather than merely over words. For phonotactics, set theory provides a convenient hierarchy of abstraction over words, taking the shape of a lattice of partial descriptions as in Figure 1. For word pairs, in contrast, the proper formal toolkit is not as evident. Is it partial descriptions of the base which are relevant? Or partial descriptions of the complex form? Or relations of partial 88 Janet B. Pierrehumbert descriptions of the base and the complex form? The research literature contains case studies which argue for all of these possibilities. As discussed in Myers (1999) and below, the /k/-/s/ alternation needs to be formalized with respect to word pairs; but this need does not in itself deﬁne the relevant universe of word pairs. For determining the pronunciation of a novel form clemicity given the base clemic, the pair conic, conicity is plainly relevant. But how about Turk, Turkism (involving a different afﬁx)? Or ferocious, ferocity (for which no bare form of the base exists)? Or morbid, morbidity (illustrating preservation of a ﬁnal stop before the same afﬁx)?
In short, the expectation (based on results in phonotactics and in psychology) that implicit knowledge of morphophonology is stochastic does not in itself deﬁne what probabilities will be relevant. Probabilities can be estimated for any formal description that can be tabulated. Many of the “analytic biases” mentioned in Steriade’s (2002) original commentary on this session can be viewed as claims about what statistics are available to the cognitive system. For example, in discussing Goldrick (2002), she suggests an analytic bias to the effect that voicing pairs should alternate alike. This is equivalent to the claim that statistics on formal descriptions which abstract over place, but not voicing, are highly available in the formation of phonological grammars.