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.

The hypothesis

In a recent handout, I discuss the following hypothesis, implicit in my dissertation (Gorman 2013):

(1) Alternation Phonotactic Hypothesis: Let A, B, C, and D be (possibly-null) string sets. Then, if a grammar G contains a surface-true rule of alternation A → B / C __ D, nonce words containing the subsequence CAD are ill-formed for speakers of G.

Before I continue, note that definition is “phenomenological” in the sense that refers to two notions—alternations and surface-true-ness—which are not generally considered to be encoded directly in the grammar. Regarding the notion of alternations, it is not difficult to formalize whether or not a rule is alternating.

(2) Let a rule be defined by possibly-null string sets A, B, C, and D as in (1). Then if any elements of B are phonemes, then the rule is a rule of alternation.

(3) [ditto] If no elements of B are phonemes, then the rule is a rule of (pure) allophony.

But from the argument against bi-uniqueness in Sound Pattern of Russian (Halle 1959), it follows that we should reject a grammar-internal distinction between rules of alternation and allophony, and subsequent theory provides no way to encode this distinction in the grammar. Similarly, it is not hard to define what it means for a rule to be surface-true.

(4) [ditto] If no instances of CAD are generated by the grammar G, then the rule is surface-true.

But, there does not seem to be much reason for that notion to be encoded in the grammar and the theory does not provide any way to encode it.¹ Note further that I am also deliberately stating in (1) that a constraint against CAD has been “projected” from the alternation, rather than treating such constraints as autonomous entities of the theory as is done in Optimality Theory (OT) and friends. Finally, I have phrased this in terms of grammaticality (“are ill-formed”) rather than acceptability.

Why might the Alternation Phonotactic Hypothesis (henceforth, APH) be true? First, I take it as obvious that alternations are more entrenched facts about grammars than pure allophony. For instance, in English, stop aspiration could be governed by a rule of allophony, but it is also plausible that English speakers simply represent aspirated stops as such in their lexical entries since there are no aspiration alternations. This point was made separately by Dell (1973) and Stampe (1973), and motivates the notion of lexicon optimization in OT. In contrast, though, rules of alternation (or someting like them) are actually necessary to obtain the proper surface forms. An English speaker who does not have a rule of obstruent voice assimilation will simply not produce the right allomorphs of various affixes. In contrast, the same speaker need not encode a process of nasalization—which in English is clearly allophonic (see, e.g., Kager 1999: 31f.)—to obtain the correct outputs. Given that alternations are entrenched in the relevant sense, it is not impossible to imagine that speakers might “project” constraints out of alternation generalizations in the manner described above. Such constraints could be used during online processing, assuming a strong isomorphism between grammatical representations used during production and perception.² Secondly, since not all alternations are surface-true, it seems reasonable to limit this process of projection to those which are. Were one to project non-surface-true constraints in this fashion, the speaker would find themselves in an awkward position in which actual words are ill-formed.^3,4

The APH is interesting contrasted with the following:

(5) Lexicostatistic Phonotactic Hypothesis: Let A, C, and D be (possibly-null) string sets. Then, if CAD is statistically underrepresented (in a sense to be determined) in the lexicon L of a grammar G, nonce words containing the subsequence CAD are ill-formed for speakers of G. 

According to the LSPH (as we’ll call it), phonotactic knowledge is projected not from alternations but from statistical analysis of the lexicon. The LSPH is at least implicit in the robust cottage industry which uses statistical and/or computational modeling of the lexicon to infer the existence of phonotactic generalizations. It is notable how virtually none of the “cottage industry” of LSPH work discusses anything like the APH. Finally, one should note that APH and the LSPH do not exhaust the set of possibilities. For instance, Berent et al. (2007) and Daland et al. (2011) test for effects of the Sonority Sequencing Principle, a putative linguistic universal, on wordlikeness judgments. And some have denied the mere existence of phonotactic constraints.

Gorman 2013 reviews some prior results which argue in favor of the APH, which I’ll describe below.

Consider the putative English phonotactic constraint *V̄ʃ#, a constraint against word-final sequences of tense vowels followed by [ʃ] proposed by Iverson & Salmons (2005). Exceptions to this generalization tend to be markedly foreign (e.g., cartouche), to be proper names (e.g., LaRouche), or to convey an “affective, onomatopoeic quality” (e.g., sheesh, woosh). As Gorman (2013:43f.) notes, this constraint is statistically robust, but Hayes & White (2013) report that it has no measurable effect on English speakers’ wordlikeness judgments. In contrast, three English alternation rules  (nasal place assimilation, obstruent voice assimilation, and degemination) have a substantial impact on wordlikeness judgments (Gorman 2013, ch. 4).

A secod, more elaborate example comes from Turkish. Lees (1966a,b) proposes three phonotactic constraints in this language: backness harmony, roundness harmony, and labial attraction. All three of these constraints have exceptions, but Gorman (p. 57-60) shows that they are statistically robust generalizations. Thus, under the LSPH, speakers ought to be sensitive to all three.

Endnotes

1. I note that the CONTROL module proposed by Orgun & Sprouse (1999) might be a mechanism by which this information could be encoded.
2. Some evidence that phonotactic knowledge is deployed in production comes from the study of Finnish and Turkish, both of which have robust vowel harmony. Suomi et al. (1997) and Vroomen et al. (1998) find that disharmony seemingly acts as a cue for word boundaries in Finnish, and Kabak et al. (2010) find something similar for Turkish, but not in French, which lacks harmony.
3. Durvasula & Kahng (2019) find that speakers do not necessarily judge a nonce word to be ill-formed just because it fails to follow certain subtle allophonic generalizations, which suggests that the distinction between allophony and alternation may be important here.
4. I note that it has sometimes been proposed that actual words of G may in fact be gradiently marked or otherwise degraded w.r.t. to grammar G if they violate phonotactic constraints projected from G (e.g., Coetzee 2008). However, the null hypothesis, it seems to me, is that all actual words are also possible words and so it does not make sense to speak of actual words as marked or ill-formed, gradiently or otherwise.

References

Berent, I., Steriade, D., Lennertz, T., and Vaknin, V. 2007. What we know about what we have never heard: evidence from perceptual illusions. Cognition 104: 591-630.
Coetzee, A. W. 2008. Grammaticality and ungrammaticality in phonology. Language 64(2): 218-257. [I critique this briefly in Gorman 2013, p. 4f.]
Daland, R., Hayes, B., White, J., Garellek, M., Davis, A., and Norrmann, I. 2011. Explaining sonority projection effects. Phonology 28: 197-234.
Dell, F. 1973. Les règles et les sons. Hermann.
Durvasula, K. and Kahng, J. 2019. Phonological acceptability is not isomorphic with phonological grammaticality of stimulus. Talk presented at the Annual Meeting on Phonology.
Gorman, K. 2013. Generative phonotactics. Doctoral dissertation, University of Pennsylvania.
Halle, M. 1959. Sound Pattern of Russian. Mouton.
Hayes, B. and White, J. 2013. Phonological naturalness and phonotactic learning. Linguistic Inquiry 44: 45-75.
Iverson, G. K. and Salmons, J. C. 2005. Filling the gap: English tense vowel plus final
/š/. Journal of English Linguistics 33: 1-15.
Kager, R. 1999. Optimality Theory. Cambridge University Press.
Orgun, C. O. and Sprouse, R. 1999. From MPARSE to CONTROL: deriving ungrammaticality. Phonology 16: 191-224.
Kabak, B., Maniwa, K., and Kazanina, N. 2010. Listeners use vowel harmony and word-final stress to spot nonsense words: a study of Turkish and French. Journal of Laboratory Phonology 1: 207-224.
Lees, R. B. 1966a. On the interpretation of a Turkish vowel alternation. Anthropological Linguistics 8: 32-39.
Lees, R. B. 1966b. Turkish harmony and the description of assimilation. Türk Dili
Araştırmaları Yıllığı Belletene 1966: 279-297
Stampe, D. 1973. A Dissertation on Natural Phonology. Garland. [I don’t have this in front of me but if I remember correctly, Stampe argues non-surface true phonological rules are essentially second-class citizens.]
Suomi, K. McQueen, J. M., and Cutler, A. 1997. Vowel harmony and speech segmentation in Finnish. Journal of Memory and Language 36: 422-444.
Vroomen, J., Tuomainen, J. and de Gelder, B. 1998. The roles of word stress and vowel harmony in speech segmentation. Journal of Memory and Language 38: 133-149.