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Sometimes the spelling of a morpheme changes depending on how it's inflected. For example in English, hat sometimes needs an extra "t", and hate sometimes needs its "e" removed.

Inflections of hat (verb):

hat: hat

hats: hat + -s

hatted: hat + t + -ed

hatting: hat + t + -ing

Inflections of hate (verb):

hate: hate

hates: hate + -s

hated: hate - e + -ed

hating: hate - e + -ing

These morphemes are completely regular in spoken English, however. They're only (slightly) irregular in written English.

Is there a standard way of recording changes to a morpheme in orthography or pronunciation? For example teeth is the plural of tooth. I think teeth is an inflection of tooth, and not a separate morpheme.

tooth: tooth

teeth: tooth - -oo- + -ee-

How do you record these differences?

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This is not a matter of recording anything. If you can spell "hatter", it can be recorded. It could be a matter of predicting something – on what basis can we predict that "hat" yields "hatter" but "hate" yields "hater"? In other words, what are the rule for spelling English words?

That question is way to broad to attempt to fully answer. What is relevant for the issue that you are pointing to is that there is a distinction between "long vowels" and "short vowels", and since we don't use accents to mark that difference, we use a different and more complicated system, involving double letters and "silent e". In "hate" (hɛit) we have a long vowel, as signaled by the "silent e". In "hat" (hæt), the basic short value shines through. When we make the agent noun or progressive, the vowels do not change, so the spelling of "hate" has to change -- drop the silent e because -ing, -er supply an orthographic vowel and the rule "long before CV" is obeyed. In "hat", we have to double-write the consonant in order to indicate that the preceding vowel is short, not long.

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  • What I'm looking for is a mathematical way of transforming a morpheme into one of its inflections. Something like "f(M) = M + 's'" which works for both example words, or "f(M) = M + 'ing'" which doesn't work for either. The "hat" in "hats" is not the same morpheme as the "hat" in "hating". – CJ Dennis Jan 28 '19 at 1:59
  • Since pronunciation doesn't change at least in these cases, it's pretty simple: possessive(X)=X-z; progressive(V)=V-ɪŋ. Since you think that your -ing rule doesn't work, I guess you don't care about pronunciation, and you're looking for spelling rules, but ones that could be reduced to a computer program. Is that right? – user6726 Jan 28 '19 at 20:52
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user6726 gave an excellent and correct answer, but I'm going to elaborate on this a bit and put it in a more mathematical-esque framework.

The key is, what's written isn't necessarily the underlying form.

The underlying form of "hat" could be written as hăt, marking a "short vowel", while the underlying form of "hate" could be written as hāt, marking a "long vowel". (The difference used to actually just be length, but now they're pronounced with different "qualities" too; I'm using these informal symbols instead of the official IPA ones to make it clearer.)

So now we've got hăt. How do we write it? Well, the rule in English is that a vowel followed by a consonant and the end of a word, is short. So we can just write hat and we're good.

But for hāt, we need a way to mark that it's long. But English to the rescue again! English has two relevant rules here:

  • An e after a consonant at the end of a word isn't pronounced
  • A vowel before a consonant and another vowel is long

Using these two, we can see that hate is the form we're looking for: the e makes the previous vowel long, and then isn't pronounced itself.

But now let's add an -er to the end. Now we have hăter and hāter. What happens now?

Well, with hăter, we need a way to mark that the vowel is short. We can't rely on the end of the word, but in English, a vowel before two consonants becomes short. So we can double the t, giving hatter.

For hāter, though, we can just write it hater: as before, the a is before one consonant and a vowel, so it becomes long.

The trick is, none of these rules about adding es and ts and such are built into the roots "hat" and "hate". Instead, they're properties of the English spelling system. If you know the underlying forms hăt and hāt, you can figure out all the rest from there.

One way of analyzing this is in terms of change rules:

  • If you have a short vowel before a single consonant and another vowel, double that consonant.
  • If you have a long vowel before a single consonant and the end of the word, add an e at the end.

In this model, you start with the underlying form, follow all the rules, and end up with the finished product. This is called the traditional model or the linear model.

Another way is in terms of constraints:

  • Don't have a short vowel before a single consonant and another vowel.
  • Don't have a long vowel before a single consonant and the end of the word.
  • You can add a final e or double a consonant at very low cost (that is, the constraints "don't add final e" and "don't double consonants" are very weak ones).

In this model, you tweak and twist your underlying form until it satisfies the constraints as well as possible. This is called the optimality model.

Both schools have their adherents, though these models are generally used for phonology (how words are pronounced), not orthography (how words are written). But, English orthography is basically lots of little relics of its historical phonology, so the models work for both! It's up to you which model you find more convincing.

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First, it's important to separate out spelling. You don't have to go to the hardcore "written language isn't part of language at all"—it's at least plausible (and empirically testable) that literate people store spellings as part of their lexemes in the same way they store phonology, class information, meaning, etc., and that they store orthographic rules in the same way they store morphosyntactic rules. But the spelling is still secondary, not primary. When you're learning new words, you generally learn the word first, then learn or work out its spelling,1 and the same goes for new coinages getting into the language.2


So, let's start by ignoring spelling, and dealing only with the spoken English language.

The words "hat" and "hate" are both perfectly regular. In both cases, just as with any other root ending in the /t/ phoneme, the 3.sing.pres suffix is pronounced /s/, the past suffix is pronounced /id/ or /əd/, etc. And the exact same goes for "hate". And the same goes for the noun sense of "hat"—the plural phoneme is pronounced /s/ after any root ending in /t/.

Notice that words with different final phonemes handle these suffixes differently. For example, "dog" takes a /z/ for 3.sing.pres, "axe" takes a /əz/. The rule isn't quite as simple as "add /s/", but it's still pretty simple, and these words all follow the rules regularly.


The word "tooth", on the other hand, is irregular—to pluralize it, you don't add the /s/ phoneme, you change the last vowel. Historically, many nouns pluralized this way, with regular but somewhat complicated rules. The same goes for verbs like "sing/sang/sung".

Traditionally, this is treated as nothing more than history. When you learn modern English, you just learn that "tooth" has a plural form "teeth".

When you try to construct "tooth + -s", something called "suppletion" happens—you remember "teeth" and it blocks "tooths" from being constructed.

The same happens for other historically productive classes, like "child + -s" being suppletively blocked by "children" (notice that this has an unusual suffix, and also has a vowel alternation in the root).

Some theories instead insist that quasiregularity is a real thing in our language, not just a historical fact. For example, why did most American dialects convert the past tense of "dive" from "dived" to "dove" if there isn't some "strong verb" rule, or some process of analogy, or something like that, active in our minds/society/whatever? Why can we jokingly make plurals like "moose/meese" and every native speaker knows what we're doing?


When you get to spelling, there are different ways to handle things. Some languages try to spell things as phonetically as possible, but English instead tries to spell things as morphologically as possible. So, we don't write "cats, dogz, axiz" because they all have different phonetic endings, we write "cats, dogs, axes" because they all have the same morpheme. English is far from perfect in this, but it's a general tendency.

This can make the spelling rules somewhat complicated. For example, to get "hatted", you need a rule something like "when adding -ed to a word ending in a short vowel and a single consonant, double the consonant".3

But "hat" and "hate" are perfectly regular in their spelling. The rules are more complicated, but they can not only be written down, they can be, and are, taught to millions of children, who learn to apply them.4 We don't have to memorize "hatted" and thousands of other past-tense spellings for verbs ending in a short vowel and a "t", they all work the same way. We do have to know which single-letter vowels really are "short vowels" to know when to apply this rule, but that's something we already need at least roughly in our heads in order to pronounce them. And then, we only have to memorize the small number that break the rules.

And "tooth" is just as quasiregular in its spelling as in its pronunciation. We don't have a rule that tells us how to spell the vowel alternation, so you have to memorize that "teeth" is the spelling of "teeth". But we do usually handle this kind of irregularity by keeping as much as possible the same (notice that "children" keeps the whole root spelled the same despite pronouncing it differently) and spelling the irregular bits as… something like the paradigm spelling for the sound (but a few centuries out of date), so the vowel in "teeth" is spelled "ee" because that's how "long e" is usually spelled, and the suffix in "children" is "ren" because syllabic "r" is usually spelled with an extra "e".

Is this quasiregularity part of our actual spelling system, or just a historical fact? The question is pretty close to the one for spoken language. After all, anyone who hears "meese" as the jocular plural of "moose" would spell it that way, and anyone who sees that spelling would interpret and pronounce it that way. But, on the other hand, it's definitely not a rule that can be applied regularly, like the "plural is spelled with s except in these cases where it's spelled -es dropping the final vowel letter if …" that just always works unless it's suppleted.


At any rate, to work out a rule to transform any English noun into its plural, there are two approaches.

The first approach is to stay purely within orthography: take the rules that are taught to children about when to double consonants, etc., and then just add in special cases for the irregular words.

The second approach—the one most linguists would probably instinctively pick—is to go from orthography to spoken language, apply the simpler and more regular (and better studied) rules there, then spell the result. Unfortunately, that may actually be a lot more complicated in English—going from orthography to speech and back may add a lot more to the problem than using the simpler rules subtracts.

And either way, you have a choice for how you want to handle quasiregularity. For example, you can just treat "sing", "sink", and "stink" as sui generis irregular verbs and store the full pattern for each one. Or you could have a "subroutine" that does i/a/u vowel alternation and just store that "sing", "sink", and "stink" use that pattern.5 It doesn't really matter what English "actually does" for your purposes; whatever's easiest to record, whatever makes the most usable record, or whatever you can turn into code, or… whatever the most important thing is for your end goal, decide based on that.


1. Cases of precocious readers certainly do happen, of course. Plenty of 80s kids read Dungeons & Dragons books and learned all kinds of uncommon words that they knew how to spell, and could use perfectly well in a written sentence, but had no idea how to pronounce. But it's not the way most words are learned.

2. Again, this is just the usual case, not the universal case—people were writing LOL for years before anyone pronounced it as a word rather than an acronym. But it's still clearly the usual case.

3. How this regular rule relates to the much more general but only quasiregular rule about double consonants for short vowels is up for debate, but let's ignore that.

4. Although you probably want something aimed at a complete description, rather than a pretty-close learnable-by-children description. Without checking (I don't have a copy handy), I'd bet that CGEL probably covers the spelling rules, and that if it does so, it does a great job.

5. And then, is "sting" a verb that uses that pattern but suppletes "stang"? Or are there two patterns that share part of the table?

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