In two earlier posts, I discussed the idea of magic, my term for the deductive necessity that some linguistic property distinguishes those morphemes which undergo or do not undergo surface-unpredictable alternations. For instance, the Spanish verb negar ‘to deny’ diphthongizes under stress (e.g., niego ‘I deny’), whereas the superficially similar pegar ‘to stick to s.t.’ does not (pego ‘I stick to s.t.’), and there must be something different about the two stems that causes this.

In a forthcoming handbook chapter, Baković, E., Heinz, J., and Rawski (in press; henceforth BHR) take up the familiar Kiparskian question of the locuses of phonological abstractness, and in doing so, they discuss several ways in which this magic might be encoded. I would like to briefly review their taxonomy.

Under the suppletive analysis, magic verbs like negar have two stems underlying, perhaps /neg-/ and /njɛg-/, the latter used when primary stress falls on the stem. Linguists have—rightly, I think—been uncomfortable with this kind of analysis when the supposedly suppletive stem allomorphs are phonologically similar, and when the distribution of the allomorphs are easily stated in phonological or morphosyntactic terms; both are the case here. However, Aronoff (1994) argues that one must recognize the existence of suppletive patterns and his major case studies (from Hebrew and Latin) involve less-similar stem allomorphs whose distributions are not so easily stated.  I am not immediately convinced by Aronoff’s arguments, but I think they should be taken seriously. BHR are similarly skeptical of the use of suppletion except in cases where the allomorphs share little material (e.g., the Korean nominative, which is realized as /-ka/ or /-i/ depending on context).²

Under the abstract diacritic analysis, magical stems bear an feature which is part of the environment for some rule. One concrete version of this is to make the diacritic literally a rule feature, such that rule R cannot apply to a stem unless that stem bears the feature [+R]. For instance, we might represent the stems of the two Spanish verbs as /neg- {+diph}/ and /peg- {−diph}/.¹ We of course need then to write the diphthongization structural change (but this is not hard) and to specify its environment (but this no more or less hard than it would be under the suppletive analysis).

Finally, under the abstract phoneme analysis, magical stems contain phonemes³ which are “abstract” (in a sense to be specified shortly) and trigger the relevant rule (here, diphthongization). BHR discern two types of abstract phonemes: absolutely abstract phonemes are feature bundles which do not appear on the surface, and restrictedly abstract phonemes consist of surface-licit feature bundles which surface in the some, but not all, of the contexts in which they are posited.⁴

The distinction between abstract diacritics and abstract phonemes seems important. It is probably not surprising that self-described morphologists seem to prefer abstract diacritics whereas phonologists prefer abstract phonemes.

Endnotes

1. One can further imagine that {−diph} is not present underlyingly but is filled in by a lexical redundancy rule early in the derivation, at least for 1st (-a-) and 2nd (-e-) conjugation verbs for which non-diphthongization seems to be the default (see Gorman & Yang 2019 and citations therein). Similar redundancy rules will be called for all rules of “pure phonology”, those which do not show morpholexical conditioning.
2. This type of analysis is closely related to Gouskova and Pater’s concept of “exceptional morphs” in Optimality Theory.
3. I note it is not exactly the phoneme itself which is abstract, but rather the overall phonemic form of the morph. For instance, according to Lieber (1987:100f.), German umlaut (a fronting of a [+back] stem vowel) is triggered by a “floating” [−back] feature which is underlyingly present in just those stems which undergo umlaut.
4. It is not clear to me whether BHR treat this distinction as an object of grammar, or whether it’s just a descriptive notion.

References

Aronoff, M. 1994. Morphology by Itself. MIT Press.
Baković, E., Heinz, J., and Rawski, J. In press. Phonological abstractness in the mental lexicon. In The Oxford Handbook of the Mental Lexicon, to appear.
Gorman, K. and Yang, C. 2019. When nobody wins. In Franz Rainer, Francesco Gardani, Hans Christian Luschützky and Wolfgang U. Dressler (ed.), Competition in inflection and word formation, pages 169-193. Springer.
Harris, J. 1969. Spanish Phonology. MIT Press.
Harris, J. 1985. Spanish diphthongisation and stress: a paradox resolved. Phonology Yearbook 2:31-45.
Lieber, R. 1987. An Integrated Theory of Autosegmental Processes. State University of New York Press.

At the Graduate Center we recently hosted an excellent lecture by Jane Chandlee of Haverford College. Those familiar with her work may know that she’s been studying, for some time now, two classes of string-to-string functions called the input strictly local (ISL) and output strictly local (OSL) functions. These are generalizations of the familiar notion of the strictly local (SL) languages proposed by McNaughton and Papert (1971) many years ago. For definitions of ISL and OSL functions, see Chandlee et al. 2014 and Chandlee 2014. Chandlee and colleagues have been arguing, for some time now, that virtually all phonological processes are ISL, OSL, or both (note that their intersection is non-null).

In her talk, Chandlee attempted to formalize the notions of iterativity and non-iterativity in phonology with reference to ISL and OSL functions. One interesting side effect of this work is that one can, quite easily, determine what makes a phonological process direction-invariant or direction-specific. In FSTP (Gorman & Sproat 2021:§5.1.1) we describe three notions of rule directionality (ones which are quite a bit less general than Chandlee’s notions) from the literature, but conclude: “Note, however, that directionality of application has no discernable effect for perhaps the majority of rules, and can often be ignored.” (op. cit., 53) We didn’t bother to determine when this is the case, but Chandlee shows that the set of rules which are invariant to direction of application (in our sense) are exactly those which are ISL ∩ OSL; that is, they describe processes which are both ISL and OSL, in the sense that they are string-to-string functions (or maps, to use her term) which can be encoded either as ISL or OSL.

As Richard Sproat (p.c.) points out to me, there are weaker notions of direction-invariance we may care about in the context of grammar engineering. For instance, it might be the case that some rule is, strictly speaking, direction-specific, but the language of input strings is not expected to contain any relevant examples. I suspect this is quite common also.

References

Chandlee, J. 2014. Strictly local phonological processes. Doctoral dissertation, University of Delaware.
Chandlee, J., Eyraud, R., and Heinz, J. 2014. Learning strictly local subsequential functions. Transactions of the Association for Computational Linguistics 2: 491-503.
Gorman, K., and Sproat, R. 2021. Finite-State Text Processing. Morgan & Claypool.
McNaughton, R., and Papert, S. A. 1971. Counter-Free Automata. MIT Press.

Kisseberth (1970) introduces the notion of conspiracies, cases in which a series of phonological rules in a single language “conspire” to create similar output configurations. Supposedly, Haj Ross chose the term “conspiracy”, and it is perhaps not an accident that the term he chose immediately reminds one of conspiracy theory, which has a strong negative connotation implying that the existence of the conspiracy cannot be proven. Kisseberth’s discovery of conspiracies motivated the rise of Optimality Theory (OT) two decades later—Prince & Smolensky (1993:1) refer to conspiracies as a “conceptual crisis” at the heart of phonological theory, and Zuraw (2003) explicitly links Kisseberth’s data to OT—but curiously, it seemingly had little effect on contemporary phonological theorizing. (A positivist might say that the theoretical technology needed to encode conspiratorial thinking simply did not exist at the time; a cynic might say that contemporaries did not take Kisseberth’s conspiratorial thinking seriously until it became easy to do so.) I discern two major objections to the logic of conspiracies: the evolutionary argument and the prosodic argument, which I’ll briefly review.

The evolutionary argument

What I am calling the evolutionary argument was first made by Kiparsky (1973:75f.) and is presented as an argument against OT by Hale & Reiss (2008:14). Roughly, if a series of rules lead to the same set of output configurations, they must be surface true, or they would not contribute to the putative conspiracy. Since surface-true rules are assumed to be easy to learn, especially relative to opaque rules are assumed to be difficult to learn, and since failure to learn rules would contribute to language change, grammars will naturally accumulate functionally related surface-true rules. I think we should question the assumption (au courant in 1973) that opacity is the end-all of what makes a rule difficult to acquire, but otherwise I find this basic logic sound.

The prosodic argument

At the time Kisseberth was writing, standard phonological theory included few of the prosodic primitives; even the notion of syllable was considered dubious. Subsequent revisions of the theory have introduced rich hierarchies of prosodic primitives. In particular, a subsequent generation of phonologists hypothesized that speakers “build” or “parse” sequences of segments into onsets and rimes, syllables, and feet, with repairs like stray erasure, i.e., deletion, of unsyllabified segmental or epenthesis used to resolve conflicts (McCarthy 1979, Steriade 1982, Itô 1986). It seems to me that this approach accounts for most of the facts of Yowlumne (formerly Yawelmani) reviewed by Kisseberth in his study:

1. there are no word-initial CC clusters
2. there are no word-final CC clusters
3. derived CCCs are resolved either by deletion or i-epenthesis
4. there are no CCC clusters in underlying form

The relevant observation that links all these facts is simply that Yowlumne does not permit branching onsets or codas, but more specifically, Yowlumne’s syllable-parsing algorithm does not build branching onsets or codas. This immediately accounts for facts #1-2. Assuming the logic of the McCarthy and contemporaries, #3 is also unsurprising: these clusters simply cannot be realized faithfully; the fact that there are multiple resolutions for the *CCC pathology is besides the point. And finally, adopting the logic that Prince & Smolensky (1993:54) were later to call Stampean occultation, the absence of underlying CCC clusters follows from the inability of them to surface, since the generalizations in question are all surface-true. (Here, we are treading closely to Kiparsky’s thoughts on the matter too.) Crucially, the analysis given above does not reify any surface constraints; the facts all follow from the feed-forward derivational structure of prosodically-informed phonological theory current a decade before Prince & Smolensky.

Conclusion

While Prince & Smolensky are right to say that OT provides a principled solution to Kisseberth’s notion of conspiracies, researchers in the ’70s and ’80s treated Kisseberth’s notion as epiphenomena of acquisition (Kiparsky) or prosodic structure-building (McCarthy and contemporaries). Perhaps, then, OT do not deserve credit for solving an unsolved problem in this regard. Of course, it remains to be seen whether the many implicit conjectures in these two objections can be sustained.

References

Hale, M. and Reiss, C. 2008. The Phonological Enterprise. Oxford University Press.
Kiparsky, P. 1973. Phonological representations. In O. Fujimura (ed.), Three Dimensions of Linguistic Theory, pages 1-135. TEC Corporation.
Kisseberth, C. W. 1970. On the functional unity of phonological rules. Linguistic Inquiry 1(3): 291-306.
Itô, J. 1986. Syllable theory in prosodic phonology. Doctoral dissertation, University of Massachusetts, Amherst. Published by Garland Publishers, 1988.
McCarthy, J. 1979. Formal problems in Semitic phonology and morphology. Doctoral dissertation, MIT. Published by Garland Publishers, 1985.
Prince, A., and Smolensky, P. 1993. Optimality Theory: constraint interaction in generative grammar. Rutgers Center for Cognitive Science Technical Report TR-2.
Steriade, D. 1982. Greek prosodies and the Nature of syllabification. Doctoral dissertation, MIT.
Zuraw, K. 2003. Optimality Theory in linguistics. In M. Arbib (ed.), Handbook of Brain Theory and Neural Networks, pages 819-822. 2nd edition. MIT Press.

One “parochial” constraint in Germanic is the absence of branching onsets consisting of a coronal stop followed by /l/. Thus /pl, bl, kl, gl/ are all common in Germanic, but *tl and *dl are not. It is difficult to understand what might gives rise to this phonotactic gap.

Blevins & Grawunder (2009), henceforth B&G, note that in portions of Saxony and points south, *kl has in fact shifted to [tl] and *gl to [dl]. This sound change has been noted in passing by several linguists, going back to at least the 19th century. This change has the hallmarks of a change from below: it does not appear to be subject to social evaluation and is not subject to “correction” in careful speech styles. B&G also note that many varieties of English have undergone this change; according to Wright, it could be found in parts of east Yorkshire. Similarly, no social stigma seems to have attached to this pronunciation, and B&G suggest it may have even made its way into American English. B&G argue that since it has occurred at least twice, KL > TL is a natural sound change in the relevant sense.

Of particular interest to me is B&G’s claim that one structural factor supporting *KL > TL is the absence of TL in Germanic before this change; in all known instances of *KL > TL, the preceding stage of the language lacked (contrastive) TL. While many linguists have argued that TL is universally marked, and that its absence in Germanic is a structural gap in the relevant sense, this does not seem to be borne out by quantitative typology of a wide range of language families.

Of course, other phonotactic gaps, even statistically robust ones, also are similarly filled with ease. I submit that evidence of this sort suggests that phonologists habitually overestimate the “structural” nature of phonotactic gaps.

References

Blevins, J. and Grawunder, S. 2009. *KL > TL sound change in Germanic and elsewhere: descriptions, explanations, and implications. Linguistic Typology 13: 267-303.

I assume you know what an allophone is. But what this blog post supposes […beat…] is that you could be more careful about how you talk about them.

Let us suppose the following:

• the phonemic inventory P of some grammar G contains t and d
• P does not contain s or z
• yet instances of s or z are found on the surface

Thus we might say that /t, d/ are phonemes and [s, z] are allophones (perhaps of /t, d/: maybe in G, derived coronal stop clusters undergo assibilation).

Let us suppose that you’re writing the introduction to a phonological analysis of G, and in Table 1—it’s usually Table 1—you list the phonemes you posit, sorted by place and manner. Perhaps you will place s and z in italics or brackets, and the caption will indicate that this refers to segments which are allophones.

I find this imprecise. It suggests that all instances of surface t or d are phonemic (or perhaps more precisely, and more vacuously, are faithful allophones),¹ which need not be the case. Perhaps G has a rule of perseveratory obstruent cluster voice assimilation and one can derive surface [pt] from /…p-d…/, or surface [gd] from /…g-t…/, and so on. The confusion here seems to be that we are implicitly treating the sets of allophones and phonemes are disjoint when the former is a superset of the latter. What we seem to actually mean when we say that [s, z] are allophones is rather that they are pure allophones: allophones which are not also phonemes.

Another possible way to clarify the hypothetical table 1 is to simply state what phonemes s and z are allophones of, exactly. For instance, if they are purely derived by assibilation, we might write that “the stridents s, z are (pure) allophones of the associated coronal stops /t, d/ respectively”. However, since this might be besides the point, and because there’s no principled upper bound on how many phonemic sources a given (pure or otherwise) allophone might have, I think it should suffice to suggest that s and z are pure allophones and leave it at that.²

This imprecision, I suspect, is a hang-over from structuralist phonemics, which viewed allophony as separate (and arguably, more privileged or entrenched) than alternations (then called morphophonemics). Of course, this assumption does not appear to have any compelling justification, and as Halle (1959) shows, it leads to substantial duplication (in the sense of Kisseberth 1970) between rules of allophony and rules of neutralization.³ Most linguists since Halle seem to have found the structuralist stipulation and the duplication it gives rise to aesthetically displeasing; I concur.

Endnotes

1. I leave open the question of whether surface representations ever contain phonemes: perhaps vacuous rules “faithfully” convert them to allophones.
2. One could (and perhaps should) go further into feature logic, and as such, regard both phonemes and pure allophones as mere bundles of features linked to a single timing slot. However, this makes things harder to talk about.
3. I do not assume that “neutralization” is a grammatical primitive. It is easily defined (see Bale & Reiss 2017, ch. 20) but I see no reason to suppose that grammars distinguish neutralizing processes from other processes.

References

Bale, A. and Reiss, C. 2018. Phonology: A Formal Introduction. MIT Press.
Halle, M. 1959. Sound Pattern of Russian. Mouton.
Kisseberth, C. W. 1970. On the functional unity of phonological rules. Linguistic Inquiry 1(3): 291-306.