Another solution to the problem of ruling out the formal combination [+high,+low] has two steps. First, consider the features [high] and [low] as privative rather than binary (equipollent) features. That is, they may be present or absent, rather than obligatorily present with one of two values. Second, assume that height is a single dimension. This may be taken as the assumption that there is an autosegmental tier in the feature geometry which may be called the height tier. At most one of the privative features [high], [low] may occupy this tier.
With these assumptions, the three possible height specifications are [high], [low] and unspecified. Unspecified height may be phonetically interpreted, quite sensibly, as mid height.3.44 These exhaust the possibilities; there is no possible combination corresponding to [+high,+low].
A problem with both n-ary and privative features is that there is no provision for making unique references to feature-values, without further formal machinery. Full use of n-ary features might allow feature specifications like
Presumably combinations like [height 19#19 1] must be explicitly ruled out. Or if privative features are used, such as [high] and [low] and [front], then, one must be able to distinguish mid height (unspecified) from any height (also unspecified). For example if a process applies to back vowels (which are unmarked for frontness), and not the front vowels (which are marked for frontness), the expression,
X Y /[ ]
is to be interpreted such that [ ] means both unspecified for height, and positively specified as non-front. But this is not formally distinguishable from a process that applies to both front and back mid vowels, where [ ] would be interpreted as positively specified as non-high, non-low, and unspecified for backness. Rules need to be able to distinguish these things.
It is evident that phonological rules must be able to state Boolean conditions on the presence or absence of privative features. A formal way of writing this is to allow the use of the negation symbol, 20#20, in the statement of phonological rules, whose interpretation is that the feature marked with 20#20 is specified to be absent from forms to which the rule applies. Then a segment that is non-back will be specified in rules as 20#20[back], while a segment that could be front or back has no specification stated in the rule. Note that this is rather different from re-introducing 15#15 values in specifying rule environments or feature structures, since 17#17 notations are not allowed. Therefore in order to make references to unmarked features unambiguous in the statement of rules, Boolean conditions on the presence or absence of privative features will be allowed in the statement of rules.
In the following discussion, I will assume that privative features represent underlying phonological vowel qualities.
After this treatment of static vowel phonology, I return to the temporal structure of vowels, describing the ways that the static and temporal structures combine so as to represent the vowel categories of Reference American.