Symmetry and feature economy

Two concepts are important in the study of the structure of the inventory: sym-metry and Feature Economy (Clements, 2003), which predicts that phonologies should make use of the features they employ as much as possible (employment means exploitation). The two are intimately linked, but in prose, we might

express the relationship as follows: In a fully economical system, all feature combinations are possible, whichever features are active in the language. In a fully symmetrical system, for every feature that is active, its counterpart is also active (this works only with binary features, but see below for an elab-oration). In other words, every intersection between the phonetic dimensions described by features is populated by a segment (feature co-occurrence). So, whereas symmetry has something to say about which features are active, econ-omy makes predictions about how they combine. It should be noted that a fully symmetrical system is also maximally economic (every feature combination is used), whereas a maximally economical system is not necessarily symmetri-cal – there might be gaps. At first glance, it would appear that Feature Co-occurrence Constraints are inherently anti-economical. This is because FCCs punish feature combinations, whereas Feature Economy would be improved if more combinations were made while keeping the number of features constant.

Below, however, we will see that the situation is more nuanced.

Even though Clements (2003) rightly argues that Feature Economy and Symmetry are not the same thing, the two are very similar. For example, a maximally symmetric inventory is also maximally economic. Both Feature Economy and Symmetry are decreased when gaps appear in the system, but they are sensitive to different types of gaps. Consider Clements’ examples 4a-c (Clements, 2003, p. 292), reproduced below:

(16) Three sound systems differing in symmetry and economy a. System A

p t c k

b d é g

f s S x

v z Z G

b. System B

p t c k

b d é g

f s S x

c. System C

p t c k

b d é g

f s x

v Z

System A is fully economical, as well as fully symmetric. System B, on the other hand, is less economical, but no less symmetrical: even though it contains gaps, the gaps occur symmetrically in their own right. System C, finally, is more economical then System B by virtue of having more segments without employing more features; at the same time, it is less symmetric because the gaps occur in less regular places.

In terms of FCCs, System A can be described with three constraints: *[lab]-[dist], *[lab][dors], and *[dors][dist]. System B is more ‘economical’ than C, because it requires only a single constraint in addition to the three PoA-constraints: *[cont][voice]. System C is predicted not to exist under the FCC approach as adopted here. It requires the exact same constraints as System A, while overpredicting precisely those segments that Clements (2003) removed for expositional purposes (see section 4.5 for an analysis of overpreditions).

Clements makes no claims with respect to the degree of likelihood for the three systems, either under Feature Economy, or in general; they remain hypotheti-cal.

By way of further illustration, the Turkish vowel inventory can be used as an example of both Symmetry and Economy. It is both fully symmetrical (there are no gaps) and fully economical – there is no restriction on the combinations of features (at least not in roots). In terms of Feature Co-occurrence Constraints, this means that all constraints banning vocalic features to be simultaneously actuated are inactive (or low-ranked, in OT terms). In this example, we clearly see a property of the c-constraint class of Feature Co-occurrence Constraints:

they are anti-economical, by enforcing to combine as little features per segment as possible (every combination will yield a violation). The i-constraints, on the other hand, promote the use of as many features per segment as possible. For every constraint F→G, a segment with F but not G will result in a violation.

The examples do serve to show that FCCs implement a degree of symmetry:

the combination of two features ([continuant] and [voice] in the example above) is banned regardless of any other feature in the segment. Put differently: the Feature Co-occurrence theory is a theory of inventorial gaps, and it predicts that these gaps are symmetrical to a degree.²

At the same time, the examples show that rather than being anti-economical, FCCs in fact implement economy, under the assumption that a system with less constraints is by some metric better than a system with more constraints.

This is easily demonstrated: a fully economical system employs every possible feature co-occurrence. In other words, no FCCs are required.³ Every gap that appears in such a system requires at least one FCC to be introduced in the grammar. An example of this is System B above. Hence, we could say that a ‘meta-goal’ of acquisition is to have as little active Feature Co-occurrence Constraints as possible. As we shall see in chapter 4, an important part of the theory is that constraints can be revoked/demoted during acquisition.

Another way to phrase the above is to say that Feature Economy is a driving

2A large-scale typological study would have to demonstrate to what degree this prediction is correct; this is clearly beyond the scope of the current thesis, but see van ‘t Veer (2008) for a first attempt.

3Note that Clements is incorrect in stating that System A is “fully economical” (p. 292), as it does not allow for segments with complex place of articulation. The economy of System A (under Clements’ feature assignment the inventory is described by 5 features) is E = 16/5 = 3.2. System A’ which includes every logically possible feature combination has a much higher economy: E = 5!/5 = 120/5 = 24.

Stage Inventory

1 p b t k m n l

2 p b t k m n l d j

3 p b t k m n l d j z

4 p b t k m n l d j z s

5 p b t k m n l d j z s r

6 p b t k m n l d j z s r V

7 p b t k m n l d j z s r V v

8 p b t k m n l d j z s r V v N

9 p b t k m n l d j z s r V v N f

10 p b t k m n l d j z s r V v N f x

Table 2.1: Development of word-initial onsets in Catootjes actual productions

force during acquisition. We see this exemplified in the data from the children in the current study, and although a detailed examination of this hypothesis is beyond our current goals, a brief exploration is promising. Take, for example, the developing segment and feature inventories of Catootje (tables 2.1 and 2.2).

Catootje’s inventory at the first stages has a fairly high degree of symmetry, especially if we consider the first two stages together: the major places of artic-ulation are occupied by stops and nasals, and also by voiced stops. There are also some anti-symmetrical aspects in Catootje’s inventory development, for example the absence of the dorsal nasal and voiced stop, both of which are not in Adult Dutch onsets (the occurrence of /N/ later is idiosyncratic). Further-more, the development of continuants is not as symmetrical as the development of non-continuants.

More importantly, comparing tables 2.1 and 2.2, we see that whereas the segmental inventory expands in a gradual fashion, every necessary feature has been activated by the second stage. This can mean only one thing: from the second stage onwards, Catootje’s inventory is becoming more and more eco-nomical. Catootje’s inventory is a striking example, but the same process can be seen in other children’s developing phonologies.⁴

In chapter 4 we will see that the process through which this economisation takes place is the demotion/revocation of Feature Co-occurrence Constraints (we will also go deeper into the methodology of the data analyses, and the definitions of notions such as ‘stage’ in that chapter). For now, we will leave it at the observation that Feature Economy appears to be a characteristic of child phonology, and that the Feature Co-occurrence Constraint theory is capable of describing the process of increasing economy.

4If Feature Economy is indeed a driving force, the question arises as to why the developing inventory – or the adult inventory for that matter – has gaps in the first place. In the case of final state (adult) inventories, the answer is diachrony. Children do not process the inventory on an inventory-level; rather, they are processing words and extracting sounds and features from these forms. We will come back to the issue of input processing in chapter 4.

Stage Features

1 [labial], [voice], [dorsal], [nasal], [liquid]

2 [labial], [voice], [dorsal], [nasal], [liquid], [continuant], [approximant]

3 [labial], [voice], [dorsal], [nasal], [liquid], [continuant], [approximant]

4 [labial], [voice], [dorsal], [nasal], [liquid], [continuant], [approximant]

5 [labial], [voice], [dorsal], [nasal], [liquid], [continuant], [approximant]

6 [labial], [voice], [dorsal], [nasal], [liquid], [continuant], [approximant]

7 [labial], [voice], [dorsal], [nasal], [liquid], [continuant], [approximant]

8 [labial], [voice], [dorsal], [nasal], [liquid], [continuant], [approximant]

9 [labial], [voice], [dorsal], [nasal], [liquid], [continuant], [approximant]

10 [labial], [voice], [dorsal], [nasal], [liquid], [continuant], [approximant]

Table 2.2: Development of features in word-initial onsets in Catootjes actual productions