The set enumerated in the list of functional domains is a heterogeneous and mostly unordered collection of such domains. As it is, it does not lend itself to an empirical generalization of the sort ‘a grammatical meaning (function, category, operation) is of such and such a nature’. However, the question is nevertheless an empirical question as long as there is no theory of language from which the answer could be deduced.

According to the relevant claim most often put forward in the literature, grammatical meanings are relational. For instance, Sapir (1921. ch. V) presents a model of notions processed by language which dubs grammatical meanings ‘relational’ (cf. also Diewald 2011: 369f). In order to assess this assertion, we need to know what relational means here. There are quite different kinds of relation which are constitutive of human language:

1. The significative relation associates significans and significatum of the language sign with each other.
2. Paradigmatic relations exist between a sign and other signs of its category.
3. Syntagmatic relations exist between a sign and other signs in the context.
4. The referential relation associates a sign of an utterance with the entity meant.
5. A sign is relational iff a certain syntagmatic relation is inherent in it.

As may be seen, relations #1 – 4 canot be meant by the assertion that grammatical signs are relational since these relations do not distinguish lexical from grammatical signs. In fact, relations #1 – #3 hold for all kinds of signs. #4 holds for some lexical and some grammatical signs. Specifically, nouns can be made to refer in discourse. Deixis is a property both of lexical signs like come and of grammatical sign like here. It is, again, a relation of type #4.

It is only the relation of type #5 which could possibly classify language signs as follows: Lexical signs may be relational or non-relational; grammatical signs are relational. Relationality in a narrow sense is the semantic property of a notion, and secondarily the grammatical property of a sign, to open a place, like a logical predicate, for an argument. In this sense, eat is relational because it can only be understood if there is an actor and an undergoer, while apple is non-relational as it is not necessarily related to anything else. Given this sense of relationality, verbs, adjectives and case relators, among others, are relational. Some nouns like top are relational, others like apple are non-relational.

There is, however, a second kind of syntagmatic relation brought about by certain signs. This is the endophoric relation afforded by pronominal elements. These do not open a position for an argument like a logical predicate and instead refer to an expression in the context with which they are, in the default case, co-referential. Examples are the personal pronouns he, she, it, which may take up referents introduced in the preceding sentence, including even the entire proposition coded by it.

Now it is true that certain lexical items are recruited for grammaticalization precisely because of their relational properties and that the reduction that they undergo in grammaticalization carefully leaves these relational properties intact because they are what these items are needed for. For instance, Cabecar grammaticalizes the trivalent verb pákä ‘tell’ (actor x tells recipient y theme z) to a causative operator for a causative construction of the form ‘causer x causes causee y to z’. The same goes for case relators, which are practically always grammaticalized from relational lexemes such as plurivalent verbs and relational nouns. Trivially, conjunctions bring about interpropositional relations. They are mostly grammaticalized from case relators. These may directly take a dependent clause as their complement, as does before; and then they are subordinative conjunctions. Alternatively, they take an anaphoric pronoun referring to the preceding sentence as their complement, as in therefore, and this anaphoric pronoun then mediates the interpropositional relation. Such conjunctions are coordinative conjunctions.

However, not all grammatical categories or formatives are relational in either of these two senses. Nominal number is not. Among pronouns, only anaphoric pronouns may be said to be relational, in the second of the above senses. Pronouns of first and second person are not relational, as their deictic relation to speech-act participants does not count (cf. Diewald 2010 for the opposite opinion). For the same reason, many other proforms like where, somewhere, here are not relational. The grammaticalized items mentioned before are relational on the syntagmatic axis, and this is what renders them useful for a structural function. Auxiliaries and case relators are relational in this sense; nominal number and first and second person pronouns are not.

The net result of this discussion is the following: It is true that the grammatical structure of a complex sign is based on syntagmatic relations between its components (leaving the paradigmatic relations aside here). Many of these syntagmatic relations are provided by relational lexical items. However, since many lexical items are not relational, but must contract syntagmatic relations nevertheless, syntagmatic relations are partly brought about by grammatical signs dedicated to this function. This does not, however, imply that all grammatical signs are relational.

Reference

Sapir, Edward 1921, Language. An introduction to the study of speech. New York: Harcourt, Brace & World.