My proposal is that there is just one level of derivation. So it is not just that there are no intermediate levels of derivation, but also that there is no underlying level, either. Yet phonological rules continue to be formulated and to apply much as they did in the original Generative Phonology -- I think of this as a revision to Generative Phonology (GP), not a totally new theory.
There are several assumptions made in GP that seem to be without any foundation. I think that all three are wrong:
- The application of phonological rules is conditioned only by what is found in their inputs, not their outputs.
- Phonological rules apply differently from syntactic and morphological rules.
- Derivational rules (phonological, morphological, syntactic) apply serially, one at a time, rather than simultaneously, with all applicable rules applying at once.
Phonologists are mostly very accustomed to thinking of the relationship between phonemic forms and surface phonetic forms as being a relationship between an underlying level of derivation of some language expression and a surface level for that same expression, but that's wrong, at least in the general case. It's not necessary for the very same expression to have both a phonemic and a surface phonetic form.
Instead, for the case where a phrase is composed of several words, each word may be a phonemic form, but the phrase may have a surface phonetic form. We couldn't do that in conventional GP, because the syntactic rules that combine words into phrase are segregated off into a separate component from phonological rules, but as I noted above, I think that is wrong.
Of course, you can tell the difference between a phonological rule and a syntactic rule, because phonological rules look at sound values, while syntactic rules don't have phonetic reference. But it doesn't follow that the two kinds of rules apply in different "components" or at different levels of derivation.
Similarly, when several morphemes are combined by a morphological rule, this often calls into play phonological rules which make detailed adjustments to the sound segments of the morphemes, and the assumption of conventional GP is that the two things happen serially, in separate components. First, you stick the morphemes together, then you apply certain phonological rules to amend the result. But why assume those two things happen in separate steps? No good reason. I propose that the combination of morphemes into words and the application of certain phonological rules (specifically, the morphophonemic rules) happen all at once.
I realize that I have a lot of ground to cover yet, to make a single level theory of phonology (and morphology and syntax) plausible. Probably the two most urgent things are to say specifically what I mean by "derivational level" and to say how feeding relationships among phonological rules can be described in the absence of multiple levels of derivation. I plan to do those things in separate answers, below.
2. Intermediate derivational stages could conceivably be necessary.
The question about whether there are intermediate stages of derivation is empirical, not just a matter of finding some theoretical symbol-pushing that manages to avoid mentioning explicitly any intermediate steps. I'll show that by giving a putative counterexample.
Consider the pronunciation of "bottle" and "Pat'll" in those American dialects that have voiced [d] for the underlying /t/ in these forms. How does the /t/ get voiced to a [d]? Well, I don't know for sure, but the following is plausible.
What ends up in the pronunciation as a syllabic [l] begins as a sequence of unstressed vowel, say lax i, and non-syllabic l, and the vowel provides the context for flapping of the preceding t (since flapping happens only intervocalically). The difference between t and flap t is that the t is an obstruent, but the flap is sonorant. (This is not entirely clear, but let's assume this.)
Sonorants tend to become voiced, so after the t has flapped, the resulting voiceless flap gets voiced by assimilation, because the preceding and following sounds are voiced (and also sonorant).
Now, the vowel before the l is lost and we are left with syllabic l after the flapped t. You can't say a flap immediately before a following consonant with alveolar contact of the tongue tip, because a flap can have only momentary tongue tip contact, so now the voiced flap becomes a [d] (because of the immediately following l), which is not a sonorant.
I have described this derivation as having a number of intermediate steps, but now let us consider whether or not I can go directly from the underlying form to the surface form by applying the phonological rules involved to make all the necessary feature changes at once, without any intermediate steps.
The answer to that is: No. My derivation above requires the /t/ at a certain point in the derivation to be a sonorant, but it is neither an underlying sonorant nor a surface sonorant, so evidently there has to be an intermediate stage of derivation, like neither the underlying nor the surface form, at which the /t/ -> [d] is a sonorant.
Of course, it will occur to you that it would be feasible to formulate a phonological rule to simply voice [t] before [l]. If you're not too picky about phonological rules being natural, maybe that will satisfy you. It makes me rather uneasy. Why would that happen only to alveolar stop and not to other stops?
I gave the example of "Pat'll", where I find that /t/ also winds up as [d], to show that one can't simply assume that "bottle" has a phonemic /d/ to resolve the difficulty.
So this shows that the difference between ordinary GP with multiple derivational steps and my version of GP without intermediate steps is real. There can be evidence to decide the matter.
How do you count derivational levels? (There is going to be more syntax than phonology in my answer to this.)
In describing the relationship between their theory of GPSG and transformational generative grammar, the authors of Generalized Phrase Structure Grammar compare the base structures of TG, generated by context free phrase structure rules, to the structures assigned by a GPSG. The first step in a transformational derivation is commonly taken to be a tree structure, i.e. a base structure, so that's one level. The forms that are subsequently derived by applying syntactic transformations are additional levels of derivation.
In GPSG, however, there are no transformations, and consequently there are no additional levels after that first one. So in GPSG, sentences have just one single level of derivation. GPSG is, according to its authors, monostratal, meaning that the grammar assigns just a single structural description, a tree structure, to each language expression it generates. TG, on the other hand, is multistratal, due to the transformations, which produce additional levels.
I'm trying hard to be clear, here, because not everyone means the same thing by these terms level, stratum, monostratal, multistratal. For instance, the theory of Relational Grammar has no transformations (according to its authors), yet a sentence generated by an RG may have many strata. So, is RG a monostratal theory? I don't know.
A terminological complication is due to the fact that phrase structure grammars are usually made to describe a tree by starting with a PSG derivation, each step produced by applying a PSR (or "production"), so in a sense, a tree structure already involves multiple derivational steps.
Nonetheless, the sense of monostratal and level found in GPSG is the sense in which I use these terms. A tree generated by a CFPSG has just a single level, which corresponds to the input to the transformations in TG. But there are no transformations, either syntactic or phonological transformations, so a given language expression never gets any additional levels after the first "base" leval, and the theory that results is monostratal.
Below, I take up a detail concerning tree representations in Categorial Grammar and how phonological rules apply in creating the structural descriptions of language expressions.
4. Trees of phonological forms.
How can phonological rules apply in a generative grammar without creating additional levels of derivation?
The most popular syntactic theory among logicians and philosophers who have needed a specific model for how human language works has been categorial grammar, CG. There are lots of variations on it, but we will have one variety if we just take a tree given by a CF grammar of the sort familiar to linguists and add the expressions represented to the categories that name the tree nodes. In CG, language forms, which have pronunciations and categories, are combined in a step by step manner to create new language forms, creating a tree structure from the bottom up.
Where a linguist might write a simple tree diagram as
| | \
Pat V NP
a corresponding tree in CG might be:
Pat eats pike,S
Pat,NP eats pike,VP
Depending on the variety of CG, the way that forms are combined does not have to be simple concatenation, as it is the above example. In the form of grammar proposed by Richard Montague, arbitrary functions are allowed to determine the result of combining forms. So, although I haven't seen this proposed elsewhere, I don't see any problem in principle with applying phonological rules to modify the result of combining forms. That is what I've done in the next example tree:
This is a single tree structure, not a sequence of trees such as you find in transformational grammar, so it is a monostratal derivation. It is neither an underlying structure nor a surface structure, because of course when there is only one derivational level, there is no meaningful way to characterize a surface versus underlying distinction.
This is my idea about how phonological rules apply in a monostratal grammar. Not only is there only one tree for the (unambiguous) example sentence above, but each of the five different language expressions involved is represented just once.
Below, I will describe how rule ordering works when there are no multiple derivational levels.
5. Rule interaction.
In the generative phonology of SPE, phonological rules apply (a) cyclically, (b) in an arbitrary linear order on each cycle, and (c) each rule applies simultaneously to any segments meeting its conditions in its input form. I agree with practically all of this, except that for (b) the order is not linear, and for (c), all applicable rules simultaneously apply to all segments meeting their conditions (not just each rule taken individually).
Furthermore, in the SPE theory, phonological rules apply opaquely, in the sense that when a rule applies to a sound segment, all conditions on the application of the rule must be met in the input to the rule. I agree with this, also, but I add another mode of transparent rule application, for which it is the output of the rule where relevant conditions on a rule's application are found.
The terms opaque and transparent are taken from Paul Kiparsky, see Phonological Opacity, who uses these terms in almost the sense I have just characterized, except that because Kiparsky was working in terms of a multi-stratal phonological framework, he understood opaque and transparent conditions to be global derivational constraints referring respectively to underlying and surface phonological forms. Since in the present monostratal theory, for the most part, Kiparsky's underlying forms are the same as the inputs to phonological rules, and his surface forms are the same as the outputs of rules, this difference between his and my usage is of no consequence.
Before dealing in more detail below with opaque and transparent application, I'll mention my interpretation of cyclic application and the matter of special phonological boundaries.
I have implied that I agree with the SPE theory of cyclic application of phonological rules. I interpret the cyclic principle in phonology as requiring that before constituents can be combined in a phrase structure tree, all applicable phonological rules must first be applied to each constituent. But this is just what I proposed in the preceding section 4 of this answer. So this monostratal theory does incorporate the cyclic principle of SPE.
A rather unhappy detail of the SPE theory is the appeal to several apparently arbitrary boundaries in forms, just to get phonological rules to work right. These include the + boundary that separates morphemes, the # boundary that separates words, the = boundary, and various labeled brackets distinguishing the categories of words. No such artificial boundary symbols are required in monostratal phonology.
6 Rule Order
Without multiple stages of derivation, phonological rules can't be linearly ordered, but they can still be ordered. We can define an ordering relation "before" which works very much like the linear "before" relation of standard Generative Phonology. (However, it's not quite an "order" in the mathematical sense.)
As an example, consider the derivation of the pronunciation of "want a pie", [wʌ̃ɾ̃̃ə̃pʰɑj]. The n of "want" nasalizes the preceding vowel and is then lost before the following voiceless stop t. The t is now intervocalic and at the end of a word, so it flaps. The flap is then nasalized under the influence of the preceding nasal vowel.
Here is a multistratal derivation:
/wʌnt/ /ə/ /paj/ underlying (phonemic) forms of the three words
## wʌnt ## ə ## paj ## a phrase is formed by syntactic rules,
leaving # marks to remember where the words begin and end
## wʌnt ## ə ## pʰɑj ## Rule 1, aspiration of the word initial p
## wʌ̃nt ## ə ## pʰɑj ## Rule 2, regressive vowel nasalization
## wʌ̃t ## ə ## pʰɑj ##, Rule 3, deletion of nasal stop before
a homorganic voiceless stop
## wʌ̃ɾ ## ə ## pʰɑj ##, Rule 4, flapping of intervocalic t across
following ## boundary
## wʌ̃ɾ̃̃ ## ə ## pʰɑj ## , Rule 5, progressive assimilation of sonorant (flap)
## wʌ̃ɾ̃̃ ## ə̃ ## pʰɑj ## , Rule 6, progressive assimilation of
sonorant (vowel) in nasality across word boundary
wʌ̃ɾ̃̃ə̃pʰɑj, convention to lose #
Here is a monostratal derivation:
/wʌnt/ /ə/ /paj/ underlying (phonemic) forms of the three words
a verb phrase is formed by syntactic rules, and
Rule 1 applies opaquely (/p/ is at the beginning of a word), and
Rule 2 applies opaquely (the vowel is followed by a nasal), and
Rule 3 applies opaquely (the /n/ is followed by /t/), and
Rule 4 applies transparently (the descendant of /t/ is intervocalic), and
Rule 5=6 applies transparently (the descendants of the
sonorants are preceded by nasal sonorants).
wʌ̃ɾ̃̃ə̃pʰɑj, surface form
Definition of "before": For two distinct rules A and B, A is before B when either A is opaque or B is transparent. For a rule that interacts with itself, an opaque rule is not before itself, but a transparent rule is before itself.
For the above example, by the definition, rule 1 is before rule 2, rule 2 is before rule 3, rule 3 is before rule 4, rule 4 is before rule 5/6, and rule 5/6 is before itself. (Other "before" relations hold as well.)
This rule order is like the linear order of multistratal Generative Phonology in that both are transitive. Specifically, for any three distinct phonological rules A, B, and C, if A is before B and B is before C, then A is before C. The proof of this follows.
"A is before B" means that either A is opaque or B is transparent, by the above definition of "before". Every rule is either opaque or transparent, but not both, so if A is opaque, this means it is not transparent. Thus, "A is before B" means "Either A is not transparent or B is transparent". This last is logically equivalent to a statement using the material implication of classical logic: "If A is transparent, then B is transparent." But logical implication is a transitive relation. QED.
7. Alternating Stress
I'm aware of three theories in Generative Phonology for describing alternating stress systems and other alternating patterns which seem to require counting syllables from the beginning or from the end of a word and doing something to every other syllable, or perhaps every third syllable. The syllables affected may be stressed, or their vowels can be shortened or lengthened.
The three theories are
- The SPE theory, which describes them as assimilations-at-a-distance and uses a special ad hoc "parenthesis star" notation with simultaneous application to describe them.
- Irwin Howard's 1972 theory of directional application, A Directional Theory of Rule Application in Phonology, which describes them as dissimilations between adjacent syllables.
- My monostratal theory.
Of these, the SPE theory is quite arbitrary and ugly -- not really worth considering, in my view. Howard's theory makes a lot of sense and works quite well (though the phenomenon itself is typically quite complex and hard to unravel). My theory is patterned after Howard's, but is simpler, and unlike Howard's treatment, does not require reference to intermediate stages of derivation.
In a rough summary, Howard's theory works like this. You determine the direction of influence of a syllable on a nearby syllable: do later syllables cause previous syllables to dissimilate? If so, you start applying the dissimilation at the end of a word and work your way back, syllable by syllable, to the beginning of the word, applying the rule to each syllable that meets the constraints on the rule.
Or, do earlier syllables cause following syllables to dissimilate? If so, you start applying the dissimilation at the beginning of a word and work your way forward through the word, syllable by syllable, to the end of the word, applying the rule to each syllable that meets the constraints on the rule.
Here is a schematic example of an alternating stress system with a regressive dissimilation that stresses a syllable before an unstressed syllable:
tata > ˈtata
tatata > taˈtata
tatatata > tataˈtata > ˈtataˈtata
tatatatata > tatataˈtata > taˈtataˈtata
tatatatatata > tatatataˈtata > tataˈtataˈtata > ˈtataˈtataˈtata
and so on.
Howard's treatment seems to me to say exactly the right thing about such systems. They have self-bleeding processes, where the application of the rule to a syllable prevents that syllable from influencing the syllable preceding. Only an unstressed syllable can cause the preceding syllable to become stressed, and after the rule has applied to make a syllable stressed, that syllable can no longer cause the preceding syllable to become stressed.
Unfortunately for me, Howard's directional theory makes crucial reference to intermediate stages of the derivation. What to do?
Well, it turns out to be more straightforward than one might have imagined. We simply assume that the stress dissimilation rule is transparent and remove all intermediate stages. Then, we get the alternating pattern, and we can forget about the special assumptions in Howard's theory about determining the direction of influence, about whether to start at the end of the word or at the beginning, and about whether to move forward or backward in the word to look for the next place the rule might apply.
To see how it works, consider the three syllable example above, /tatata/. It looks at first sight as though there are two different syllables to which the dissimilatory stress rule might apply, either the first or the second syllables. But it turns out that this is not so. If we apply the rule to the first syllable, we get a form [ˈtatata], which is incorrect, since the middle syllable has not been stressed, even though it satisfies the rule's condition, that the following vowel in the output form be unstressed.
Also, we cannot apply the stress rule to both the first and second syllable to get [ˈtaˈtata], since here the rule has applied to the first syllable even though its condition, that the following syllable in the output be unstressed, is not met. The only way to apply the rule to all and only the syllables that meet the rule's condition that the following syllable in the output be unstressed is to stress just the middle syllable. And that is the correct result.
Similarly for all the longer examples given above, when the rule is transparent and there are no intermediate stages, the alternating pattern predicted by Howard's theory is the only possible result.
Part 8. Feeding and bleeding. (draft)
Kiparsky's terms feeding and bleeding have often been used in discussions of phonological rule interaction:
A rule A *feeds* a rule B when the application of A makes it possible
for B to apply, and A and B both apply.
For example, in the example derivation above in part 6, rule 3 feeds rule 4. In the SPE theory, we order A before B. In monostratal phonology, rule B is transparent.
A rule A *is counterfed by* a rule B when the application of B would make it possible
for A to apply, but A does not apply, even though B applies.
No examples so far. In SPE we order A before B. In monostratal phonology, A is opaque.
A rule A *bleeds* a rule B when the application of A makes it impossible
for B to apply, and A applies, furthermore B does not apply.
For example, the alternating stress rule of part 7 bleeds itself. In the SPE theory, we order A before B, but it is not possible for a rule to interact with itself in this way -- instead, the special parenthesis star notation is used. In monostratal phonology, rule B is transparent.
A rule A *is counterbled by* a rule B when the application of B would make it impossible
for A to apply, yet A and B both apply.
For example, above in part 6, rule 2 is counterbled by rule 3. In SPE, we order A before B. In monostratal phonology, rule A is opaque.