Editor for this issue: Andrew Carnie <carnielinguistlist.org>
Scobbie, James M. (1997) Autosegmental Representation in a Declarative Constraint-Based Framework , Garland Press, New York. [Revision of 1991 PhD dissertation, University of Edinburgh] [*]
University of Arizona
Jim Scobbie's dissertation, recently published in the Outstanding Dissertations in Linguistics Series through Garland Press, is an excellent example of a pre-Optimality-Theory attempt at a constraint-based phonology that has received insufficient attention in the phonological community. This is extremely unfortunate, as the thesis makes a number of interesting proposals that are well worth considering today.
The dissertation is not in the usual vein of American phonology theses. It's not an in-depth analysis of some particular array of data. Rather, it appears to fit a much more European template, with more attention paid to placing the author's proposal in the context of previous ideas. Despite this very different approach, there is much to recommend it.
The general hypothesis pursued is that phonological generalizations and representations are best cast as attribute-value structures. These formal devices are drawn from the HPSG (Head-Driven Phrase-Structure Grammar) literature (Pollard & Sag, 1987). The basic idea is that dominance is expressed as something roughly equivalent to a featural distinction. For example, in a standard phonological representation the fact that a vowel might be high is expressed by assigning the vowel a '+' for a feature [high], e.g. [+high]. Expressed in attribute-value formalism, the attribute [high] has the value '+'. HPSG goes one step further and encodes dominance in the same fashion. Thus, the fact that a syllable has a [+high] nucleus is expressed by positing a nucleus attribute for a syllable element and then allowing the nucleus attribute to itself have [+high] as an attribute-value pair.
The formal object above denotes a syllable with a [+high] nucleus. (I've indicated irrelevant information with ellipses.)
In the context of these representations, Scobbie's central claim is that autosegmental association can be formalized as dominance in an attribute-value structure. Phonological representations also encode linear order, but in Scobbie's theory, linear order is formalized only for root nodes (and is indicated with indices). A string of segments would then be represented as a set of indexed root matrices, essentially of the following sort.
Indices are ordered by the relation IMMEDIATE PRECEDENCE ' '.
With these structures, Scobbie goes further and suggests that phonological rules should be traded in for constraints. These constraints, he suggests, are formally indistinct from the representations they apply to. (A rather similar position has been advanced in OT. See Russell, 1995 and Hammond, to appear.) For example, a generalization excluding mid nasal vowels would be expressed as follows.
Such an expression rules out an element which is simultaneously specified [-low], [-high], and [+nasal].
Constraints don't actually "apply" to representations. Rather, Scobbie proposes, constraints are unified with representations. Unification allows to representations to meld, just so long as they don't conflict. For example, a representation consisting solely of ifferent elements. For example, the index variables below indicate that the two matrices share the token value for A, but merely share the type value for B.
Scobbie develops this formalism in a number of ways. First, he argues that representations like the one above are subject to what he calls the Sharing Constraint (p.93).
(7) Sharing Constraint
If a structure is dominated by two paths of type P with indices i and j, where , then for every index n where there is a path dominating M.
The immediate effect of this is to rule out cases where noncontiguous root elements share a token value. Scobbie argues that the evidence for such cases is weak. (Cf. a very similar proposal in Archangeli & Pulleyblank, 1994.)
A more interesting consequence is that Scobbie uses this constraint in an attempt to derive the No-Crossing Constraint (NCC), part of Goldsmith's (1976) more general Well-Formedness Condition on autosegmental representations. This is the constraint that rules out crossing autosegmental association lines.
Sagey (1986; 1988) first proposes to derive the NCC from a treatment of autosegmental association as overlap. However, Hammond (1988) argues that this notion is formally problematic proposing a different characterization of association as a transitive, irreflexive, and asymmetric relation. Hammond's approach, however, does not derive the NCC without stipulation. Scobbie's approach also involves an asymmetric characterization of association (as dominance), but does derive the NCC.
Scobbie's derivation of the NCC is based on the assumption that there are no contour values. That is, while two different root nodes might share a value token as in the second picture below, one root node cannot bear two different values, as in the first picture below (where "S" indicates a segment or root node and "T" indicates a tone or value token).
This is a necessary position given his formalization of sequencing: only root nodes bear an index for linear position; nonroot tokens are unsequenced. (A similar position is developed in Heiberg, in prep.) Were contour values to be allowed, there would be no way to distinguish their ordering. On the other hand, when two root nodes share a value, their ordering is distinguished in terms of indices, as in (6).
The upshot of the prohibition on contours is that violations of the NCC can only arise when there is an independent Sharing violation. That is, NCC violations look like (9), and (9) necessarily includes a Sharing violation.
This is a very nice result, but comes at the cost of i) ruling out discontinuous association, and ii) excluding contour values.
Scobbie also argues that his approach allows him to derive the phenomenon of geminate integrity (Hayes, 1986; Schein & Steriade, 1986). The basic idea of geminate integrity is that geminates resist epenthesis. (See Guerssel, 1977; 1978 for an early treatment and Suh, 1997 for a recent proposal.) The standard account of this is that geminates resist epenthesis because the result would entail crossing association lines, and a violation of the NCC, as in (9) above.
The problem with this, as noted by Scobbie and others as well, is that if the epenthetic vowel is featureless (10) or inserted on another tier (11), then no violation of the NCC occurs.
Scobbie's own proposal is simple and direct. Epenthesis into a geminate structure results in a violation of Sharing, regardless whether the epenthetic vowel has features or whether its features might appear on some other tier.
Scobbie goes on to consider the possibility that geminate inalterability might also follow from the Sharing Constraint, but here his proposal is a lot more speculative. The basic idea pursued is that geminate inalterability results from default rules. The problem is that Scobbie doesn't really offer a clear proposal on the nature of default rules. On the face of it, they would seem to be a glaring problem for the monotonic theory he proposes.
In his final substantive chapter, Scobbie treats the problem of long-distance association, as in, e.g. Arabic verbal morphology. He offers some well-taken criticisms of the traditional autosegmental approach, but does not really offer an explicit declarative counterproposal.
In sum, this book is well worth reading. It offers a very interesting alternative constraint-based view of phonology with much to recommend it. On the other hand, there are a number of unresolved questions. What about floating segments? Scobbie speculates on this, but offers no satisfying solution. As noted above, contour segments are also ruled out, though the evidence for these in the tonal domain is unimpeachable. 
[*] Thanks to Jim Scobbie for useful discussion. Any misinterpretations, lapses, or other errors are my own.
 Though as Scobbie (p.c.) points out, ordering these with precedence instead will allow for a treatment of epenthesis, morphological intercalation, and the like.
 My expository characterization is procedural, but of course, unification is not formally so.
 A number of similar ideas are developed in Bird (1995).