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Paradigm structure

The constructional character of inflectional forms underscores an important difference between ‘analyzability’ and morphemic ‘decomposition’. An individual word form is often analyzable into parts that recur elsewhere in its inflectional paradigm or in the morphological system at large. But the ‘recurrent partials’ that distinguish a pair of word forms need not function as signs that are directly associated with the difference in grammatical meaning between the word forms. Instead, the variation exhibited by parts may serve to differentiate larger forms in ways that identify their place within a larger set of forms. The idea that variation is not individually meaningful but “locates” a form “in a paradigm” reflects a classical WP conception in which, as Matthews (1991) remarks, paradigms are the primary locus of part- whole relations:

In the ancient model the primary insight is not that words can be split into roots and formatives, but that they can be located in paradigms. They are not wholes composed of simple parts, but are themselves the parts within a complex whole. In that way, we discover different kinds of relation, and, perhaps, a different kind of simplicity. (Matthews 1991:204)

Treating paradigms as fundamental units of grammatical organization conveys the same kinds of advantages as treating words as the basic grammatical signs. Just as words may have properties that cannot be assigned to their parts, sets of words may express information that cannot be associated with individual words. The forms in Table 4.3 illustrate both patterns. Recall from Section 4.1.2 that a partitive singular can be analyzed into a stem and theme vowel, but partitive case cannot be assigned to either part. A comparison of the forms in Table 4.3 likewise identifies the stem and vowels in Table 4.4.

The inventories in Table 4.4 imply the existence of the pairs kukke/kuke, lukku/luku, pukki/puki and sukka/suka. But they do not supply the interpretation of these pairs, given that nouns with a strong and weak stem may follow either of two gradation patterns (Erelt et al. 2000). In the ‘weakening’ pattern in Table 4.3, the partitive is strong and the genitive is weak. In the ‘strengthening’ pattern in Table 4.5, the genitive is strong and the nominative is weak.

A comparison of the forms of a paradigm will usually identify a set of stems and exponents. But in isolation these elements often do not provide enough information to reconstitute the original forms. As noted in Section 4.1, the forms in the Russian paradigms in Table 4.1 can be reduced to three stems and three partially overlapping sets of case endings. However, from these parts alone, there is no principled means of reassociating stems and endings. Because class is marked

Table 4.4 First declension stems and theme vowels

Strong Stem

kukk

lukk

pukk

sukk

Weak Stem

kuk

luk

puk

suk

Theme Vowel

e

u

i

a

Table 4.5 Strengthening patterns in Estonian (Murk 1997)

Nom Sg

hape

kate

loke

sete

Gen Sg

happe

katte

lokke

sette

Part Sg

hapet

katet

loket

setet

‘acid’

‘covering’

‘bonfire’

‘sediment’

Table 4.6 Qualitative weakening gradation (Murk 1997)

Nom Sg

lugu

suga

Gen Sg

loo

soa

Part Sg

lugu

suga

Illa2 Sg

lukku

sukka

‘tale’

‘sley’

by the distribution of endings, removal of the endings leaves formally indistinguishable stems. The Estonian paradigms in Tables 4.3 and 4.5 can likewise be reduced to stems and theme vowels, which can be recombined to recover strong and weak forms. Yet the distribution of these forms in the paradigm of an item is not recoverable from the parts.[1]

Even the contrast between strong and weak stems depends on their distribution in a paradigm rather than on morphosyntactic or phonetic properties. The partial paradigms for lugu and suga in Table 4.6, like those for lukk and sukk in Table 4.3, contain the forms lukka and sukka. Yet whereas lukk and sukk function as strong stems in Table 4.3, they occur solely within the short illative singular forms in Table 4.6. Gradation in the nouns in Table 4.6 follows a ‘qualitative’ pattern, in which the strong forms lugu and suga differ segmentally from the weak forms loo and soa. The contrast between the homophones lukku ‘lock’ and ‘tale’ and sukka ‘stocking’ and ‘sley’ does not lie in their internal structure, as each pair is composed of a common stem form and theme vowel. Instead, the difference reflects their external relations to larger sets of forms, relations that are not preserved in an inventory of stems and theme vowels.

In sum, words (or sets of words) may exhibit patterns and relations that are difficult to express declaratively in terms of general principles that govern the combination of sub-word units. Regular nouns in English can be described in terms of a set of stems and a regular plural suffix that exhibits phonologically predictable allomorphy. In Russian, the stems and endings require additional class features. In Estonian, the contribution made by combinations of elements makes it difficult to apportion the properties of a form to sub-word units and general combinatorial principles, even if guided by features. This ‘informational asymmetry’ between sets of words and their recurrent parts motivates the perspective of Kurylowicz (1949), on which words are basic units, and stems and exponents are abstractions “founded on” words:

Table 4.7 Grammatical case forms of pukk ‘trestle’

Sg

Plu

Nom

pukk

pukid

Gen

puki

pukkide

Part

pukki

pukkisid

Illa2/Part2

pukki

pukke

For the notion of the stem is dependent on the concrete forms composing the paradigm: one finds the stem in disengaging the elements that are common to all the case forms of a paradigm (when dealing with declension).9 (Kurylowicz 1949:159)

In addition to predicting a common stem and the variation in exponents, the forms of a paradigm also imply information about each other. The paradigms in Table 4.1 illustrate a number of general dependencies in Russian declensions. A nominative singular in -a identifies a second declension noun. A nominative singular that ends in a soft consonant identifies a first declension noun if the noun is masculine and a third declension noun if the noun is feminine. It is conventional to assign items to classes based on the forms that realize a given paradigm cell. However, the opposite deduction, which classifies items based on the meaning they associate with a given form, is equally effective. In the paradigms in Table 4.1 the forms in -u are diagnostic. A form in -u that realizes dative singular identifies a first declension noun, one that realizes accusative singular identifies a second declension noun, and one that realizes instrumental singular identifies a third declension noun.

The effectiveness of these deductive procedures is not a quirk of Russian but reflects the general implicational structure of inflectional systems. Even tighter patterns of mutual implication operate over Estonian declensions. For example, each of the partitive singular forms in Table 4.3 implies the rest of the forms in its paradigm. This striking pattern of deductions can be illustrated with reference to the paradigm of pukk ‘trestle’. The full set of grammatical case forms, given in Table 4.7, is directly implied by the partitive singular form.

In a paradigm containing a strong vowel-final partitive singular such as pukki, the remaining singular forms are fully predictable. The short illative singular pukki is identical to the partitive, the nominative singular pukk is related by truncation, and the genitive singular puki is a weak variant of the partitive singular. The ‘stem partitive plural’ pukki also reflects the default i^e ‘exchange pattern’ for nouns with theme vowel -i (or -e). The long partitive plural pukkisid and genitive plural pukkide follow the general first declension patterns, adding -sid and -de to the partitive singular base. The nominative plural pukid exhibits a class-neutral pattern in which -d is added to the genitive singular base. Furthermore, all of the remaining [2]

Table 4.8 Semantic case forms of pukk ‘trestle’

Sg

Plu

Illative

pukisse

pukkidesse

Inessive

pukis

pukkides

Elative

pukist

pukkidest

Allative

pukile

pukkidele

Adessive

pukil

pukkidel

Ablative

pukilt

pukkidelt

Translative

pukiks

pukkideks

Terminative

pukini

pukkideni

Essive

pukina

pukkidena

Abessive

pukita

pukkideta

Comitative

pukiga

pukkidega

‘semantic’ (or ‘local’) case forms are predictable from the genitive singular and plural forms in Table 4.7. As the forms in Table 4.8 show, the semantic case endings do not inflect for number, so that stem selection represents the only variation in these forms.

A strong genitive singular such as happe in Table 4.5 licenses comparable deductions within the paradigms of nouns that exhibit strengthening gradation. Other classes exhibit other characteristic patterns of interdependency, which are recognized in nearly all descriptions of Estonian.[3] [4] In keying these deductions to the informativeness of the partitive singular, the present description follows the classical practice of identifying class based on a distinguished ‘diagnostic form’. However, this overstates the informational asymmetry between partitive singulars and other forms. A genitive singular such as puki is also diagnostic of a weakening declension. Although morphologically weak, the stem puk is phonetically long (or ‘second quantity’ Q2). A Q2 genitive singular can only occur in a paradigm with an overlong (‘third quantity’ Q3) nominative and partitive singular.11 The genitive plural is also diagnostic, since the removal of the ending -de identifies the partitive singular base. Moreover, since all of the semantic case endings are invariant, each of the semantic case forms identifies the corresponding genitives. Hence, nearly every form is either diagnostic of class or identifies a form that is diagnostic.

The informativeness of individual words and the symmetry of interdependencies give rise to particularly efficient deductions in Estonian. However, an implicational structure defined by interdependent alternations is characteristic and even definitive of inflection class systems. It is these patterns of mutual prediction that act as the primary force binding inflected forms into the “complex whole” that Matthews specifies on p. 75 above. Individual patterns are frequently noted in descriptions of inflectional systems and often serve as the basis for assigning items to classes. Yet because these patterns are so transparently represented by exemplary paradigms, there have been comparatively few attempts to express implicational relations symbolically (or sub-symbolically, via networks), in a format that abstracts away from the sets of forms that exhibit those relations. The Paradigm Structure Conditions of Wurzel (1984) represent the most systematic attempt to capture mutual interdep endency:[5]

Observation of complicated paradigms shows that implicative relations do not only obtain between one basic inflexional form, either lexical (sobaka [Russian ‘dog’ JPB]) or non-lexical (Manner [German ‘men’ JPB]), and all the other inflexional forms, but exist throughout the whole paradigm: all paradigms (apart from suppletive cases) are structured on the basis of implicative patterns which go beyond the individual word, patterns of varying complexity. Of particular complexity in this respect is, for example, the implicative pattern of the i-declension in Latin: /im/ in the A.Sg. D /I/ in the Abl.Sg. D /is/ in the A.Pl. D /ium/ in the G.Pl. D ... From the A.Sg. form we can derive, via a number of steps, all other forms, but not vice-versa. Since the implicative patterns determine the structure of the paradigms of a language we call them implicative paradigm structure conditions (PSCs). (Wurzel 1984:208)

Although this passage is phrased in terms of a process that “can derive, via a number of steps, all other forms”, PSCs can also be interpreted non-derivationally, as wellformedness constraints, or ‘paradigm admissibility conditions’. This interpretation is highly compatible with a classical WP perspective in which part-whole analysis largely involves determining whether a particular set of forms comprises a paradigm or whether a particular form belongs to a given paradigm. Yet PSCs are also fundamentally limited by their use of the material conditional ‘d’ to model implicational relations. This restricts the application of PSCs to exceptionless patterns, and excludes any statistical patterns involving strongly but not invariably correlated dependencies. The challenge of modelling probabilistic dependencies was not met in any general way until the development of modern implicational WP models, and it is in the context of discriminative, information-theoretic approaches (discussed in Chapters 7 and 8) that the most promising solutions appear to lie.

  • [1] In fact, the theme vowels in Tables 4.3 and 4.5 do provide some information about gradation. Apartfrom isolated examples such as louna ‘south, noon, strengthening gradation is confined to nouns withthe theme vowel -e. Hence a noun with a strong and weak stem and a theme vowel other than -e willalmost always follow the weakening pattern. However, this deduction is again not attributable to theproperties of individual formatives but to the distribution of theme vowels over the paradigms of thelanguage.
  • [2] Car la notion du theme est posterieure aux formes concretes composant le paradigme: on trouve letheme en degageant les elements communs a toutes les formes casuelles du paradigme (quand il s’agitde la declinaison).
  • [3] One model of the structure of the Estonian inflectional system is outlined in Blevins (2007,2008a).More traditional classifications, which differ mainly in where they draw the line between classes andsubclasses, are presented in Erelt et al. (1995), Murk (1997), Saagpakk (2000), Erelt et al. (2000), Erelt(2003) and Erelt (2006).
  • [4] Stops do not contrast in voicing in Estonian, and the orthographic pairs associated with voicingcontrasts in English are used to express length contrasts. The series b/d/g is short (Qi), the seriesp/t/kis long (Q2), andpp/tt/kk are all overlong (Q3).
  • [5] In much the same way that the Unaccusativity Hypothesis of Relational Grammar(Perlmutter 1978) provides a general statement of the descriptive generalizations about argumentstructure offered in descriptive grammars, PSCs provide a formalized statement of the formcorrespondences noted in reference and pedagogical grammars.
 
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