2.2 The featural metalanguage
2.2.2 Value and notation
The second key aspect of a feature system concerns how it defines and represents values. The ac- tual usage of feature values involves more complexity beyond the classification in §2.2.1.1. First, while values arguably are only defined for nonprivative features, in practice logically privative features are often given quasi-valued presentations too, perhaps due to the prevalence of value- oriented thinking. For example, the epp feature is often introduced as being present on some categories and absent on others, but this contrast tends to be denoted by [±epp].20 This un- fortunately overloads the ± symbolism, because in ordinary bivalent features like [±nasal], ± represents a positive/negative (rather than present/absent) contrast.21 Another example of quasi- valued features is the vacuous use of +, as in [+mood], [+topic], and the like, where + merely “flag[s] something as a feature” in Adger & Svenonius’ (2011: 51) words, as the relevant minus values are not in use (at least not in the same theoretical context). I call logically privative but no- tationally quasi-bivalent features like [±epp] and [+mood] bivalently presented privative features to distinguish them from bona fide bivalent features like [±nasal].22
Second, the feature-value boundary is often blurred due to different notational conventions and theoretical assumptions. For example, in Panagiotidis’ (2015) approach to lexical categories, the categorial features [n] and [v] are privative on the one hand and values of another feature [perspective] on the other hand. Similarly, given two specifications like [+pst] and [tns: pst], pst is usually called a “feature” in the former but a “value” in the latter. What is reflected in the terminological variation is the relative nature of feature and value, as stated in (6).
(6) In a bipartite feature specification with components 𝑎 and 𝑏 (formally an ordered pair ⟨𝑎, 𝑏⟩), if the information in 𝑎 is extended to a more specific state by the information in 𝑏, then call 𝑎 a feature and 𝑏 its value.
As such, the terms feature and value are only informative when a system’s valency-based classi- fication is specified; conversely, we may also deduce a system’s valency setting by examining its 19Kay (1966: 22) describes this scenario as a “perfect paradigm,” which are rare in naturally evolved symbol sys-
tems due to their “zero redundancy.” Dresher (2009: 29) has a similar remark on the inadequacy of feature space diagrams in categorizing natural language phonemes.
20As a recent concrete example, Levin et al. (2018) propose two types of transitive v0, one with epp ([+epp]) and the
other without it ([−epp]).
21Biberauer et al.’s (2014) reformulation of epp as a movement diacritic (denoted by ^) is free from such ambiguity. 22Harbour (2011: 583–584) similarly calls a [±F] that encodes a single two-way distinction “plus∼minus privativity.”
usage of these terms. So, strictly speaking, if Panagiotidis (2015) recognizes the relation between [perspective] and [n/v] as one of feature and value, then his system is not really privative but only locally privative, in contexts where [perspective] is not considered.23
Due to complications like bivalently presented privative feature and the often blurred feature- value boundary, the notion of value and its underlying logic deserve more careful investigation. The use of feature values in the literature is lax in both form and meaning. In form, [+pst] and [tns: pst] represent two popular formats for feature specifications: [𝛼F] and [F: 𝛼]. While the two formats are mutually convertible (e.g., [+pst] ↔ [pst: +]), they are preferred for different scenarios. Values typically written in the [𝛼F] format include the boolean ±, the underspecified 0, and scale-based values like 5 in [5round] (Clark et al. 2007: 384); I call these coefficient values (following Chomsky & Halle 1968: 65 inter alia). A key characteristic of coefficient values is that they cannot stand alone but must be attached to something else (e.g., /b/ = [+] is ill-formed because + lacks a host). On the other hand, the [F: 𝛼] format is typically used for attribute-value pairs; I call values in this format attributive values. Attributive values can stand alone, and in systems where attributes are conventionally hidden from featural descriptions, they effectively become the “features.” Occasionally we also see quasi-coefficient values appearing in the [F: 𝛼] format, as in GPSG [aux: ±] and [bar: 0/1/2]. According to Bird (1995: 159), the values in such cases are abbreviations for fuller attributive forms; thus, [spread: ±] = [spread: ±spread]. So, while the value slot in [F: 𝛼] is by design attributive, part of the attributive value may be coefficient. Besides, in systems that hide attributes, if the attributive values qua “features” are allowed to have a coefficient part, then that part becomes the “value” (e.g., + in [(num:)+sg], with the parenthesized attribute omitted); if no coefficient part is allowed, then the stand-alone attributive values become “privative features” (e.g., n/v in Panagiotidis’ [(perspective:)n/v]).
In meaning, the denotation of a coefficient value 𝛼coef (in an appropriate semantic model) maps its base’s denotation 𝑑 to a modified denotation 𝑑𝛼 of the same type (whatever that type
is).24 For example, + and − respectively denote the identity and the negation function over their host’s denotation (usually conceived as a first-order predicate), as in (7).
(7) a. J+K(JvoicedK) = JvoicedK = 𝜆𝑥 . Voiced(𝑥) b. J−K(JvoicedK) = ¬JvoicedK = 𝜆𝑥 . Nonvoiced(𝑥)
So a coefficiently valued feature like [+voiced] denotes a modified predicate, and a descrip- tion like /b/ = [+voiced] abbreviates the evaluated functionJvoicedK(/b/) = 1 (“it is true that /b/ is voiced”). By comparison, attributive values usually just denote first-order predicates (e.g., J(num:)sgK = 𝜆𝑥 . Sg(𝑥)), which is why they can stand alone. Since stand-alone attributive val- 23This valency mixture is problematic in the sense of §2.2.1.1, as both [n]/[v] (privative) and [perspective: n/v]
(multivalent) are used for the same (lexical-category-defining) purpose.
24More formally, a coefficient value denotes a generic (or polymorphic) function whose application is not dependent
on argument type; this may be expressed in second-order typed lambda calculus (𝜆2 in Barendregt’s 1991 lambda cube) asJ𝛼coefK = 𝜆𝜏∶ ∗ . 𝜆𝑑∶𝜏 . 𝑑𝛼∶Π𝜏∶ ∗ . 𝜏 → 𝜏 (read “a function mapping 𝑑 of any type 𝜏 to 𝑑𝛼of type 𝜏”).
ues are just called “features,” the first-order predicate interpretation of attributive values in effect blurs the boundary between features and (taxonomic) categories, as in (8), for the latter are also commonly interpreted as first-order predicates.25
(8) a. JvocalicK = 𝜆𝑥 . Vocalic(𝑥) (a feature)
b. JVowelK = 𝜆𝑥 . Vowel(𝑥) (a category)
Note that the first-order predicate model for the featural metalanguage is popular but not unan- imous. Take the +/− symbols for example. Apart from the predicate modifier interpretation, they are used in the literature in at least two other ways:
(9) a. Unary functions from predicate pairs to pair components, such as J+[voc/cons]K = J+K(⟨JvocK, JconsK⟩) = JvocK,
J−[voc/cons]K = J−K(⟨JvocK, JconsK⟩) = JconsK,
J±[voc/cons]K = J±K(⟨JvocK, JconsK⟩) = JvocK ∧ JconsK.
[in Jakobsonian phonology; see Jakobson & Lotz 1949 and Jakobson et al. 1952 inter alia] b. Binary functions from lattice structures to lattice structures, such as
J+author(𝜋)K = JauthorK ⊕ J𝜋K = {𝑎 ⊔ 𝑏 ∶ 𝑎 ∈ ℒ𝑎𝑢, 𝑏 ∈ ℒ𝜋},
J−author(𝜋)K = JauthorK ⊖ J𝜋K = {𝑏 ⧵ 𝑚𝑎𝑥(ℒ𝑎𝑢) ∶ 𝑏 ∈ ℒ𝜋}.
[based on Harbour 2016: 75, for person features] In (9a), the base specifications voc and cons still denote first-order predicates, but +/− no longer denote identity/negation functions; they denote the projection functions of ordered pairs instead (which map pairs to their components). On the other hand, (9b) is based on a completely differ- ent model, where base specifications do not denote predicates but denote lattices. Specifically, [author] and [𝜋] respectively denote the “author lattice” (ℒ𝑎𝑢) and the “social ontology lattice”
(ℒ𝜋), while + and − denote the lattice-theoretic operations “disjoint addition” and “cumulative
subtraction.” The combined symbol ± only has a principled interpretation in the Jakobsonian model; it does not occur in Harbour’s model and is merely ornamental in the first-order predicate model (by flagging something as a feature).26
Corbett (2012: 1, 31) points out that superficially similar notations sometimes hide differ- ences in the “underlying logic” and the “substantive semantics” of features, and that different conventions can lead to confusion “lurking behind the apparent formal tidiness.” Exactly the same moral can be concluded from our discussion in this section. In the feature system adopted in this dissertation, I reserve the [𝛼F] format for coefficient values and the [F: 𝛼] format for at- tributive values, and stick to the first-order predicate model unless otherwise declared.27
25The blurred feature-category boundary in turn opens the gate to further componential analyses for features (by
treating them as categories), which is an atom-breaking process that pushes the analysis to a higher granularity.
26This flagging ± is common in Chomsky’s work, as in [±tense], [±wh], [±anaphor], etc. (Chomsky 1981, 1995). 27This does not mean that the first-order predicate model is necessarily better. I merely use it because it is familiar