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A phonological rule describes the change of one sound into another in a certain environment.

In its chapter on Attic Greek, the Cambridge Encyclopedia of the World's Ancient Languages, there is also a list of "combinatory changes", some of which could - from my understanding - not be described with this simple pattern:

  • t(h)y → s
  • p(h)y → pt
  • k(h)(w)y → t
  • g(w)y → zd

(the superscripted h and w are optional, copied from the source, and not relevant for the question)

Is there a (standardized or conventional) extension to the SPE-style notation, which allows to describe the sound change more than one sound? What am I missing?

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Wikipedia misstates what a phonological rules is: a rule is any (single) mapping of substring-class to substring-class, not just single segment to single segment. If you are interested in rule-based theory, you might consult Introducing phonology.

There are two sub-complications in your examples. The first is trivially dealt with in SPE: how do you refer to classes of sounds (not just single sounds). In all theories, this is done by decomposing segments into cross-classifying features, and stating the rule as applying to the set of segments that are references by a particular feature expression. If we had to refer to /p,t,k/ and exclude /f,s,x,b,d,g/ – unifying three segments, to the exclusion of others – we appeal to the conjunction [-voice,-continuant] to pick out those segments. You simply leave out the features involved with the "parenthesized" related segments, by not saying whether the stop is [+spr.glot] or [-spr.glot].

The other issue is that sometimes, a rule can turn 1 segment into 2 ("diphthongization"), or 2 into 1 ("fusion"). Since there are also processes of metathesis (/lpa/ → [pla]) changing the order of segments, and possible rules affecting two segments simultaneously (compensatory lengthening is a famous class of examples), some other mechanism especially in rule-writing technology is necessary. This turns out to be possible but non-trivial

Now note that "SPE-notation" refers to two or more things. Classically, it refers to the actual publication, Sound pattern of English; but it also refers to "how people did it before autosegmental phonology won". Less well known is that SPE itself has its "actual practice" which dominates most of the book, but also a formal theory which is a dozen-page appendix that few people read. Rules that affect two segments at once are not formalizable in the formal theory, yet they exist. So we have to instead look at how they actually deal with the question in the main part of the book. The solution is, simply, to adopt standard transformational syntax notation. You provide a sequence of variables that describe the substrings that you are looking for, number the elements, then manipulate the numbers.

Suppose for example that you want to write the change /kj/→[tʃ] (where "tʃ"=č, that is, a unit segment and not a sequence), also suppose that this only affects /k/ and not /g/. The input segments are [+back,-voice] = k, [-back,+hi,-syl] = j, [+coronal,+del.rel] = č. The rule itself is

[+back,-voice] [-back,+hi,-syl]     [+coronal,+del.rel]
       1           2             →         1

That is, it looks for a sequence composed of 2 segments, the first being k and the second being j, it adds [+coronal,+del.rel] to the first (that gives you č), and deletes the second.

Similar uses of this transformation notation allow you to chance two segments into two different segments as in your last example. This requires no extension to SPE, except in the formal appendix where they do in fact give a Wikipedia-style 1-segment theory of rule (limiting rules to single units). But they admit that there are rules that change two segments, it is simply a matter of working out a formal redefinition of phonological theory that handles the various things that they admit that they can't formalize.

Post-SPE (autosegmental) theories would primarily handle those phenomena by "compensatory" mechanisms that are analogous to tone preservation. When two segments merge, what happens is that part of the features of one segment are deleted, which causes an ill-formed segment, which then joins with the other segment that triggered the change – like the case of /kj/→[č]. Diphthongization is a harder nut to crack, but it is usually dealt with in one of two ways. First, the more common "Hayes" subset is where a long segment splits, so a long vowel becomes two distinct vowels or a long consonant becomes two distinct consonants. This is the case where the features linked to the two skeletal positions shifts so that it is only associated to one segment. The much rarer case is where a short segment splits, e.g. /hena/ → [henda], where nasal n also bears an oral feature from the following vowel. However, theses are treated as analogous to affricates, and are not considered to be a sequence of two segments.

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    Thank you for your detailed answer. I found that chapter 8 of SPE actually refers to transformational rules, commenting on a contraction rule: "This rule deviates from the rules so far considered in that it must have two segments rather than one on the left-hand side of the arrow", and replacing the underline with segment numbers. Will now have a look at "autosegmental".
    – devio
    Mar 18, 2022 at 18:08

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