Of absent mothers, strong sisters and peculiar daughters: The constructional network of English NPN constructions

3.2.1 Descriptive statistics: frequency and productivity

Overall, 14,998 examples of NPNs were identified. 26 different nouns and 11 different prepositions are being used in the construction; we find 86 different constructional types among them 21 hapaxes (e.g., season upon season, dusk to dusk, minute per minute).^[14]

The ten most frequent constructional types are listed in Table 2. Figure 1 reveals which nouns are used most frequently in the construction.

Figure 1:

Used nouns in the [CN_sg,time ⁱ P CN_sg,time ⁱ]_Cx (raw frequency).

Day, year and night are the temporal nouns recruited most often in the noun slot in terms of token frequency. This comes as no surprise, as year, day and night (in that order) are also the most frequent temporal nouns in general. We can assume that speakers simply like to talk more about their days and nights than about their millennium.

Table 3 ranks the used prepositions based on their frequency. To is the most frequently used preposition (used in about one half of the cases), followed by after and by. Then, lagging behind with a much lower frequency, we find over, upon, for and the rest.

After is the most productive preposition in the sense that it combines with 22 different nouns followed by to (20), by (17), upon (8), for, on, over (all 5), through, onto, following, and within (all 1). These findings extend Jackendoff’s list of prepositions which states that after, by, upon, to and for are used in the construction.

Figure 2 shows prepositions (purple) and nouns (green) together in a productivity graph in which two nodes are linked if they surface in the [CN_sg,time ⁱ P CN_sg,time ⁱ]_Cx template at least once, while the size of a node corresponds to its frequency in the analyzed data set. The graph shows a large number of nodes and edges. After, to and by are both central in the graph (being linked to many nouns) as well as relatively frequent. Additionally, some prepositions and nouns, such as day and by, productively pair up in the sense that they are linked and have a high frequency.

Figure 2:

Productivity graph of nouns and prepositions in [CN_sg,time ⁱ P CN_sg,time ⁱ]_Cx constructions. Two nodes (purple: prepositions; green: nouns) are linked if they surface together at least once in [CN_sg,time ⁱ P CN_sg,time ⁱ]_Cx. Node sizes scale with log-frequency of the respective item in the data set of about 15,000 tokens.

3.2.2 Collostructional analysis

In order to shed more light on the lexical preferences (i.e., repulsion/attraction strength) in the construction, we conducted a simple collexeme analysis (e.g., Stefanowitsch 2006, 2013; Stefanowitsch and Gries 2003) with some minor adjustments to overcome statistical shortcomings (see Schmid and Küchenhoff 2013). Although collostructional analysis à la Stefanowitsch and Gries has been criticized for various reasons (e.g., Divjak 2008; Schmid 2010; Schmid and Küchenhoff 2013), it is a useful method to calculate the association strength between a construction and the lexical items filling a slot in it.

For every temporal noun, we measured the strength of association with the [CN_sg,time ⁱ P CN_sg,time ⁱ]_Cx template. We computed a 2-by-2 contingency table containing four different scores for frequencies of occurrence; namely the frequency of the target lexeme in the target construction (A), the frequency of the target lexeme in the corpus in general (B), the frequency of the construction filled with other lexemes than the target lexeme (C) and the frequency of all other constructions with lexemes other than the target (D). From these frequencies, one can derive the expected frequency of occurrence and whether the observed frequency of the noun in the construction deviates significantly. From the contingency table, we derived log odds ratio together with 95% confidence interval for every noun (Schmid and Küchenhoff 2013). If the log odds ratio is significantly positive, the noun is said to be attracted to the construction. If it is significantly negative, it is considered to be repelled.^[15]

The results are visualized in Figure 3 (numerical results can be found in Table A2 in the Supplementary Materials). It can be seen that six nouns are significantly attracted by the construction (purple bars), whereas others are repelled (green bars). In other words, in contrast to their raw frequency distribution, the nouns show a slightly different ranking when it comes to their attraction strength. For example, the nouns millisecond or hour are used relatively more often in the construction than the high frequency nouns night or week. In contrast, other nouns like morning, winter and Christmas are repelled. Compared to their rather frequent overall usage in the corpus, they do not show up as often as expected in the [CN_sg,time ⁱ P CN_sg,time ⁱ]_Cx template.

Figure 3:

Collostructional strengths of all [CN_sg,time ⁱ P CN_sg,time ⁱ]_Cx constructions. Strength is measured by log(OR) (horizontal axis). Error bars denote 95% confidence intervals. Purple denotes attracting constructions (‘attractor’; log(OR) significantly positive); green denotes repelling constructions (‘repellor’; log(OR) significantly negative); light gray denotes constructions which are neither repellors nor attractors.

We can also assess collostructional strength for each preposition separately. This allows us to inspect, for example, which nouns are attracted most by the [CN_sg,time ⁱ after CN_sg,time ⁱ]_Cx template. We performed a collostructional analysis as above for each preposition in our dataset (by just filtering all corresponding items and then computing log(OR) for each noun as described before). Based on the collostructional analysis we determined the significantly attracting nouns for each preposition.

All nouns and prepositions were again arranged in a graph in such a way that a noun and a preposition are linked if the preposition is significantly attracted by that noun as determined through the collostructional analysis. The resulting graph is displayed in Figure 4 (nouns are green; prepositions are purple; arrows denote attraction). Such an analysis is both more revealing and statistically robust than the production graph in Figure 2. Evidently, not all prepositions are attracted by the same set of nouns in the construction. For example, after and by only share three attracting nouns (hour, month, day), and each of the two features additional attractors as well (decade, night, week, millennium for after; minute, millisecond for by). Conversely, not all nouns (apart from month and day) point to the same prepositions. In particular, year and day (both of which represent attractors for the more abstract construction as seen in Figure 4) have almost disjoint sets of attractees.

Figure 4:

Attractor graph for nouns (green) and prepositions (purple) in [CN_sg,time ⁱ P CN_sg,time ⁱ]_Cx templates. Two nodes are linked if one node is significantly attracted by the other node (gray arrow pointing to the attractee). Attractors were determined by computing a collostructional analysis for each preposition separately.

How are these results relevant for our constructional analysis? In general, a usage-based framework assumes that “the frequencies of repeated processing events translate into different strengths of associations in the network representing linguistic knowledge” (Schmid and Küchenhoff 2013). The postulation of constructions (as separate nodes in the cognitive network) can be based on their degree of entrenchment and their attraction strength. Although there is not always a direct link between corpus data and degree of entrenchment, it is usually assumed that a construction is more strongly cognitively entrenched, if it is frequently encountered (Blumenthal-Dramé 2012; Bybee 2010; Diessel and Hilpert 2016; Hilpert and Diessel 2016; Schmid 2010). If a string is cognitively strongly entrenched, this warrants its constructional status as a separate node in the construction.

Thus, it is possible to argue that constructions like year after year or day by day (see Table 2) deserve to be represented as individual separate nodes in the network due to their high frequency. Although they are rather compositional and transparent in their meaning, they are extremely frequent in contrast to the other temporal NPN constructions. At the same time, collostructional analysis reveals that a noun like minute is also recruited relatively often into the construction. So even if minute has a rather low token frequency at first sight, it can be argued that speakers hear minute relatively often in the NPN pattern in contrast to how often they hear it in other ‘normal’ NPs. Moreover, as can be seen from Figure 4, minute has its own dedicated attractee for, which is not shared with any other noun. This may lead to the cognitive strengthening of this low frequency pattern as well.

3.2.3 Modification and complementation

As has been mentioned in the introduction, modification is another aspect worthy of investigation.^[16] In the research literature on the topic, it is stated that modification and complementation patterns in these constructions are quite rare.

Jackendoff points out that only those NPs which function as arguments can take complements (examples [19] and [20]).

Additionally, Jackendoff claims that modification is only possible with after, by and upon. No study however, has so far investigated the frequency and nature of these modified patterns. Our analysis reveals that a handful of examples with the preposition to exist (21) and that NPNs with complementation can also function as adjuncts as well (22).

The results confirm that, overall, modified and complemented examples are extremely rare. As Table 4 reveals, only 62 examples have a modified second noun. In contrast to thousands of hits without a modifier, this corresponds to less than 1% of temporal NPNs that were found. 12 different noun types take a modifier. Modified examples can be found with four different prepositions, although in the vast majority of cases (54) the preposition is after. In only three examples we find modification of the first and the second noun (see examples in Table 4). Jackendoff’s claim that only the second or both nouns can be modified, never the first turns out to be correct. In none of the examples, only the first noun gets modified.

Post-modification is slightly more frequent with 142 examples. Again, complementation patterns only occur with the prepositions after, by, to and upon and again NPNs with after take complementation most often.

In the corpus, there is only one example in which modification and complementation occur together: day after desperate day of unbroken siege. The extremely low frequency of modification and complementation in this type of binominal constructions highlights their status as constructions with a rather high degree of fixedness. What this means for constructional modeling will be discussed below.

4.1.1 The semi-specified midlevel and why it exists

The corpus analysis presented in section 3 shows that speakers often encounter constructs like day after day, night after night or year after year. Subscribing to a usage-based model of acquisition we assume that the language learners at one point detect formal and semantic similarities between the constructions and abstract a more general schema, namely [CN_sg,time ⁱ after CN_sg,time ⁱ]_Cx.

The question is how many of those semi-specified templates we intend to postulate? The empirical analysis has revealed that 11 different prepositions are being used. This could make us postulate the following templates:

We could position all these semi-specific templates next to each other as sister nodes with horizontal links between them.^[19] However, at the same time, the empirical analysis shows that the first three templates are extremely frequent (14,574 examples) and make up more than 97% of all the examples. Does this mean that only the first three types should be given constructional status? The crucial question is how frequent a construction has to be in order to deserve its own node in the network. For example, only 15 examples of the [CN_sg,time ⁱ for CN_sg,time ⁱ]_Cx type can be found in the sample. Similarly, we have 55 cases with upon and 41 one with on. Is this frequent enough to get entrenched as a separate node in the constructicon? If one assumes [CN_sg,time ⁱ for CN_sg,time ⁱ]_Cx [CN_sg,time ⁱ on CN_sg,time ⁱ]_Cx or [CN_sg,time ⁱ upon CN_sg,time ⁱ]_{Cx ,} they might not be as strongly entrenched as the others. Especially the for template seems unwarranted; still the empirical analysis has shown that minute for minute is a very special combination which stands out. In fact, any template that shows a significant attraction relationship as shown in Figure 3 can be argued to have its own midlevel node in the network. After all, these templates surface more often than what is expected by chance – and crucially irrespective of how frequent they are. Any potential weaker entrenchment can be visualized by dotted lines around the upon-template in Figure 5. Still, a model which allows redundant storage in an inventory-based approach has no problem to postulate 11 or more sister nodes.

Figure 5:

Partial network sketch of temporal NPN constructions.

There is a second modelling solution if one wanted to reduce the number of nodes. With four prepositions, only one example was found (month following month, century through century, decade onto decade, time within time). Although these examples can and should not necessarily be dismissed as ill-formed structures or typos, we see them as creative one-offs which most people may consider odd. Their extremely low frequency motivates the following line of argumentation: It could be argued that constructs like this are not separate nodes but are rather licensed by a more abstract template namely [CN_sg,time ⁱ P CN_sg,time ⁱ]_Cx. Speakers identify semantic and formal similarities and abstract a more general schema with an unspecified P slot over the frequent four, which are presumable also diachronically the older ones.

Once such an abstract template is in place on a higher level (see Figure 5), other prepositions can creatively get recruited (a case of host-class extension).^[20] This template is also able to ‘generate’ the upon, for and on cases. In other words, the template basically takes care of creative extensions and the low frequency prepositions.^[21] This modelling solution is quite elegant, as it reduces the number of nodes. Moreover, it is not unlikely that speakers will become aware of the semantic similarity of the various subtemplates and abstract and schematize an overarching more general meaning of {temporal succession}.

At the same time, we would like to stress that the postulation of this template is somehow problematic. The ‘problem’ we see is that the P slot is completely underspecified which means that in principle any preposition could be inserted by the speakers. Still, we observe that many prepositions are not recruited into the construction at all (e.g., under, behind, in). The postulation of this schema thus licenses constructs which basically do not exist and would be considered ill-formed. This is why one could also argue against the postulation of this mother node in order to explain the lexical restrictions and limitations which clearly exist in this constructional family. That means to simply stop at mid-level and to postulate the existence of many sisters where the preposition is specified. We are in favor of the second solution, even if it is less elegant. Ultimately, however, we are aware that this is a question up for debate, which we have tried to express by the red question mark in Figure 5. One of the crucial questions in Construction Grammar is if it is always feasible, cognitively realistic and necessary to assume the existence of higher, more abstract nodes in the construction. In other words, the question is if (a) speaker(s) – in the case of our NPN templates – abstract to the higher level in the bottom up acquisition process. We will come back to the issue of mother nodes in 4.2; before that, however, we would like to zoom in on the semantics of the semi-specific and the fully specified level.

The postulation of any construction can but should not only be based on frequency, attraction or formal peculiarity. Semantic idiomaticity has always been the strongest argument for the postulation of a construction. In UCCxG, constructions are defined as form-meaning pairings. This begs the question which meaning and discourse-pragmatic function the speakers will assign to the schemas just mentioned and if they are very different from each other. In the case of [CN_sg,time ⁱ after CN_sg,time ⁱ]_{Cx ,} the data analysis (also see the examples in the previous sections) suggests that the semantic ‘pole’ of this construction can be described by {succession of time units}. At the same time, there is a difference between (a) She tries to survive every day and (b) She tries to survive day after day. Every day sounds rather neutral whereas day after day – by iconically reduplicating the temporal noun – foregrounds some intensification, highlighting the aspect of repetitiveness and strenuousness. In the vast majority of examples, the NPN string has a negative touch. The speaker stresses that an action is being performed and repeated in a loop-like manner. Therefore, we argue that the NPN construction expresses some interpersonal stance. As a reaction, we postulate the following form-meaning pairing:

The [CN_sg,time ⁱ to CN_sg,time ⁱ]_Cx is slightly different. In a sentence like She tries to survive day to day, it is possible to assign a similar reading like the one postulated for after, namely {every day/many days in succession}. Often, however, the NPN expresses some kind of temporal transition, in the sense of {from one month to the next month}.^[22] Again, this template often expresses some negative stance:

The preposition by in [CN_sg,time ⁱ by CN_sg,time ⁱ]_Cx, mostly expresses {succession} but somehow foregrounds the procedure of measuring/scrutiny. Using this template does not express annoyance or any negative stance compared to the other templates (Computers track each operation second by second/ hour by hour/ day by day).

It would go beyond the scope of this paper to discuss the meanings of all templates in detail; the three examples suffice to show that the prepositions can often be used synonymously but some semantic interpretations are restricted to a particular preposition. This is why one simply cannot ‘delete’ the semi-specific level to increase the model’s efficiency or to avoid redundancy. In other words, the network cannot ‘work’ with only a [CN_sg,time ⁱ P CN_sg,time ⁱ]_Cx node.

The semi-specified level also helps the construction grammarian to show that the construction has certain lexical biases (not all prepositions and nouns are productive; see Figure 4). Speakers keep track of those statistical biases (Goldberg 2019; Hilpert 2014; Stefanowitsch and Gries 2003). Studies have shown that speakers retain a highly detailed record of linguistic usage events in memory. Similarly, we have also shown that the different prepositions attract different nouns. The postulation and concreteness of the lower levels in the network mirrors this psychological reality. Finally, the semi-specific level helps in modelling because it subsumes all the fully-specified constructions below it. This relates to another issue, which shall be discussed with the help of the day to day example.

4.1.2 Peculiar daughters: the fully specified level

In the case of day to day, we could argue that all the found examples are licensed by the [CN_sg,time ⁱ to CN_sg,time ⁱ]_Cx node. For instance, in example (28), where the NPN functions as an adjunct, the meaning of the construction can be described as {from one day to the next day}.

This semantic interpretation is supported by the fact that in 366 examples, day to day is preceded by the preposition from.

In all those cases, it is safe to assume that the construct is either licensed by the [(from) CN_sg,time ⁱ to CN_sg,time ⁱ]_Cx template or even another construction [from N to N]_Cx (from January to March, from morning to evening, from paragraph to paragraph, from London to New York, …) (Zwarts 2013).

However, in the following examples the meaning of day to day is very different:

In example (30), day to day functions as a subject complement with the following semantics: {unstable as a player}. In example (31), day to day means {every day/daily}. In example (32), day to day means {daily routines}, a semantic interpretation which is triggered by its usage as a nominal head in a noun phrase. In all these cases, it is necessary to postulate the existence of a polysemous, fully-specified [day to day] construction with very idiomatic behavior that is not inherited from the higher levels. This [day to day] construction – following the current conventions of CxG modelling – is positioned on the lowest level of the network (see Figure 5). In contrast, the {from one day to the next day} reading is the default and is stored in the [CN_sg,time ⁱ to CN_sg,time ⁱ]_Cx node.^[23]

Also, from a quantitative point of view we have good arguments for the existence of these low-level nodes. In our preposition-specific collostructional analysis (synthesized in the collostructional graph in Figure 4), we clearly see that for a given noun not all prepositions function as productive attractees. For example, even though [hour P hour] can be argued to have a mid-level node in the construction network (as argued in 4.1.1), there is no empirical evidence for a low-level node [hour on hour]. This is because hour and on do not show a robust attractor relationship in Figure 4. In contrast, hour and after (as well as by and upon, respectively), for example, do show such a relationship: within [hour P hour], after surfaces as preposition significantly more often than expected by chance. This renders the existence of such a low-level node plausible.

Note that again a diachronic aspect can be integrated here. It is quite plausible that these low-level constructions with their specific, non-compositional meaning developed later in time,^[24] after the establishment of other, more abstract templates. Thus, we can assume a case of network reconfiguration at one point, where new expressions are constantly added to the construction.

In a usage-based approach, following Goldberg’s (2006) definition of what a construction is, also high frequency warrants the postulation of a separate node. As was already discussed in section 3, year after year or day after day despite being quite transparent and compositional in their meaning, deserve constructional status as fully specified, frozen chunks on the lowest level due to their high frequency and attraction strength (see Figure 5).

4.1.3 More complex templates: modification and complementation

Let us now briefly return to the cases with modification and complementation.

In the introduction, we asked whether constructs as in example (33) should make us schematize the following template with optional modification slots: [(ADJ_mod) CN_sg,time ⁱ P (ADJ_mod) CN_sg,time ⁱ (of X_compl)]_Cx. In other words, should all of our templates postulated so far be extended by these optional slots? We argue against this modeling strategy. The empirical analysis has shown that modification and complementation are very rare in NPN constructions (see section 3.2.3). Postulating optional modifier slots disregards the rather frozen character of the constructions. An extended template somehow suggests a high degree of compositionality which many of these constructions do no longer have. We believe that only in the case of after and perhaps upon and by, an additional extended schema makes sense. For example, something along the lines of [(ADJ_mod) CN_sg,time ⁱ after (ADJ_mod) CN_sg,time ⁱ (of X_compl)]_Cx.

Related to this extended template, two open questions are left for future research. The first one would be how and if such a template is connected to and inherits from a default NP template [DET + ADJ + N + Comp]_Cx. The second question relates to the scope of the adjective and how we can express that any modifier or complement is interpreted across the board, in the sense that every day is day of unbroken siege which is desperate.