On Rule-Writing

A student writes (a propos of my lecture on extensions of OT):

If I was to rewrite [...] pre-fortis clipping, [Canadian] raising and flapping in rules, would the following be correct:

1. V → V [short] / ____ C [−voice] (Is [short] really a phonological feature?)

2. V [diphthong] → V [diphthong] [high] / ____ C [−voice] (But the raised diphthong isn’t necessarily high - would [−low] be better?

3. [t] [d] → [ɾ] / V ___ V (But there are also rules to do with stress - i.e. the preceding syllable must be stressed - how would I best accommodate this in a generative rule?)

There are, potentially, two answers to this question, because there are two different purposes for which you can use rewrite rules in synchronic phonology:

Sometimes, a rule is just used descriptively, as a concise statement of the facts of a particular generalisation. People working in OT often do this as a preliminary to formulating an appropriate constraint ranking. In the particular case of raising and flapping, you’d use rules primarily descriptively if your focus is on how the generalisations interact, rather than on the precise conditions of the generalisations themselves. This was the case in my lecture, of course, because I was primarily talking about opaque interactions, rather than the phonology of Canadian English.

A descriptive rule can get away with being less fussy about writing everything with features, or more generally about committing to a particular theory of representations, since its purpose is primarily communicative: you’re using it to explain to the reader what happens to a sound under what conditions. If this is the mode you’re working in, you can write the rules like this:

1. V → V̆ / ____ C̥

Notice that we’re not committing to any particular feature theory: instead, we’re using IPA diacritics to express the sense of the generalisation as concisely as possible. On the other hand, if features are the most concise way to put it, we can still use them in the descriptive mode, as for Raising:

2. V[+low] → V[−low] / ____ V C̥ (The features in parentheses would probably normally be written as subscripts right after V, but I have no faith in our respective email clients to get those across properly!)

Here again we’re not too worried about the niceties of feature theory, we can feel free to use a binary feature like [±low] if that makes our rule more expressive.

3. [t,d] → [ɾ] / ˈV ___ V

Another notation you see quite commonly in the literature for “stressed vowel” is V́ (that’s a capital V with an acute accent, in case it’s not showing up properly). I’m sure you saw this convention when you covered foot structure in Michaelmas term: acute accent = primary stress; grave accent = secondary stress.

I will mention at this point that the true domain of [t,d]-Flapping is actually a bit more complicated; you can find some useful references on the handout at http://www.bermudez-otero.com/tromsoe.pdf if you want to read more.

This descriptive form of rule is adequate if you’re taking a high-level view: for example, if you’re giving a number of examples of opacity in order to show what any theory of phonology has to be able to handle, then it’s probably better to write your rules descriptively, so that they can be understood readily by the reader without getting into the nitty-gritty of a particular theoretical approach.

On the other hand, if you’re working within a particular theoretical formalism that uses rules, so SPE-style generative phonology or any of the formalisms that have built on it, such as Lexical Phonology, then your rules need to be a good deal more rigorous. The idea behind a formal theory like the one used in SPE is that rules, and the representational units that they manipulate, have to have detailed definitions and defined behaviours of the sort you can reason about purely mathematically, so that ideally the rule is explanatory, as well as descriptive. So, things like whether your features are privative or equipollent, and what tree-structures you use to represent length and stress and so on become important. Specifically, it becomes important to be consistent about every choice you make about such things across every rule you write. Consequently, it becomes more difficult to formulate a rule, because you have to look at the controversies surrounding every issue within theories of representation, and make a decision one way or the other about how they apply to the data you’re interested in.

Pre-fortis clipping in particular is a difficult rule to formalise, because, to answer your parenthetical question, no, [short] isn’t usually considered a feature. Most theories of representation treat segmental length in terms of some kind of timing unit, such as the mora. Pre-fortis clipping poses a challenge for theories like this, because its outputs require twice as many different lengths as we normally expect to have to deal with: instead of long vs. short, you’ve got long, short, clipped long and clipped short. One approach is to think of the rule as a lengthening process rather than a “clipping” one. On such an analysis, we claim that a vowel preceding a voiced consonant comes to share the timing unit of the consonant, and so is realised as longer:

This is one way of writing the rule; there are of course as many different ways as there are theories of representations that can handle pre-fortis clipping!

For raising, the way is mercifully smoother, although again, [diphthong] isn’t usually considered a feature. Instead, a sequence of two vowels is considered a diphthong iff they are constituents of a syllable nucleus. And you’re right to suggest that [low] is the feature we’re interested in. Probably the best formulation of the rule is to say that the on-glide of a diphthong gets its low feature deleted if the following consonant is voiceless:

[voc,low] → [voc] / [nuc ____ [voc] nuc] [cons,−voi]

(This assumes that you’re working in a feature system where you’re allowed to refer to [−voice])

You can use symbols like V, C etc. in a rule that is intended to be explanatory, as long as they have a well-understood definition in terms of the theory of representations you’re using. Similarly, you can use the IPA sign for a given segment, provided that you know (and preferably have already said!) what feature specification it expands to. So we might write the Flapping rule (under the assumption that the environment is {stressed vowel} ____ {vowel}) like this:

[plos,cor] → [ɾ] / [σ́...V...]____V

...so long as we’ve already stipulated that [ɾ] means a segment with the features [cons,obs,cor,rho] (or whatever features you want to propose), σ́ means a syllable that is the head of the foot that dominates it, and so on (you can usually get away without explicitly saying that V expands to [voc,son] or whatever, as long as it’s clear what the characteristic features of a vowel are, within the system you’re using).

This kind of theoretically explicit rule, that has explanatory power as its goal, tends to be less readable than a more descriptive one, but that’s the price you pay for the sort of formal rigour that this kind of analysis requires.

So, as I say, the kind of rule you write depends on the goal of whatever you’re writing. If you’re using Raising and Flapping as an example of opacity, and making the point that opaque interactions are attested and therefore something any theory of phonology has to be able to handle, then descriptive rules are fine. If, on the other hand, you’re doing a study that is based in one particular theoretical formalism that uses rules, then your rules need to be expressed strictly in terms of the notation and theory of representations that your formalism makes use of.