Testing paradigmatic relations

Depending on the type of linguistic unit tested, linguistic units that it may have paradigmatic relations with include the following:

1. members of the same paradigm s.s.
2. members of the same lexical class
3. members of the same word class
4. members of the corresponding syntactic class at the next higher or lower level of grammatical complexity
5. zero.

Substitution test

In the cases #1 – #3, a substitution test will restrict itself to substituting elements of the same complexity level in the context in question, substituting, e.g., der ‘the’ for ein ‘a’, astronomer for physicist and astronomer for noun, resp. Variety #4 of the test ascertains whether categorial uniformity holds for the substitution class in question. Categorial uniformity holds for a grammatical category of a given kind (e.g. a particular word class) iff it forms a distribution class with grammatical categories of lower and/or higher levels of grammatical complexity. For instance, the German forms er ‘he’, dieser ‘this (one)’ and several others form a certain word sub-class of substantival pronouns. This falls into the same distribution class as certain proper names such as Erwin ‘Irvin’ and Galileo Galilei, and again as definite singular noun phrases such der Astronom ‘the astronomer’. Consequently, there is one distribution class – call it ‘definite noun phrase’ – which comprises elements of different grammatical levels. Therefore, categorial uniformity holds for this class. On the other hand, assume that the modal verb is defined as an element that occurs in the context [    [ X ]_V.inf ]_VP (where nothing intervenes in front of X). Then the only possibility of expanding the string preceding X is to insert a particle such as nicht ‘not’ or doch ‘yet’; but it cannot really be replaced by a syntagma of a higher or lower syntactic level. Consequently, categorial uniformity does not hold for the modal verb.

The latter result is, indeed, more typical for grammatical formatives, while the former result is something special of these German pronouns.

Free variation

A common situation in linguistic analysis is the confrontation with two expressions that appear to be synonymous. For instance, at a certain point, the analyst may be confronted with the German words als ‘when, after’ and nachdem ‘after’, which in his corpus so far only occur in contexts such as and .

So far, then, the two conjunctions appear to be synonymous. While full synonymy does occur in languages, given the nature of the language system, it is the exception rather than the rule. Consequently, abiding by such a state of affairs would be against the basic task of the linguist, which is to account for linguistic variation. The task is therefore to falsify the hypothesis that the two items are synonymous.¹

The test for synonymy is free variation. The methodological problem is, therefore, to test for substitutability in all contexts. There are more than one way to confront this challenge. One is to use a corpus:

1. generate a concordance for each of the items in question
2. sort the passages listed by the preceding or following context
3. classify the contexts
4. compare the kinds of contexts that the two items occur in.

Another procedure is to test informed hypotheses on which factors might condition a difference in distribution. In the case at hand, we already know that the items in question are temporal conjunctions.² An obvious hypothesis is therefore that their choice might be conditioned by (or else, might condition) the tense of the predicate of the subordinate clause.

The substitution of nachdem for als in yields an ungrammatical sentence. This so far shows that the distribution of nachdem is more restricted than the distribution of als, since it appears to be bound up with the pluperfect appearing in and , but not in .

While this hypothesis brings us a good deal further, it is not the whole story. Consider .

Here the same past tense appears which excludes nachdem in . Thus, there must be yet another factor, apart from pluperfect, which renders nachdem possible. Now, apart from tense, temporal relations are also coded by temporal particles. Closer inspection of the two past tense examples shows that contains the particle noch ‘yet’, while features wieder ‘again’. The former signals that the situation designated by its clause holds while the situation designated by the main clause is the case, while the latter signals that a change precedes the situation designated by the main clause. The situations designated by the subordinate clauses in , and have it in common that they are completed at the time that the situation designated by the main clause starts. This then gives rise to the hypothesis that nachdem is restricted to anterior relations, while als may be used both in anterior and in simultaneous situations.

This result is representative for the far majority of cases of apparent synonymy. On the other hand, full synonymy can never be proved: The thesis of full synonymy of two linguistic items implies that there is nothing that conditions the variation between them. This is a hypothesis on the non-existence of something in an infinite universe, which by nature is not verifiable.

Complementary distribution

Aspectual suffixes on Yucatec Maya verbs

The first inflectional suffix of the Yucatec Maya verb is a so-called status suffix. It is one out of a paradigm of six morphemes, called completive, incompletive, perfect, subjunctive, imperative and extrafocal. The first two are essentially aspectual morphemes. The choice between them is, however, 100% conditioned by prior choice of the auxiliary preceding the verb, as follows:

• the imperfective, terminative ... auxiliaries condition incompletive aspect,
• the perfective auxiliary conditions completive aspect.

The two aspectual suffixes are, thus, in complementary distribution in verbal complexes.

Pronominal cross-referencing on Yucatec Maya verbs

In Yucatec Maya, there are two sets of pronominal cross-reference indices on the verb:

• a paradigm of preverbal clitics that cross-reference the intransitive and transitive subject
• a paradigm of verb suffixes that cross-reference the actant of a monovalent predicate and the object of a transitive verb.

On intransitive verbs, the two sets are in complementary distribution conditioned by the status category, as follows:

• Incompletive aspect on the verb requires subject clitics for the actant ()
• while completive aspect (.a), subjunctive mood (.b), imperative and extrafocal require absolutive suffixes.

Since the status suffixes themselves are conditioned as explained in the preceding section, the conditioning of the pronominal cross-reference markers is purely morphological; i.e. their alternation is not syntactically conditioned.

Contextual constraints

A principle of information theory says that the element that appears in a given position of a message is the more expectable the larger the context – esp. the preceding context – that is considered. is a simple example:

The slot in .a can hold one of the suffixes -s, -ed and -ing. Instead of a suffix, there could also be almost anything else, as e.g. in call your daughter!. In .b, choices are already severely restricted: the slot has to be occupied by one of the suffixes -s or -ed. In .c, finally, the only possible filling of the slot is -ed.

This example is representative. The principle is:

The larger the context considered, the more constrained the choice at a given position.

This has the following consequence for the paradigmatic relations: In .a, the three suffixes mentioned are in opposition to each other; and the whole paradigm is in opposition with zero.

In .b, -s and -ed are still in opposition with each other, but their relation to -ing has changed: while -s can appear in the context .b and not in .d, with -ing it is the other way round. Thus, considering .b and d, -s is in complementary distribution with -ing. More generally, the principle is:

What may be in opposition at a lower level (i.e. upon consideration of a narrow context) may be in complementary distribution at a higher level (i.e. upon consideration of a larger context). The converse does not occur.

This is a logical consequence of the former principle, since the paradigmatic relation of opposition implies that there are no constraints on the choice between two elements (other than what the speaker wants to convey), while the paradigmatic relation of complementary distribution implies that there are constraints on the choice between two elements imposed by the language system or the context.

Here is another relevant example. Observe the distribution of Spanish conocer and saber, both ‘know’, as an example:

The facts in f argue for a complementary distribution between conocer and saber. Obviously, the verb meaning ‘know’ must be represented by conocer if the object is non-propositional, while it must be represented by saber if its object is propositional.

If we pronominalize the object in the above example sentences, we get .a for .a and .b for .b.

Now here the two verbs conocer and saber occur in the same context, viz. as the only other element of a sentence after the pronoun lo. .a and b are not synonymous: .a implies that the anaphoric direct object is a non-propositional entity, while .b implies that it is a propositional entity. Consequently, the two verbs are by definition in opposition. Thus, depending on the kind of context in which we apply the substitution test, the two verbs appear to be either in complementary distribution or in opposition.

This kind of problem is typical for selection restrictions. Selection restrictions are weaker than semantic features. In the case of a clash, the semantic feature of the selected argument wins out against the selection restriction. For instance, in a context where has just been uttered,

.a and not .b would be a grammatical answer. This means that even in , choice between saber and conocer is conditioned by the context, in this case by the reference of lo. We can conclude that saber and conocer occasionally appear to be in opposition; but under appropriate analysis, they turn out to be always in complementary distribution.

As a last example, let us take up the aspect suffixes of the Yucatec verb. At the level of the verb form, the two suffixes are in opposition. At the level of the verbal complex, they are in complementary distribution.

More discussion in German

Limits of applicability

No paradigmatic relation obtains between items that occupy different syntagmatic positions. This concerns, obviously, items with different functions, say foot and how. It concerns, less obviously, items fulfilling cognate grammatical functions. For instance, many languages have a paradigm of personal pronouns and a paradigm of pronominal clitics. Members of these two paradigms may contract syntagmatic, but no paradigmatic relations. Cf. on komplementäre Verteilung.

¹

The principle of no synonymy is postulated in Bolinger 1968.

² We simplify the problem here by restricting ourselves to Standard German, to the temporal (as opposed to causal) use of nachdem and to the conjunctional (as opposed to comparative) use of als.

Reference

Bolinger, Dwight L. 1968, "Entailment and the meaning of structures." Glossa 2(2):119-127.