Features and Sound Inventories

Post on 04-Jan-2016

35 Views

Category:

Documents

0 Downloads

Preview:

Click to see full reader

DESCRIPTION

Workshop on Features, Segments, Tones Konstanz, 30 October-1 November, 2005. Symposium on Phonological Theory: Representations and Architecture CUNY, February 20-21, 2004. Feature-based Explanation in Phonological Inventories. Features and Sound Inventories. Nick Clements - PowerPoint PPT Presentation

Transcript

1

Features and Sound Inventories

Nick ClementsLaboratoire de Phonétique et Phonologie,

ParisE-mail: clements@idf.ext.jussieu.fr

Symposium on Phonological Theory: Representations and ArchitectureCUNY, February 20-21, 2004

Feature-based Explanation in Phonological Inventories

Nick Clements

Laboratoire de Phonétique et Phonologie, Paris

clements@idf.ext.jussieu.fr

Workshop on Features, Segments, TonesKonstanz, 30 October-1 November, 2005

2

Features and Sound Inventories

Nick ClementsLaboratoire de Phonétique et Phonologie,

ParisE-mail: clements@idf.ext.jussieu.fr

Symposium on Phonological Theory: Representations and ArchitectureCUNY, February 20-21, 2004

Summary

Phonological inventories are structured in terms of a number of interacting principles which operate on distinctive features, rather than segments or phonetic parameters.

Five general principles are discussed and exemplified with respect to data drawn from a large sample of segment inventories:

• feature bounding• feature economy• marked feature avoidance • robustness• phonological enhancement

3

INTRODUCTION

4

A common observation: not just any set of consonants and vowels can make up a sound system.

A central finding of the earliest work in phonology was that sound systems are structured in terms of correlations defined in terms of recurrent features. (see e.g. Trubetzkoy 1939, Martinet 1955, Hockett 1955)

WHY DO LANGUAGES TEND TO HAVE CERTAIN SETS OF SPEECH SOUNDS

AND NOT OTHERS?

5

In recent years, however, the question of inventory structure has been more vigorously debated among phoneticians than among phonologists. This work has tended to minimize the role of features. Examples:

• Adaptive dispersion theory (e.g. Lindblom 1986, Lindblom & Maddieson 1988):

- maximal (or sufficient) dispersion- articulatory ease

• Gestural economy (Maddieson 1995): - economize gestures

6

Work in mainstream Optimality Theory has tended to neglect inventory structure, since constraint systems evaluate individual forms rather than system-wide generalizations.

See, however, Boersma (1997), Flemming (2002) for proposals to incorporate system-level principles such as dispersion, symmetry and articulatory effort into OT.

• Paul Boersma, Functional Phonology, 1988

• Edward Flemming, Auditory Representations in Phonology, 2002

These approaches, too, have sought explanation in phonetic, rather than phonological principles.

7

ARE FEATURES NECESSARY AT ALL?

Some phonologists have concluded that phonological

theory no longer requires a restrictive inventory of

distinctive features but that "phonological representation

can include the entire sea of predictable or freely varying

phonetic detail"

(Kirchner, Robert. 2001. "Phonological contrast and articulatory effort," In Linda Lombardi, ed., Segmental Phonology in Optimality Theory, p. 112.)

8

A FEATURE-BASED APPROACH

This talk reviews a range of evidence showing that features play a central role in the structuring of sound systems.

• It proposes a number of general principles stated in terms of features, and

• shows that these principles make largely accurate predictions regarding the structure of speech sound inventories.

9

FEATURE FRAMEWORK

1. A fairly conservative set of features will be sufficient for our purposes (e.g. Halle & Clements 1983, Sagey 1986)

2. For phonetic feature definitions, we assume the framework of Quantal-enhancement theory as developed by Stevens and his collaborators (e.g. Stevens 1972, 1989, 2004, Stevens & Keyser 1989, 2001)

10

METHOD

11

DATA BASE

Evidence is drawn primarily from the expanded UPSID data base (Maddieson & Precoda 1989). Properties:

• contains 451 phoneme inventories (representing 6-7% of the world's languages)

• geographically and genetically balanced

• electronic database facilitates rapid searches

• results can be independently verified by others

12

PROBLEMS WITH THE UPSID DATA BASE:

• inevitable genetic skewing (e.g. Niger-Congo = 55 languages, Basque = 1 language)

• heterogeneity of sources, disagreements in analyses

• inclusion of some allophonic details but not others (e.g. dental vs. alveolar stops, but not apical vs. laminal stops)

• many coding errors

To a considerable exent, these problems are alleviated by the sheer size of the sample; however, care must be taken in interpreting results (see Basbøl 1985, Maddieson 1991, Simpson 1999, Clements 2003)

Statistical testing (chi square) is used here to evaluate trends.

13

FEATURE BOUNDING

14

FEATURE BOUNDING

Features set an upper limit on the number of sounds and contrasts that a language may employ in its lexicon and phonology.

• a language using 2 features can have up to 4 sounds (22)

• one using 3 features can have up to 8 sounds (23), etc.

Given a set of n features, a language may have at most 2n distinctive sounds.

For example,

1) Sounds:

15

EXAMPLE: MAJOR PLACE CATEGORIES

The features [± posterior] and [± distributed] define four major place categories in coronal sounds.

apico- lamino- retroflex postalveolar/ anterior anterior palatal

posterior - - - -distributed - + - +

16

2) Contrasts

Features also set limits on the number of contrasts a language may have.

Maximum number of contrasts = (S * S-1) / 2, where S = number of sounds.

Example:

4 sounds define 6 contrasts: (4 * 3) / 2 = 6

Since the two binary features [± posterior] and [± distributed] define up to 4 sounds, they predict as many as 6 contrasts, and no more.

17

ALL 6 CONTRASTS PREDICTED BY FEATURE THEORY ARE ATTESTED

contrast: example: found in e.g.:

apical anterior vs. laminal anterior apical t vs. laminal t Temneapical anterior vs. apical posterior apical t vs. retroflex Yanyuwaapical anterior vs. laminal posterior apical t vs. palatal c Arrernte

laminal anterior vs. apical posterior laminal t vs. retroflex Arrerntelaminal anterior vs. laminal posterior laminal t vs. palatal c Hungarian

apical posterior vs. laminal posterior retroflex vs. palatal c Sindhi

• Moreover, no other primary coronal contrasts were discovered in either plosives or affricates in a survey of several hundred languages (Clements 1999).

18

PHONETIC CATEGORIES ARE LESS RESTRICTIVE

Traditional phonetic theory provides 7 (or more) different place distinctions within this region ("apico-dental", "apico-alveolar", "lamino-dental", "lamino-alveolar", "palato-alveolar", "retroflex", and "palatal"). It projects as many as 21 contrasts.

Max no. sounds Max no. contrasts Feature theory 4 6 Traditional phonetic theory 7 21

19

FEATURE ECONOMY

20

• Feature Economy is the tendency to maximize feature combinations in a given system

- Clements (2003a,b) after sources in de Groot (1931), Martinet (1955, 1968)

• This principle can be observed in most speech sound inventories, regardless of their size.

...

21

A STANDARD VARIETY OF ENGLISH: 24 CONSONANTS

phth th kh

b d d g f s v z m n w l r y h

• [+voiced] cross-classifies all obstruents

• [+continuant] doubles the number again

• [+nasal] creates nasal stops at three places of articulation

22

THE ECONOMY INDEX

Feature economy can be quantified in terms of a measure called the economy index. Given a system using F features to characterize S sounds, we can define its economy index E (to a first approximation) by the expression

E = S/F

• Example: English has 24 consonants and requires a minimum of 9 features to distinguish them :

[labial], [dorsa]l, [continuant], [voiced], [glottal], [strident], [posterior], [nasal], [lateral]

• The economy index of the English consonant system is therefore 24/9, or 2.7

23

Examples:sounds features E

English 24 9 2.7 English + 1 sound 25 9 2.8 English - 1 feature 24 8 3.0

Feature Economy can now be more exactly defined as the tendency to maximize E.

This goal can be accomplished either by:

- increasing the number of sounds S, or

- decreasing the number of features F

24

TESTING FEATURE ECONOMY

A testable prediction of feature economy is Mutual Attraction:

"A given speech sound will have a higher than expected frequency in inventories in which all its features are distinctively present in other sounds."

For instance, a stop with a certain laryngeal feature L should occur more frequently in systems having other stops with the same feature L.

Let us look at an example.

25

COMPARISONS OF PAIRS OF STOPS SHARING MANNER FEATURES, BUT DIFFERING IN PLACE

B< vs. D<

B< vs. G<

D< vs. G<

Bh vs. Dh

Bh vs. Gh

Dh vs. Gh

B vs. D

B vs. G

D vs. G

P’ vs. T’

P’ vs. K’

T’ vs. K’

Ph vs. Th

Ph vs. Kh

Th vs. Kh

P vs. T

P vs. K

T vs. K

• All comparisons are positive at a high level of significance (p<.0001). That is, languages having one member of each pair tend strongly to have the other.

26

CROSS-CATEGORY ATTRACTION

For example, it predicts that a language having the sounds

P T K, B D G, and F S X

will tend to also have the sounds V Z , thereby maximizing the use of [+voiced] and [+continuant].

Result (Clements 2003):

• voiced labial fricatives V are much more frequent than expected in languages also having P, B, and F

• analogous results hold for Z and • these trends are significant at the .0001 level

Feature economy also applies across manner categories.

27

MARKED FEATURE AVOIDANCE

28

Markedness is understood here as the systematic avoidance of certain widely disfavored feature values -- the marked values (Trubetzkoy 1939, Jakobson 1941, Greenberg 1968, Chomsky & Halle 1968, Kean 1980, Calabrese 1994, 2005, Rice 2002).

Markedness counteracts the free operation of Feature Economy:• in the absence of markedness, sound systems making

use of n features would be expected to display the

theoretical maximum of 2n sounds

• no languages come close to approaching this maximum; instead, segments characterized by marked

feature values tend to be avoided

29

phth th kh

b d d g f s v z m n w l r y h

Recall the English consonant system:

Absent feature combinations correspond largely to cross-linguistically disfavored consonant types

30

At the same time, Feature Economy counteracts Markedness

• voiced fricatives involve the marked feature values [+voiced] and [+continuant].

• voiced fricatives are absent in roughly half the world's languages.

• however, due to the effect of feature economy, if a language has one voiced fricative, it is twice as likely to have another.

/ . . .

Example: voiced fricatives

31

VOICED FRICATIVES IN UPSID

[labial] V (overall: 32.6 %) in languages having no other voiced fricative: 13.5% in languages having another voiced fricative: 60.3 %

[coronal] Z (overall: 38.6 %) in languages having no other voiced fricative: 16.3 % in languages having another voiced fricative: 73.7 %

[dorsal] (overall: 15.5 %) in languages having no other voiced fricative: 3.3 % in languages having another voiced fricative: 29.2 %

32

HOW DO WE KNOW WHICH VALUE OF A FEATURE IS MARKED?

• Phonetic approaches

Phonetic theory involves an extremely rich set of interacting principles that frequently lead to conflicting expectations.

example: which value of [±nasal] is marked?

• Statistical approaches

The likelier (more frequent, more predictable) value of a feature is its unmarked specification (Kean 1980, Hume 2004)

A statistical approach has the advantage of relating markedness to observable frequency distributions that can be readily extracted by language learners (Pierrehumbert 2003)

33

As pointed out by Greenberg (1966) and others, markedness is reflected in frequency differences at many levels. For example, sounds bearing marked feature values tend to be less frequent:

• in the lexicon• in running texts• in early stages of language acquisition• in adult sound inventories

34

A PROPOSED CRITERION: MARKEDNESS AS NONUBIQUITY

A feature value is marked if it is absent in some language in classes of sounds it which it is potentially distinctive; otherwise it is unmarked. Examples:

[+continuant]obstruent continuantsobstruent stops

[+sonorant]sonorant consonantsobstruent consonants

[+posterior]posterior soundsanterior sounds

[constricted glottis]glottalized soundsunglottalized sounds

[spread glottis]aspirated soundsunaspirated sounds

[+stridentl]strident soundsnonstrident sounds

[+nasal]nasal soundsoral sounds

marked feature value:some lack:all languages have:

35

THE MARKED SUBSET PRINCIPLE (MSP)

"Within any class of sounds in which a given feature F is potentially distinctive, sounds bearing marked values of F are less frequent than sounds bearing unmarked values of F"

In other words, languages tend to avoid marked feature values, regardless of the class of sounds they occur in.

The prediction is that this principle will hold except where overridden by a competing principle.

36

SOME PREDICTIONS OF THE MARKED SUBSET PRINCIPLE

( < is to be read “are less frequent than”)

a. in the class of vowels, nasal vowels < oral vowels (marked feature: [+nasal])

b. in the class of consonants, sonorants < obstruents (marked feature: [+sonorant])

c. in the class of obstruents, fricatives < stops (marked feature: [+continuant])

Do these predictions hold? Consider again English.

s

37

phth th kh

b d d g f s v z m n w l r y h

Prediction (a): nasal vowels < oral vowels true (English has no nasal vowels)

Prediction (b): sonorants < obstruents true (see below)

Prediction (c) : fricatives < stops false ! why ?

38

A COMMON TYPE OF EXCEPTION TO THE MARKED SUBSET PRINCIPLE

English: fricatives = stops

Ikwere: nasal vowels = oral

vowels

The number of marked sounds is often equal to the number of unmarked sounds. Examples:

In such cases, Feature Economy overrides the MSP

39

A FURTHER PREDICTION OF THE MSP:

Example (K = any dorsal stop, velar or uvular): by the MSP,

• labialized ejectives Kw' should be present only if their simpler counterparts K' and Kw are also present

• similarly, K' and Kw should be present only if K is present

Marked segment types usually appear in larger inventories than their unmarked counterparts.

Thus, on average, • Kw' should occur in the largest inventories;• K' and Kw in the next largest inventories;• K in the smallest inventories.

... what are the facts?

40

FREQUENCIES IN UPSID CONFIRM THESE PREDICTIONS

sound: marked features total lgs. av. no. of cons.

Kw’ 2 23 35.8

K’ 1 68 29.0 Kw 1 69 26.4

K 0 450 19.7

41

MARKEDNESS: SUMMARY

Marked feature values are defined as those that are not present in all languages (Nonubiquity)

Marked feature values tend to be avoided in inventories (Marked Feature Avoidance)

This tendency holds in all classes of sounds (the Marked Subset Principle), but can be overridden by other principles (Feature Economy)

Marked segment types generally appear in larger inventories than their unmarked counterparts

42

PHONOLOGICAL ENHANCEMENT

43

PHONOLOGICAL ENHANCEMENTEnhancement is the name given to the reinforcement of acoustically weak feature contrasts by

increasing the auditory distance between their members (Stevens, Keyser & Kawasaki 1986, Stevens & Keyser 1989, 2001).

Two forms of enhancement:

1) phonological enhancement, in which a redundant feature is activated in the phonology to reinforce a contrast

example: [+back] vowel [+rounded]

to reinforce the acoustic contrast with / i /

2) phonetic enhancement, in which an articulatory gesture is activated to reinforce a contrast

example: the posterior fricative / / tends to be somewhat rounded in English to reinforce the acoustic contrast with /s/

44

PHONOLOGICAL ENHANCEMENT

typically involves the activation of a marked feature value to reinforce an existing contrast. Reinforcement may take place:

A) along the same acoustic dimension:

example: [coronal,+posterior] stop [+strident]

dimension 1 (posterior): lower spectral frequency of fricative noise

dimension 2 (strident): higher amplitude noise

example: [+back,-low] vowel [+rounded]

acoustic dimension: F2

B) along a separate dimension:

45

Enhancement creates a class of regular exceptions to the predictions of the MSP whenever the marked values which enhance a contrast become more frequent than the corresponding unmarked values.

For example, [+rounded] is the marked value of [±rounded], yet /u/ is commoner than / / in vowel systems with / i /

• / u /, bearing the marked value [+rounded], is more frequent than its unmarked counterpart / /.Here, then, Enhancement overrides Markedness.

ENHANCEMENT INTERACTS WITH MARKEDNESS

46

EXAMPLES OF FEATURE ENHANCEMENT

[+rounded] (22)y [+rounded] (33) [-rounded] (62)

a [-rounded] (448)i [-rounded] (449)u [+rounded] (444)

e. low vowels nonlow front vowels nonlow back vowels

pf [+labiodental] (7) [+labiodental] (7) [-labiodental] (82)

p [-labiodental] (446)

[-labiodental] (34)

f [+labiodental] (199)

d. labial stops labial sonorants labial fricatives

[+nasal] (102)nt [+nasal] (57)l [-nasal] (428)

a [-nasal] (451)

t [-nasal] (451)

n [+nasal] (445)

c. vowels obstruents sonorants

ts [+strident] (148)c [-strident] (138)

t [-strident] (450)

t [+strident] (235)

b. anterior coronal stops posterior coronal stops

t [+strident] (291) [-strident] (105)

t [-strident] (450)s [+strident] (397)

a. coronal stops coronal fricatives

less frequent:more frequent: in the class of:

47

FEATURE ECONOMY INTERACTS WITH ENHANCEMENT

Redundant features used to enhance contrasts tend to be used maximally:

System A System B

48

ROBUSTNESS

49

ROBUSTNESS

Robustness is the principle according to which

• features are organized in terms of a hierarchy of

preference which is similar across languages, and

• in the composition of sound inventories, higher-ranked

features are made use of before lower-ranked features.

(Sources: Jakobson 1968, Jakobson & Halle 1956, Chomsky & Halle 1968: 409-410, Kean 1980, Stevens & Keyser 1989, Dinnsen 1992, Calabrese 1994)

50

• robust contrasts are, in general, those that are mastered

fairly early in the process of language production -- one

criterion of articulatory ease -- and that allow one sound

to be easily distinguished from another, even in rapid

speech and under conditions of noise

• robust contrasts tend to increase the overall

communicative value of a system by maximizing salience

and economy at a low articulatory cost.

The idea underlying robustness is that certain feature contrasts have a higher "survival value" across time and space, and are accordingly commoner in sound inventories.

51

EXAMPLES OF MORE VS. LESS ROBUST FEATURE CONTRASTS

more robust: less robust:

sonorant / obstruent apical / laminal

labial / coronal / dorsal lateral / central

nasal / oral plain / aspirated

stop / continuant plain / glottalized

voiced / voiceless implosive / explosive

52

UNLIKE MARKEDNESS, WHICH INVOLVES FEATURE VALUES, THE ROBUSTNESS HIERARCHY INVOLVES

CONTRASTS

Markedness: "[+sonorant] is marked with respect to [-sonorant]"

Robustness: "the [±sonorant] contrast is more robust than the [±lateral] contrast"

The latter statement is based on the observation that

• almost languages all have a contrast between sonorant and obstruent consonants,

• while considerably fewer have a contrast between central and lateral consonants

53

COMMONEST CONSONANT CONTRASTS IN UPSID

contrast example % features

a. sonorant / obstruent N / T 98.9 [±sonorant] dorsal / coronal obstruent K / T 99.6 [dorsal] vs. [coronal] labial / coronal obstruent P / T 98.7 [labial] vs. [coronal] labial / dorsal obstruent P / K 98.7 [labial] vs. [dorsal] labial / coronal sonorant M / N 98.0 [labial] vs. [coronal]

b. oral / nasal sonorant L / N 92.2 [±nasal] continuant / stop obstruent S / T 91.6 [±continuant] consonantal / vocoid J / T 89.1 [±consonantal]

c. voiced / voiceless obstruent D / T 83.4 [±voiced]

d. glottal / non-glottal consonant H / T 74.5 [glottal] vs. Ø e. posterior / anterior coronal stop TŠ / T 60.7 [±posterior] central / lateral approximant R / L 60.5 [±lateral]

54

A TYPICAL CORE INVENTORY

These are the fifteen commonest consonant types in UPSID.

A speech sound inventory having just these contrasts would typically include the consonant and glide types shown below (assuming default realizations), among others:

P T TŠ K

B D G

S H

M N

W R L J

55

A PROPOSED ROBUSTNESS SCALE FOR CONSONANT CONTRASTS

1. [±sonorant], [labial], [dorsal], [coronal]

2. [±continuant], [±posterior]

3. [±voiced], [±nasal]

4. [glottal]

5. others: [±strident], [±distributed], [±lateral], etc.

56

THE ROBUSTNESS PRINCIPLE

Within any class of sounds in which two features are potentially

distinctive, contrasts involving the lower-ranked feature will be less

frequent than contrasts involving the higher-ranked feature.

C(Fn+1) < C(Fn )

One prediction: In stop systems, contrasts with

[± strident] (rank 5) should be less frequent than

contrasts wtih [± voiced] (rank 3).

57

EXAMPLES

system A system B system C

P T TS K P T TS K P T TS KB D G D DZ

System A is consistent with the Robustness Principle (RP):

system A: 1 [±strident] contrast, 3 [±voiced] contrasts

Systems B and C violate the RP in the class of stops: system B: 2 [±strident] contrasts, 2 [±voiced] contrasts

system C: 1 [±strident] contrast, no [±voiced] contrasts

System B, however, is allowed by Feature Economy, since it maximizes the use of [±strident] .

58

Like markedness statements, the robustness scale represents a preferred, but not exceptionless trend

Spanish makes use of [±lateral] (rank 5) but not [glottal] (rank 4)

Zoque uses [±strident] (rank 5) while not making use of [±voiced] (rank 3):

p t ts t c ks

Examples:

However, such exceptions are fairly limited:

Most involve lower-ranked features which are not far apart on the scale (1 or 2 ranks)

59

ILLUSTRATIONS

60

Let us see how Feature Economy, Marked Feature Avoidance, Phonological Enhancement, and Robustness interact to distinguish likely from unlikely consonant systems.

A number of unlikely systems, illustrating violations of each principle, are shown in the following slides.

61

SYSTEM A: VIOLATES FEATURE ECONOMY ("MAXIMIZE FEATURE COMBINATIONS")

economy index: 1.1 (13/12)

62

SYSTEM B: VIOLATES MARKEDNESS ("MARKED SOUNDS IMPLY THEIR UNMARKED COUNTERPARTS")

• voiced fricatives but no voiceless fricatives

• voiceless nasals without voiced nasals

• labialized ejective stops without plain labialized and plain ejective stops

• posterior lateral [] without anterior lateral [ l ]

63

SYSTEM C: VIOLATES ENHANCEMENT ("ENHANCE WEAK CONTRASTS")

bilabial fricatives [instead of the preferred labiodentals [f v]

nonsibilant fricatives [] instead of the preferred sibilants [s z]

nonsibilant posterior stops [t d] instead of the preferred sibilants [t d]

• oral sonorants [w l] instead of nasals [m n]

64

SYSTEM D: VIOLATES THE ROBUSTNESS SCALE ("SELECT HIGHER-RANKED FEATURES FIRST")

• Lacks the robust obstruent vs.

sonorant contrast

65

CONCLUSIONS

66

The principles of Feature Bounding, Feature Economy, Marked Feature Avoidance, Robustness, and Enhancement operate together to define the shape of preferred (likely) sound inventories and to exclude many imaginable, but highly unlikely inventories.

It appears that nothing much more complicated than a ranked list of features indicating marked values, together with principles of feature economy and enhancement, can predict the statistically preferred design features of sound inventories to a very good first approximation.

67

WHAT ABOUT PHONETICS?

Finer-grained phonetic detail does play a rolem however, in optimizing the way phonological contrasts are realized. Examples:

• Phonetic enhancement (as discussed earlier)

• Gesture economy: sounds of a given class tend to have uniform phonetic realizations (Maddieson 1995, Keating 2003)

example: anterior coronal stops tend to be uniformly dental or alveolar in a given language

Such principles can be said to "fine-tune" the values of the speech sounds defined by the feature system.

68

TWO WAYS IN WHICH SOUND SYSTEMS CAN BE UNDERSTOOD AS CONSTRAINED

BY PHONETIC FACTORS:

a "direct access" theory: all systemic generalizations must make direct access to the vast number of articulatory and acoustic parameter values provided by phonetic theory.

a "feature-mediated" theory: phonetics constrains phonology largely through the mediation of the phonetic definitions associated with the small set of universal distinctive features, and in fine-tuning phonetic realizations.

This talk has offered support for the second of these views: the major generalizations governing sound inventories appear best captured in terms of principles stated in terms of the features of which speech sounds are composed.

69

Why should this be so? The answer may lie in observations

concerning early language acquisition: • Very young infants (including newborns) perceive speech

sounds in terms of acoustic categories corresponding very closely to the features of adult languages, and are relatively insensitive to finer-grained distinctions.

• In the course of early language acquisition, this "grid" becomes coarser as categories that are not distinctive in L1 become merged

• If basic representational categories are fixed at a very early age, perhaps by the end of the first year, adult languages would be expected to inherit these categories and not to add new ones.

(For a review of these points and alternative views, see Peperkamp 2003.)

70

top related