2.2 The featural metalanguage
2.2.1 Classification
The first key aspect of a feature system is its classification based on the number and nature of specification states it makes available for each feature. A specification state of a feature is a form it may occur in. The number of specification states corresponds to a valency-based classification, and the nature of specification states corresponds to a pollency-based classification.
2.2.1.1 Valency-based
Three classes of features are generally distinguished based on their valency (i.e., value set size), as in (4). I defer a formal definition of value to §2.2.2 and here simply treat a value as an extra piece of information attached to a base specification (so each value defines a specification state).13 (4) a. Privative features have no value-defined specification state.
b. Bivalent features have exactly two value-defined specification states.
c. Multivalent features have more than two value-defined specification states.
For example, the feature [blue] is privative if this is the only form it may occur in; namely, an object in the universe of discourse is either specified as [blue] or not; by comparison, [blue: 13The converse is not true; i.e., not every specification state is defined by a value. Failure to distinguish the two
notions may lead to contradictory statements like “X is unvalued and has an empty set value” and “Y lacks a value and has as value lack-of-value.” The italic value in both statements should be replaced by specification state.
yes/no] is bivalent since it has two value-defined forms, and [blue: yes/no/half/light/dark] is multivalent since it has five. We can define privative, bivalent, and multivalent feature systems as systems consistently using privative, bivalent, or multivalent features, though in practice many feature systems have mixed valency. This is innocuous as long as features of different valency are used for separate purposes. Thus, in Adger & Svenonius’ (2011) minimalist feature system gram- matical features are multivalent (e.g., [per: 1st/2nd/3rd]) while categorial features are bivalent (e.g., [d: ±]). Similarly, Clements (2003) employs privative and bivalent phonological features respectively for articulatory places and manners (e.g., [labial] and [±voiced]).14
Nonprivative features may be further subclassified based on their value set pattern. Consider the following bivalent features (written in the Jakobsonian style15 for expository convenience) for example: (i) [blue/nonblue], (ii) [black/white], (iii) [gray/silver], (iv) [gray/blue], and (v) [gray/circle]. Among the five features, (i) encodes a boolean switch, (ii) is not boolean but merely encodes a bipolar opposition, (iii) is not bipolar but merely scale-based, (iv) is neither bipolar nor scale-based though still distinctive, and (v) is not even distinctive (for there can be gray circles) but merely distinct. The five patterns correspond to five subclasses of bivalence as structured in Figure 2.1 and exemplified in (5). (The subclassification of multivalence follows the same pattern except that it stops at the scale-based vs. non-scale-based level.)
value set pattern
nondistinctive distinctive non-scale-based scale-based nonbipolar bipolar nonboolean boolean
Figure 2.1 Subclassification of nonprivative features
(5) a. Jakobsonian “joint” features like [vocalic/consonantal] (Jakobson & Lotz 1949: 152) are nondistinctively bivalent; they are nondistinctive since their components may be joined (e.g., liquid phonemes are vocalic and consonantal).
b. Morphosyntactic features like [masc/fem] are usually distinctive but non-scale-based. c. Continuously multivalent features are rarely used outside phonetically based phonol-
ogy; an example is Flemming’s (2004) [F1: 1, F2: 6, F3: 3] (for IPA [i]).
d. Nonjoint phonological features like [nasal/oral] are usually scale-based and bipolar. 14The mixed valency would be problematic (i.e., make the system inconsistent) if there were also multivalent cate-
gorial features in Adger & Svenonius’ system or bivalent place features in Clements’ system.
e. Bipolar features can often be rewritten in the boolean format; for example, [nasal/oral] → [nasal/nonnasal].
Among the five subclasses, the nonboolean/boolean contrast is mostly one of analytical per- spective. In some situations the boolean perspective has additional advantages; for example, in Dresher’s (2009: 16) successive division algorithm (SDA) as illustrated in Figure 2.2, [nasal] is only applied if [voiced] is true; hence, the boolean values +/− (or 1/0 or true/false) serve a control flow purpose and efficiently establish a contrastive-scope-based ordering in the feature inventory (here [nasal] < [voiced]).16
[voiced]
/p/ [nasal]
/b/ /m/
− +
− +
Figure 2.2 Boolean features in algorithm design
2.2.1.2 Pollency-based
A feature may have more specification states than those defined by its values. Any feature may have an unspecified state ([ ]), and nonprivative features may additionally have an underspecified state ([F: ]).17 Such incomplete specification states have long been deployed in phonology to establish nonequipollent or more exactly markedness-based contrasts, such as the contrast be- tween the presence and absence of a privative feature (à la Prague school) and that between the +/− and 0 values of a bivalent feature (Kiparsky 1982). Pollency-based feature classification es-
sentially concerns the comparative theoretical status of a feature’s specification states, and in this sense its application is not confined to phonology. In syntax, for example, Chomsky (2000, 2001) uses unvalued features to trigger Agree, and GPSG/HPSG recognize the empty set as a possible feature structure, called an “archicategory” (a Praguian term) in Gazdar et al. (1985: 26) and a “top”18feature structure that “subsumes all other feature structures” in Pollard & Sag (1987: 30, 37). Such a value-less feature structure may seem trivial, but from another perspective being empty also means being free in unification. Underspecification-induced combinatorial freedom is precisely what underlies the defective category theory to be presented in Chapter 3.
Since the unvalued features in minimalism and the empty feature structure in GPSG/HPSG are theoretically special, the feature systems in both frameworks are nonequipollent, though that 16As Theresa Biberauer (p.c.) points out, the boolean format also allows us to do more with a single feature; e.g.,
both nasal and oral may be covered by manipulating nasal.
17Neither unspecified nor underspecified is the same as a negative value. Adger (2010: 192) recognizes “lack of value”
as an “empty set value,” and Harbour (2013) similarly argues that “not plus” is not equivalent to “not there.”
has nothing to do with markedness. In fact, to the extent that incomplete specifications are used, most existing feature systems are nonequipollent at the system level, and equipollence only exists in special, restricted contexts; for example, in Chomsky’s [±n, ±v]-based definition of lexical categories, since both features must always be valued and all value combinations are exploited,19 no specification state is more special than others and therefore this tiny subsystem is equipollent.