A construction comprises
- elements
- each of which belongs to a certain category
- and which have certain relations to each other.
A formula brings out these three kinds of information by formally distinct devices:
- An element may be either a particular individual or just any member of the category in question.
- A particular element is represented as a lexical item, at the suitable level of abstraction, i.e. by its functional label, in morphophonemic, in allomorphic, in orthographic etc. representation.
- Any element belonging to the category in question functions like a variable. Variables are represented by letters of the alphabet, provided, if necessary, by numerical subscripts.
- The category of an element or a complex syntagma is represented by a categorial subscript.
- Relations between elements and syntagmas may be represented in various ways:
- Relations of constituency are indicated by angled brackets enclosing the syntagma (phrase) in question.
- A relation of dependency is indicated by an arrow pointing from the head to the dependent element.
- An anaphoric or agreement relation may be indicated by identical subscripts (indices) or other graphic devices linking the two elements in question.
A complete construction schema has the following structure, using adjective attribution in English as an example:
| aspects | examples | |
|---|---|---|
| components | X | Y |
| syntactic categories | [ Adj | N ]Nom |
| syntactic functions | attribute | head |
| semantic functions | modifier | core notion |
As may be seen, categories, syntactic and semantic functions are clearly distinguished. It is important to have symbols that represent the components, since these are used in the accompanying text, like ‘the number of the Nom is only coded on Y’. Symbols like X and Y (or more mnemonic ones) are needed in addition to both the category and the function symbols. The category symbols cannot be used, because an expression (like X) is not the same as its category (like Adj). The function symbols cannot be used, because the schemata show paradigmatic relations between constructions. They can fulfill this task only if components of two such constructions that correspond to each other, i.e. which maintain identity across constructions, have an identical representation. This cannot be ensured if they are represented by their function because the function is what typically changes by such transformations. It is an essentialy feature of the paradigmatic relations between the first and the following construction schema that what is represented by X in the former is the same as what is so represented in the latter.
| aspects | examples | |||
|---|---|---|---|---|
| components | Y | which | is | X |
| syntactic categories | [ N | [ Rel | Cop | Adj ] S ]Nom |
| syntactic functions | head | subject | predicate | |
| semantic functions | core notion | modifier | ||
The line showing the syntactic categories may be used to show constituent structure, too, by labelled brackets.
The following example series illustrates these conventions by the English measure phrase. At the same time, it illustrates taxonomic and meronomic relations among constructions. Some parts of the analysis are ad hoc, as no complete English grammar can be presupposed here.
Postnominal nominal attribute (PNA)
[ of [ X ]NP ]PNA
E.g. of the apples
Postnominal mass-noun attribute (PMNA)
The postnominal mass-noun attribute is a postnominal nominal attribute where a mass noun (MN) takes the position of X in the construction.
[ of [ X ]MN ]PMNA
E.g. of water
Numbered nominal (NN)
[ [ X ]Num.α [ Y ]Nom.α ]NN.α
where α is a variable for the grammatical number of the expression (either singular or plural).
E.g. three tables
Numbered mensurative (NM)
The numbered mensurative is a numbered nominal where a mensurative takes the position of Y in the construction:
[ [ X ]Num.α [ Y ]Mens.α ]NM.α
E.g. five liters
Measure phrase MP)
[ [ X ]NM.α ([ Y ]PMNA) ]MP.α
E.g. four pounds of butter
Common mistakes include the following:
- Symbols for variables are repeated in a formula although no identity is implied. E.g. in a formula for coordinated sentences [ [C [A]S] [C [B]S] ]S, ‘C’ is supposed to represent the coordinating connective; but the notation implies that the same element has to be repeated, excluding, thus, English both ... and.
- Category symbols are placed instead of variables representing elements, e.g. [ NP ] instead of [ X ]NP. This pseudoformalism breaks down as soon as one formula contains more than one syntagma of the same category. The preceding example also features this mistake.
Methodological role of construction formulas
In addition to the general methodological role of formalization in linguistic description, construction formulas have a specific expository function in a grammatical description. Here again, the distinction between the process of scientific research and knowledge production, on the one hand, and the order of presentation of pieces of knowledge, on the other, must be observed. Since formalization of an analysis presupposes a complete and accurate understanding of all the factors determining a fact, it often comes as one of the last steps in the epistemic process. In a grammatical description, however, a construction formula does not play the role of the ultimate culmination of a scientific demonstration. Instead, it primarily serves to represent the components of a construction and their combination in a visual form so the reader can imagine the construction and that both author and reader can use the symbols appearing in the formula for reference in the explanation. It is therefore convenient to present a construction formula early in the description of a particular construction.