Two-Level Rules

Linguistics 581
Koskenniemi

Koskenniemi's two-level rule formalism is a proposal for a formal theoretical farmework for writing phonological rules. It is inspired by the possibilities opened up by FST implementations of phonological rules. Among other things, it tries to do without rule-ordering.

Explicitness

Key idea number one is that the logical requirements of rules can be implemented directly in FSTs (as we have already seen) but one must be very explicit about those logical requirmeents.

Hence Koskenniemi introduces a more explicit notation tied to the FST idea of relating an underlying and surface form.

  • a:b <= c ____ d (ALWAYS realize a as b in this environment)
  • a:b => c ____ d (ONLY realize a as b in this environment, and you don't have to even then)
  • a:b <=> c ____ d (ALWAYS realize a as b in this environment and NEVER realize a as b anywhere else)

(a)

    a:b <= c ____ d:
    cad : cbd OK
    cad : cad BAD
    cae : cbe OK
(b)

    a:b => c ____ d
    cad : cbd OK
    cad : cad OK
    cae : cbe BAD
(c)

    a:b <=> c ____ d:
    cad : cbd OK
    cad : cad BAD
    cae : cbe BAD
Note that rule (c) is just the conjunction of rules (a) and (b), So only what is OK by both rules is OK.

Finally, note that all 3 rules allow:

    cbd : cad
    cbe : cae
These rules constrain only surface forms that arise from "a"
Environment Idea number two: Rules environments, in keeping with the FSTs ideas, may mention either underlying or sufrace forms.

This means that forms do not "disappear" when they are rewritten. A rule may refer to the underlying form of an environment, thus making the rule independent of any changes the environment undergoes because of another rule.

Example

As an example, consider the case of ih-insertion, which we argued needed to be ORDERED with respect to z-devoicing. Here are the two-level rules for both:

  • ih-insertion: ∅:ih <=> [+ syb]:   ^:∅ ____ z: #
  • z-devoicing: z:s <=> [- vcd]:   ^:∅ ___ #
These rules give us:
    (a)  f ah k s ^ z : f ah k s ih z   (fox ~ foxes)
    (b)  s ah k ^ z : s ah k s  (sock ~ socks )
If z-devoicing could apply before ih-insertion, it could fire in case (a), giving us the incorrect
    (c) * f ah k s ^ s : f ah k s ih s   .
The final segments of (c) would have the following alignment of surface and underlying forms:

    Underlying s[- vcd,+ syb ] ^ ∅ z #
    Surface s[- vcd, +syb ] ∅ ih s #
This does obey the ih-insertion rule, but notice this DOESNT obey z-devoicing as stated above, which requires that the surface s IMMEDIATELY follow an underlying morpheme boundary. Here the surface s immediately follows a surface ih that realizes ∅.

Technical question: How do I know that this is the ONLY alignment of surface and underlying forms that corresponds to (c)?
Answer: It is the only one allowed by our feasible pairs (our "alphabet" of possible surface and underlying pairings).

For example,

    Underlying s[- vcd,+ syb ] ^ z #
    Surface s[- vcd, + syb ] ih s #
would obey both rules, but ^:ih is not a feasible pair! The only feasible pair which has ^; as an underlying form is ^:∅ (underlying morpheme boundaries must always be erased).

Summarizing: The ih-insertion rule makes the following claims about underlying and surface forms, among others:

Underlying   [+ syb ] ^ ∅ z #
Surface ok [+ syb ] ∅ ih z #
* [+ syb ] ∅ ∅ z #
   
Underlying   [- syb ] ^ ∅ z #
Surface * [- syb ] ∅ ih z #
ok [- syb ] ∅ ∅ z #

The z-devoicing rule makes the following claim about underlying and surface forms:

Underlying   [- vcd ] ^ ∅ z #
Surface * [- vcd ] ∅ ih s #
ok [- vcd ] ∅ ∅ s #
   
Underlying   [- vcd ] ^ z #
Surface ok [- vcd ] ∅ s #
* [- vcd ] ∅ z #

These claims are not incompatible. In the particular, z-devoices ONLY those z's that immediately follow a morpheme boundary on the surface.

The two transducers: