Given my rudimentary knowledge in phonology, I am somehow struck by this question of phonological rule condensation.
There are three phonological rules:
a. A → B / C__D
b. A → B / __DE
c. A → B / C __E
Now can you help me to collapse these three rules into a single rule schema? I would appreciate your help!
Thank you, Pankaj, but this rule would generate A → B / C__DE, which is not in the original three.
@Ivo Thank you very much, I will download and give it a serious reading.
The only way to condense a. and c. into one line is if there is some shared feature that D and E share that in combination with some other feature(s) being marked + or - excludes all other segments in the phonemic inventory. b. cannot be condensed to the same line as a. and/or c.
The best you can do is line up the three cases and list them in curly brackets, one on top of the other, on the right side of the slash (if the former suggestion does not work). That puts them in one rule, but not one line, which is what I think you were aiming for.
Note Matthew that A => B / C __ DE is a legal string according to the original three. Anything (including C) can come before the target segment, so CBDE is a well-formed result from CADE.
It's often useful to try specific strings to see how competing rules would handle them.
Consider the strings:
CAD
ADE
CAE
but also
CA
AD A
ADX
AE
In the original rule set and also the single rule suggested by Matthew Yu, the first three become:
CBD
BDE
CBE
while the others remain unchanged.
However, I think the rule:
A → B / (C)__(D)(E)#
because all of the environmental constraints are optional, would also change the last five strings to:
CB
BD
B
BDX
BE
before the # boundary.
Chris has pretty much said it all. But it may also be a useful reminder to point out that the A → B / X _ Y notation is simply an abbreviation for the rules, implied by Chris:
CAD → CBD : A→ B / C_D
ADE → BDE : A → B / _ DE
CAE → CBE : A → B / C_E
Matthew's solution (in a linearised notation)
A → B / { C_{D,E}, _DE}
separates a distinct context from two similar contexts and is sound and complete in that all and only the original operations are captured, as Chris notes, and Pankaj's formulation is complete in that all the operations are covered, but not sound, in that other operations are included.
(Btw, the original rule set makes no reference to word boundaries '#'.)
Dafydd,
That does put it all in one line, but just wasn't an option in my training. It is an option now! I like it.
Dear Dafydd, thank you for your lucid explanation, and for the linear notation (a new option for me).
Note that Pankaj's formulation with everything in its own parenthesis would permit the linearization A→B/ _ which the original data do not permit. think about what this means in words: A becomes B either word or syllable-initially, or after C, and either D or E or both must appear after it.
I'm tempted to say that abbreviations are only useful (in phonology as elsewhere) if one remembers what they mean. Oops, I said it! Please bear with me, formalisms are so pedantic ...
1. Pankaj's formulation says nothing about word-initial position. The rules can apply anywhere within a word, initially or not, provided that the context terminates at a word-final boundary.
2. The rule
A→B/_
actually means that A is replaced by B everywhere (whether there is a word boundary or not). But Pankaj's formulation implies simply
A→B#
which means that A is replaced by B only before a word boundary (forgetting the other rules for a moment).
3. The full resolution of Pankaj's formulation
A → B / (C)__(D)(E)#
is the following set of 8 rules (i.e. 2^3 rules, as there are 3 binary options):
CADE# → CBDE#
CAD# → CBD#
CAE# → CBE#
CA# → CB#
ADE# → BDE#
AD# → BD#
AE# → BE#
A# → B#
This means that I have to revise my previous comments, as I had ignored the word boundary in the formulation. The solution is neither sound (in that it generates unwanted items) nor complete (in that it only generates contexts which contain a word-final boundary). In contrast, the original rule apply whatever follows, i.e. whether there is a word-final boundary or not (since no word boundary is specified in the rules).
4. Interestingly, in a context CADE, application of the rules is indeterminate: either of the following original rules can apply:
CAD → CBD
ADE → BDE
In each case, the output would be CBDE.
If the two rules had different rule changes, e.g. if the second of these two were
ADE → GDE
it would mean that a principle of rule ordering would be needed in order to decide whether the output should be CBDE or CGDE. Since the output is the same in each case in the given example, the ordering is irrelevant and the rules can be said to be unordered.
Next challenge: find a real language to which rules with comparable structural descriptions and structural changes apply! :)
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