From their point of view: the article category as a hierarchically structured referent tracking system

2.1 The geographical spread and historical emergence of article systems

The grammatical category of articles is rather uncommon from a typological perspective. Dryer (1989: 86) reported, based on a survey of 399 languages, that only 125 or about a third of the languages in his sample had articles. More strikingly, only 31 or 8 % of all languages surveyed, were found to have both definite and indefinite articles. Globally, the definite article is more widespread than the indefinite article: out of the 620 languages surveyed for the WALS, 377 had a definite article of some kind (Dryer 2013). A language that has a definite article is very likely to also have an indefinite article, yet the converse does not hold (Heine 1997: 69): only 45 languages in the sample had an indefinite article but no definite article of any kind. Most of the languages that have both definite and indefinite articles are geographically clustered in Europe and in Western Europe in particular.

The fact that the definite article is more widespread than the indefinite article has been taken to indicate that definite articles emerged earlier than indefinite articles (De Mulder and Carlier 2011). Overall, the grammatical category of articles is a relatively “recent” phenomenon: its origins only date back to the 11th century. The emergence of an article category has been attributed to the loss of case and aspect systems in early Germanic (Leiss 2000), which offer alternative ways of expressing definiteness. Interestingly, a common grammaticalization process seems to underlie the formation of the article category: in most cases, the definite article traces back to a (weakened) demonstrative while the indefinite article developed from the numeral one (De Mulder and Carlier 2011). Sommerer (2018) sketches, for English, how the definite article the emerged in Late Old English from the dependent usage of the demonstrative se (se was also used independently as a complementizer or pronoun such as that, which, who); due to the length of its existence, it is more grammaticalized. Next, the indefinite article a developed from the numeral one in Middle English, and was applied to singular count nouns only, with non-counts and plurals not requiring an overtly marked article. Due to the fact that it is not overtly marked, the emergence of the zero article is more controversial (see Sommerer 2018: 59 for details). It can be argued that it appeared in Old English as a contrast between a marked definite and an unmarked indefinite or that it correlates with the emergence of the obligatory marking of indefinite a in Middle English. In present-day English, the indefinite remains unmarked for plural and non-count nouns.

2.2 Articles as a referential category: from world to discourse

In English, and many other European languages, articles are often considered part of a larger category of determiners which also contains demonstratives and various other words that occur in the same position within noun phrases (Dryer 2013): articles are typically not found when another determiner such as a possessive, demonstrative, distributive or quantifier is present (De Mulder and Carlier 2011). Determiners constitute a core part of the referential system of a language and are used to express the reference of a noun used in context. In English, demonstratives typically express the relation of the nouns they modify to the speaker. For example, demonstrative this indicates relative closeness to the speaker while that signals relative distance from the speaker. Possessives likewise take the speaker as source, with different determiners referring to the speaker (I), the addressee (you, singular and plural), combinations including both speaker and addressee (we) or agents remaining outside of the conversation (his/her/their). It is unsurprising, then, that with few exceptions, articles have been interpreted from that same vantage point.

Within philosophy and the philosophy of language, much work on referring expressions sits within the discussion of denotation and revolves around the notion of presuppositions or the assumptions a speaker makes about a listener’s knowledge. Definiteness, which includes the definite article the, has attracted the most attention (but see Burton-Roberts 1976). In philosophy, it was long thought that the notions of existence and/or uniqueness held the key to the appropriate use of definite descriptions and that they required reference to an entity in the real world (Russell 1905). Strawson (1950) moved away from real-world reference, thus reflecting the start of a pragmatic turn. This turn was further strengthened by work in psychology on audience design (Clark and Murphy 1982) which highlighted the importance of taking into account the knowledge of the hearer in encoding and resolving reference. Clark’s (1996) notion of “common ground”, or “the sum of [two people’s] mutual, common or joint knowledge, beliefs, and suppositions” took hold in linguistics. Later, in philosophy, Roberts (2003: 288) argued that the presupposition alludes to the information available to the discourse participants rather than to the world. Hence, use of a definite Noun Phrase (NP) presupposes a familiar discourse referent that is unique among the discourse referents; familiar here does not require previously mentioned but merely entailed by the context of interpretation. The latter is illustrated in (1) from the BNC: the use of the before local estate agency indicates that the speaker assumes that the addressee is aware of the existence of said agency.

Linguistics, long dominated by Structuralism,^[1] likewise welcomed the focus on definiteness: the could be considered as the marked member of a privative opposition. Seeing articles as a privative opposition between the active, marked the and the inactive, unmarked a would have encouraged the search for an invariant meaning of the, bypassing the larger discourse situation. Crosslinguistically, articles have been said to encode definiteness (for an overview see Kibort 2008). The linguistic interpretations of definiteness can be classified as based on either familiarity (Christopherson 1939, elaborated by Kamp 2013; Heim 1983) or (unique) identifiability (for a definition of uniqueness see Kadmon 1990; for identifiability see Chafe 1976 or DuBois 1980 or Lyons 1999; for unique identifiability see Givón 1984 or Hawkins 1978). Clark’s (1996) notion of “common ground” operationalized Chafe’s (1976) sense of the importance of the speaker’s conception of what their addressee knows, and the idea of shared knowledge also runs as a red thread through Lambrecht (1994). Note that in linguistics, too, reference is to the discourse: real-world reference is not required (for discussion see Langacker 1991: 97–98).

(Unique) identifiability and familiarity are not equivalent (Birner and Ward 1994: 96–97): (unique) identifiability requires the referent of the Noun Phrase introduced by the to be the only entity of that type within the discourse and uniquely identifiable to the hearer, while familiarity requires only that the referent of the NP introduced by the has already been introduced into the discourse (Kadmon 1990: 274, 279; Birner and Ward 1994: 93; Epstein 2002: 336). Although most contemporary approaches to definiteness opt for either uniqueness (Abbott 1999; Hawkins 1978; Kadmon 1990) or familiarity (Chafe 1976; Green 2012), very often, identifiability and familiarity apply simultaneously: entities that are part of the discourse are identifiable, as in (2) below, where speaker and hearer both know there is a garage and that there is only one in that location, which makes it the only possible referent.

It has also been argued that neither property alone can account for all acceptable uses of the definite article (Birner and Ward 1994: 101; Farkas 2002; Roberts 2003; Schwarz 2013): familiarity would be neither necessary nor sufficient (the can refer to an unfamiliar entity as long as it is uniquely identifiable) while unique identifiability is sufficient but not always necessary (the can be used when the entity is believed to be uniquely identifiable). In Example (3) below, the hearer does not need to know about these theme parks beforehand because the description around the head noun makes the entity identifiable.

2.3 The learnability of the English article system: the tandem of identifiability and familiarity

Different from work in the logical-philosophical and linguistic traditions, which has focused on referential the, studies exploring how mastery of the article system emerges in L1 and L2 have to account for the whole range of uses of the article system. For this purpose, acquisitional approaches have typically relied on a combination of (unique) identifiability and familiarity, and more specifically on a re-interpretation of these concepts as Specificity of the Referent (SR) and Hearer Knowledge (HK). Crucially, these two core concepts have been treated as existing on par. This is also the case in Huebner’s (1983, 1985 so-called semantic wheel, which is one of the most widely used models for classifying noun phrase environments in English article acquisition studies. The two properties, HK and SR, can be present or absent, yielding the four basic types shown in Table 1 (cf. Thomas 1989). The types are not intended to give an exhaustive picture of article use in English but capture the major environments relevant to article use. Note that, except for Type 2, all types allow at least two articles; which of the allowed articles will be used is co-determined by the lexical properties of the noun, i.e., singular or plural, mass or count.

Importantly, these four basic types map neatly onto the major categories used in studies from the logical-philosophical and linguistic traditions. As discussed in Section 2.2, in linguistics, referentiality has been key. However, while most attention has gone to the study of definite reference and its interpretation, the categories of indefinite and generic reference likewise exist, as does non-referentiality. The focus of the acquisition literature on how the article system, in all its complexity, is mastered, has ensured a more balanced treatment of the four categories. This more balanced treatment of the article system, alongside the focus on acquisition or learning, makes the variables HK and SR excellent candidates for use in the current study in which learnability plays an important role.

The acquisition of referential systems, and of the article system in particular, has attracted quite some attention in the community of researchers working on first language acquisition, indeed. Brown (1973) was the first to document the development of article use (among other morphemes) in non-elicited spoken English longitudinally and showed that the number of errors children make is very low, and all involve specific referents: children erroneously used a for specific referents that were known to the hearer and the for specific referents that were unknown to the hearer. Early experimental studies were aimed at further assessing children’s understanding of the presupposedness of referents, i.e., Hearer Knowledge. Work by Maratsos (1976) and Warden (1976) confirmed that the most typical error stems from using the definite article when the referent is specific but not known to the hearer. This data was later reused by Cziko (1986) to test and support Bickerton’s (1981, 1984 language bioprogram hypothesis (LBH), which states that children are biologically programmed to make the specific/non-specific distinction (Referent Specificity). This would explain why children would initially only correctly use the in cases where the entity is specific and presupposed and a in cases where the entity is specific but not presupposed. Yet, data collected by Karmiloff-Smith (1979), who studied French-speaking children between the ages of 3–11, revealed a U-shaped pattern of development, where children start off with relatively accurate usage across the board, then move through a phase with many errors, before returning to accurate usage.^[2] The notion of Hearer Knowledge appears to be the one that poses the most conceptual difficulties to learners and is the later of the two to develop, but it does start developing earlier than LBH would predict. For a recent discussion of the relation between Hearer Knowledge and Referent Specificity and how they impose bounds on variability, see Romain et al. (in press).

Yet, different from what we observe in L1, Hearer Knowledge and Referent Specificity do not seem to be sufficient to explain the use of articles to L2 learners whose L1 lacks articles (Ionin 2003; Trenkic 2008 and later work). For example, recent work by Shin and Kim (2017) summarizes that the is overgeneralized to contexts where the indefinite article is required; that L2 English learners also overuse a/an in definite contexts; and that those L2 English learners whose L1 does not have an article system tend to avoid using articles altogether. This comes as no surprise since few grammars rely on Hearer Knowledge and Referent Specificity (see also Trenkic 2000: 25) and those that do rely on these concepts do not clearly distinguish between the two. For example, the British Council (LearnEnglish) states that the should be used when the speaker and hearer know what they are talking about or can identify the referent and a when this is not the case. Authoritative grammars such as Greenbaum (1996) and Biber et al. (1999), instead, rely in the first instance on countability to differentiate between the and a, and HK takes second place: the is used when the noun phrase is assumed to be known to both speaker and hearer. Interestingly, Lyons (1999: 2–3) does make a distinction between the, used when the referent is assumed to be clear to both the hearer and speaker and a, used for a specific referent which is unknown to the hearer.

To remedy the problem, alternative accounts of article use have developed. Master’s (1990) model of the English article system is one such account that has been subjected to classroom-based testing. Instead of relying on (assumed) Hearer Knowledge, known as Definiteness in his models, and Referent Specificity, Master proposed a binary, hierarchical system that collapses these features into one, and contrasts Identification (the) with Classification (a, zero). In a sense, this approach acknowledges the natural alignment and predominance of [Def+ Spec+] and [Def− Spec−] and promotes the primacy of Definiteness over Specificity for pedagogic purposes; we will return to this point in Section 6.3. While entities that are identified always take the, for entities that are classified, Countability and Number play an important role in distinguishing between a and zero: countable singular nouns take a, while countable plural nouns and non-countable nouns take zero. Within the subgroups, further semantic distinctions are considered that function as rules for article use, such as first mention (a) versus subsequent mention (the) and defining (a) versus limiting (the) post-modification.

2.4 From identifiability to accessibility

Cognitive-linguistic accounts of article use highlight one possible reason why explanations fail in L2: although most accounts do focus on Definiteness, they emphasize Reference and Identifiability at the expense of human cognition, and the dynamic relation between speaker and hearer in discourse in particular (Hinenoya and Lyster 2015: 398).

Chafe (1976: 54) insisted on the importance of what the speaker assumes the addressee to know or be aware of: the speaker chooses from different ‘packaging statuses’ “on the basis of his assessment of what the addressee’s mind is capable of at the time”. Continuing this idea, and expressing it in terms of the storage metaphors for memory which were prevalent at the time, has led to referential systems being likened to file-card systems (DuBois 1980: 210). “For every indefinite, start a new card. For every definite, update an old card.” (Heim 1983: 168). It has, indeed, been argued that grammatical reference is not even about reference to an entity that exists in some world but about reference to a memory trace (Ariel 1988, 1994; Epstein 2002; Givón 1992). In this tradition, Ariel (1994) promoted “accessibility” instead of identifiability as defining feature of a referential system: the definite article marks that the discourse referent is accessible and can be interpreted with the information available in the discourse context. It is the task of the speaker to choose an appropriate referential expression and the task of the hearer to identify the intended mental representation that corresponds to that referring expression (Ariel 1994: 38).

The reference to memory plays a crucial role in the historical development of the article category. König (2018: 169) describes the stages in the development of definite articles. In cataphoric use, identification is possible due to sufficient description. In anaphoric use, identification is supported by the preceding context. The change to recognitional reference or emploi mémoriel (4) and then associative reference (5) involves a major change in the type of context required for identification: there is a shift “from an external, situational or textual context to a more abstract context of association, of memorizing or of general availability in a universe of discourse”. Associative use, typically the last to appear historically, is often regarded as the crucial step in the development of a definite article, since this use is not available for demonstratives (König 2018: 173–174).

Epstein (2002: 371) takes this idea one step further and, following Fauconnier (1994), casts the accessibility of nouns introduced by the in terms of Mental Spaces. Like Givón (1992), he considers the definite article as a mental processing instruction that triggers the processing procedure by which discourse referents are accessed, but the definite article is a marker of low accessibility: it signals “that the means for interpreting the NP in which it occurs is available somewhere in the configuration of mental spaces, as long as the appropriate spaces, elements and connections – i.e., the access path – can be constructed by the addressee.” On this approach, listing the meanings of the becomes futile: the definite article indicates that the referent of the NP should be processed as accessible information. The exact interpretation is not specified by the grammar but determined by the context (Epstein 2002: 368).

As attractive as it may sound, this high-level specification of the function of the provides little guidance for the correct use of articles in context; as we saw in Section 2.3, grammatical restrictions associated with the historical origins of the articles still apply. For this reason, we examine a variety of variables proposed in the literature, with specific emphasis on variables used across studies of the development of article usage in L1 and L2: this ties in with our interest in the role learnability plays in the emergence and maintenance of linguistic systems. We aim to determine which dimensions of the linguistic and extra-linguistic experience are important for the correct usage of articles, whether and how the relevant dimensions interact, and how their interaction affects learning.

4.1 A classification tree

The classification tree for the article data, based on all variables presented in Section 2 above,^[4] is presented in Figure 1. Each split in the tree is labeled with a decision rule. Before determining the rule at each node, the algorithm inspects several predictors and selects the one that is most useful; in this case, the best prediction results were obtained if two variables were considered at each split. The algorithm does not look ahead, however, and cannot consider decisions that would yield a slightly worse split locally but would do significantly better globally. This is known as a greedy approach.

Figure 1:

Classification tree based on manually annotated discourse chunks extracted from the BNC, excluding set phrases and nouns that have no number.

The first node (in the oval) in this tree is based on Hearer Knowledge. The accompanying p-value indicates that articles are well separable if we know whether the item referred to was or was not (presented as) known to the hearer. Hearer Knowledge thus plays a crucial role in distinguishing between the articles: Hearer Knowledge is found highest up in the tree, executing the first split.

The search for the locally best-performing splitting criterion is now repeated for the remainder of the data. At each next branch, a new decision rule is presented that directs us further down the tree past increasingly purer nodes. In cases where Hearer Knowledge is not assumed, the property that comes into play next for splitting the remainder of the data as best as possible is Number. If the noun is plural, we are led to a terminal leaf node of 184 items where zero is the article of choice, with few exceptions. But if the noun is singular, further properties come into play. If the singular noun is a count noun, we are led to another terminal node of 587 items where a is the article of choice, with few exceptions. If the singular noun is uncountable, elaboration plays a role (albeit with p = 0.025 this split is the least reliable of all splits): in the 50 cases where the elaboration follows the noun or is absent, zero is the preferred choice; in the 40 cases where the elaboration precedes or both precedes and follows the noun, the choice is divided between zero and a, in a 70/30 split.

The other side of the tree captures the situation in which Hearer Knowledge is assumed. If a noun is (presented as) known to the hearer, Referent Specificity plays an important role in further categorizing the data. If the noun has a specific referent, we are immediately led to a terminal leaf node (613 instances) for which the article of choice is the. If the referent of the noun is not specific, however, we are led down a more complicated path via Countability and Number: if the noun is uncountable and plural, we arrive at a terminal node (7 instances) with the as the preferred choice, but if the noun is uncountable and singular, only 30 % of cases get the, and zero is preferred. If the noun is countable and singular (105 instances), the is strongly preferred, whereas if the noun is plural (72 instances), Corpus plays a role: in the Written corpus, about 80 % of cases are marked with zero, while the other 20 % gets the, while in the Spoken corpus, the proportions are inverted. We will come back to this observation in Section 4.2.

All in all, the tree correctly classifies 94.6 % of all instances, scoring 356/411 for zero articles, 569/587 for a articles and 749/770 for the articles (Table 3). This is three times as good as randomly choosing, which would yield 1/3 correct.

Moreover, in our tree-based model all three articles are most often predicted correctly, i.e., the highest values are on the diagonal in the table, signaling that the classification accuracy is good for all three articles. That being said, the zero article is slightly less well predicted than the two other articles. Yet, incorrect classifications are also revealing. Instances of zero that are incorrectly predicted are most often predicted as the, while incorrect predictions of the and a are typically predicted as zero.

A single tree is likely to overfit the data, however; growing a forest based on resampling mitigates against this risk. On our data, a random forest of 500 trees reaches a very similar correct prediction rate of 94.57 %. These results are outstanding, with only 13.4 % of all zero instances (55/411), 2.7 % of all the instances (21/770) and 3.1 % of all a instances incorrectly classified (18/587). Details are provided in SupMat_3.

On the basis of the forest, the importance of each variable can be calculated. Using random permutation of the labels of each variable, the relative importance of the different predictors for the classification accuracy of the model is assessed. The result is shown in Figure 2 where the left panel reveals that Hearer Knowledge is the strongest predictor by far:^[5] if removed, there is an 81.8 mean decrease in prediction accuracy (i.e., the mean difference of error rates in standard units). HK is followed by Number, the removal of which would trigger a 65.9 decrease in prediction accuracy, and by Count which would trigger a 51.5 decrease. Removing Referent Specificity reduces prediction accuracy by 26 only, while removing Elaboration and Corpus reduces the prediction accuracy by 10.6 and 11.2 respectively. In other words, Elaboration and Corpus are “fine-tuning variables” (Divjak 2015) and taken on their own do not contribute much to the correct classification of articles in use. For a discussion of the Gini values, displayed in the right panel, see SupMat_3.

Figure 2:

Mean decrease in classification accuracy per removed variable.

4.2 Interpretation

Overall, the picture that emerges from the classification exercise reveals that the situation becomes simple when we move away from referentiality and let Hearer Knowledge occupy the dominant position. The fact that Hearer Knowledge comes out as the single strongest predictor by far and that Referent Specificity turns out to be a rather unreliable predictor is unexpected given the literature on article usage, surveyed in Section 1. Although accounts of articles tend to mention the hearer, the hearer is not typically their primary concern. Rather, work across philosophy and linguistics has attempted to pin down the meaning of the concept “definiteness” within the framework of referentiality; this has led “definiteness” to be interpreted as (uniquely) identifiable, which is easily re-interpreted in terms of specificity.

If the referent is (presented as) known to the hearer a choice needs to be made between the (787 cases) and zero (118 cases), with very little option for a (2 cases). In other words, the is the default in the case of HK+, as in (9a). For zero to be used if the referent is (presented as) known to the hearer, the referent cannot be specific (i.e., it needs to be SR−), and the noun needs to be either uncountable singular (9b) or countable plural (9c).

If the referent is (presented as) unknown to the hearer a choice needs to be made between a (582 cases) and zero (271 cases), with no option for the (8 cases). In this case, a can be considered the default (10a). For zero to be used if the referent is (presented as) unknown to the hearer, the noun needs to be either uncountable singular (10b) or plural (10c). This restriction follows straightforwardly from a having developed from the numeral one: one can only be used with singular, countable nouns.

In other words, Hearer Knowledge is a very powerful predictor of article use and the default for either of its values (presence or absence of hearer knowledge) is overridden in the same way, i.e., by the noun being singular uncountable or plural.

On the HK+ side, within SR−, countable plural nouns prefer zero in written language, as in (11a) but the in spoken language, as in (11b). These could be considered cases of weak definites (cf. Aguilar-Guevara and Zwarts [2010] for a discussion of plural weak definites), where the definite article is used even though the referents are not uniquely identifiable. In spoken language, referents may be more grounded in discourse and therefore more likely to be paired with the definite article.

Also in the case of SR−, the is occasionally retained with uncountable singular nouns, e.g., (12) where the noun phrase does not signal a specific referent but the is licensed by the assumption that mention of wetland plants implies the presence of moisture. In these cases, the referent is not specific per se, but because the referent’s existence can be inferred from the context or because the noun phrase contains some form of elaboration, as in (13), it is considered as known to the hearer and thus may take the.

In the case of HK−, the presence of elaboration can make a acceptable in the case of singular, non-count nouns, as in (14), (15) and (16).

In addition to showing which variables contribute more or less (see Figure 2), the classification also reveals that not all articles are governed by the same variables and that not all variables occupy the same place in the hierarchy for all articles. If the entity is presented as known to the hearer, Referent Specificity is more important than Countability, which in turn is more important than Number. If the entity is presented as unknown to the hearer, however, we see the variables reversed in terms of importance: Number is more important than Countability, while Referent Specificity plays no role.

In sum, our classification approach has revealed major differences in the importance of various available indicators for achieving success in selecting an article for use given the context. It has enabled us to turn that information into a decision tree which helps select the most likely outcome, given properties of the context. Arguably, this approach, which is rooted in probability calculations run post-hoc, once the body of observations is complete, is not how L1 users navigate language. In Section 5, we introduce a different kind of algorithm, rooted in human cognition, to gain an understanding of how dimensions of contexts of use might become associated with an article incrementally, as experience accumulates.

5.1 Error-correction learning

Classification trees and forests may well reveal the complexity and (un)systematicity inherent in the system, but they do not represent a viable account of the hypothesized process by which articles are selected for use. Classifiers do not learn from data the way humans do. Hence the question remains: can real language users learn to master the English article system using the variables we tested in Section 4, and do they assign the same relative importance to each of these variables as the classifier suggested? Learning English articles from a set of simple binary opposites (e.g., known/unknown to hearer, specific/non-specific referent, singular/plural, etc.), generated from a sample of sentences attested in the BNC, represents an interesting language modeling challenge. First and foremost, the statistical classifier suggested that the relationship between cues (variables) and outcomes (articles) is only partly systematic at best. In other words, the set of cues does not map straightforwardly onto the three article outcomes, as the cues differ in both their general importance and in their specificity – in being informative about one or more possible article outcomes. Our computational model will give us the opportunity to observe what gets learned as the dynamics of error correction and cue competition unfold.

To shed light on the mechanisms that drive the learning and maintenance of the English article system, we ran a computational simulation study using an error-driven learning algorithm, the Widrow-Hoff rule (WH: Widrow and Hoff 1960). This rule is, in essence, identical to the one introduced in psychology by Rescorla and Wagner (RW: Rescorla and Wagner 1972; Rescorla 2008). In a nutshell, the rule defines how an organism learns from its own errors in order to adapt to the task at hand. More specifically, the rule learns incrementally, i.e., on an event-by-event basis, to associate the presence or absence of an outcome (here, one of the three articles) with that of the presence of a cue (in this case, one of the variable values, for example, HK+). The rule is incremental (i.e., event-by-event) as it re-estimates connection strengths or weights from each cue to each outcome on each trial, which for us is after each (annotated) sentence. If, over learning trials, a given cue is consistently present when an outcome is present, their connection is strengthened, but if a given cue is repeatedly present when the outcome is absent, the weight on the connection between them is weakened. Since the weights are updated as experience accumulates, over time, some cues become indicative of an outcome, while many become irrelevant; as experience accrues, any systematicity in cue-outcome (re)appearances becomes apparent and it is those systematicities that are learned. The overall support that an outcome gets from the cues, its activation, is the sum of the weights on the connection between those cues and the outcome.

The dynamic re-estimation ensures minimal error against the backdrop of all prior experience, including so-called positive and negative evidence, i.e., evidence of the presence of a particular outcome given a specific cue, but also evidence of the absence of an outcome that could have occurred or would have been expected given a specific cue. In other words, learning continually evolves and is driven by the discrepancy between the current “best guess” and the true outcome. A mismatch between the best guess and the true outcome causes weights to weaken, while matches between the best guess and the true outcome encourage weights to strengthen. What drives the process of learning is the competition between cues to carry weight for matching an outcome. Crucially, cue competition happens organically as cue-outcome contingencies are typically imperfect (see Tolman and Brunswik [1935] for the original proposal, and Romain et al. [2022] for a recent application), especially in language which appears to be the perfect opposite of simple one-to-one, univocal mappings. This constitutes a rich basis for error-driven learning (cf. Baayen et al. 2011; Chen et al. 2008; Divjak et al. 2021; Ellis 2006a, 2006b; Haykin 1999; Milin et al. 2017a, 2017b; Ramscar et al. 2010).

5.2 Computational simulation

For our learning simulation we used the same data as for the construction of the classification tree and forest, described above in Section 3. There were 1,768 events that could take one of three articles, a, the or zero. Each event consisted of specific values for the five variables Hearer Knowledge (yes/no), Referent Specificity (yes/no), Number (singular/plural), Countability (yes/no) and Elaboration (before/after/both/none). For example, the boldfaced sentence in (17) was encoded as indicated in (18), where the article represents the outcome, and the variable values are the cues.

For the current learning setup there are some specifics that need to be mentioned. First, in addition to the 12 cues we have assumed that the type of language, spoken versus written, constitutes a context cue or constant learning background; this essentially means that everything else in the context of learning is considered an undifferentiated whole (i.e., equally informative or uninformative). A constant background is informative about the relative frequency of an outcome (e.g., how many times did an outcome occur overall) as well as about the number of trials on which cue and outcome are not coupled (see background rate: Rescorla 1968). In the present study, the background was implemented as an additional cue that was present on all trials.^[6] Second, the training assumed the learning rate parameter γ = 0.01 which is set in advance and kept constant; this is a commonly used value, small enough to guarantee incremental learning (cf. Enquist et al. 2016; Rescorla and Wagner 1972). Slow or incremental learning is expected to be rather typical for animals and humans, although rapid and/or dramatic changes are known to be possible too. Somewhat simplified, smaller learning trusts accumulated experience that is summarized in the connection weights, while high (er) rates of learning would allow more pronounced changes in those weights (this is tightly related to the Principle of Minimal Disturbance; cf. Widrow and Lehr 1990; Chen et al. 2008; Milin et al. 2020). Third, the order in which examples are presented is important in WH learning. In the current simulation, the order of events was randomized: although the model is eminently sensitive to the order of presentation, we do not assume that anyone would see these examples (which constitute a random sample drawn from the BNC) in the order in which they occur in our dataset.

5.3 Interpretation

The learning process is visualized in Figure 3 which displays how the grammatical category of English articles would be learned from exposure to naturalistic data, enriched with those properties that have been proposed in the literature as governing article usage. Each of the panels represents an outcome, zero (left panel), a (middle panel) or the (right panel). The variables are contrastively color-coded, with all values per variable encoded in different shades of the same color, e.g., Known to Hearer is shown in light blue while Unknown to Hearer is pictured in dark blue. Cues above the zero line are positively associated with the outcome, while cues below the zero line are negatively associated (dissociated from) with the outcome.

Figure 3:

Computational simulation of learning the English article system from a sample of authentic sentences with an incremental, error-correction learning algorithm. Left panel: learning of the outcome zero; middle panel: learning of the outcome a; right panel: learning of the outcome the.

Across the three articles, we observe different types of learnability dynamics. The exact values of the weights, registered at each quartile of training, are given in SupMat_6.^[7]

The article the shows a specific learning profile: one cue stands out as strongly associated (Known to Hearer) at 0.44 and another one as strongly dissociated (Unknown to Hearer) at −0.33. The second strongest positively associated cue, Countability, stands at 0.15 having started off at 0.12, followed by Specificity of the Referent, which starts off strong at 0.19 but ends up at 0.13; the opposite values, Non-Specific and Uncountable, show the same pattern at the negative end. The trend lines for most other variable values are parallel and remain flat throughout the training.

The article a shows a different profile: three cues are relatively strongly associated with a and their opposites are relatively strongly dissociated from a. These are, in order: Unknown to Hearer (0.34, and −0.28 for Known to Hearer), Singular (0.25, and −0.19 for Plural) and Countable (0.19, and −0.13 for Uncountable). The remaining cues show some association or dissociation initially but return to zero halfway through the training, i.e., they become irrelevant.

The learning profile for the zero article resembles the learning profile for a in that more than one cue stands out from the rest; these are Uncountability (0.35) and Plurality (0.32), followed by Non-Specificity of Referent and Unknown to Hearer (both around 0.17). Here too, some of their opposites are negatively associated with a; these are Countable (−0.15) and Singular (−0.12). Different from a, many cues develop a weakly positive association with the zero outcome (values ranging from 0 to 0.10). Interestingly, the two properties zero is best learned from, Plurality and Uncountability, are not exclusive to zero: they are strongly negatively associated with a and weakly positively or negatively associated with the.

In other words, each article has a different learning profile. While the is characterized by one strong cue for and against, a relies on three cues for and against, while zero adds a large number of weakly positively associated cues into the mix. Moreover, the learning simulation confirms that the relevant dimensions of experience intersect: not all articles are learned from the same properties, and not all properties are equally important for all articles. For the, learning is dominated by Hearer Knowledge and being known to the hearer is the strongest cue for the. This variable is also important for the article a, but here being unknown to the hearer is the requirement. In addition, Number (singular) and Countability (countable) play important roles for a too. The tree & forest model suggested that the zero article competes with both a and the. It shares some core properties with a, but requires different values: Number (plural) and Countability (uncountable). The same is the case for its relation with the with which it shares its dependence on Referential Specificity but zero requires non-specificity rather than specificity.

In drawing parallels between the results from a well-known statistical classifier such as the tree and forest model and a simple error-correction model it is interesting to note that they yield highly comparable results. The fact that the hierarchy of variables, reflecting their importance, is virtually identical across both models speaks to the reliability of our learning algorithm. However, in our learning simulations, the hierarchy emerges organically as iterative error correction proceeds: quite rapidly, Widrow-Hoff (Rescorla-Wagner) develops a strong taste for associating hearer knowledge (HK+) with the definite article; less rapidly, hearer knowledge (HK−) gets associated with the indefinite article and number (singular) and countability (countable) with the zero article, while some cue-outcome associations appear promising initially but later on lose their appeal (such as SR for the), and others never really develop. These insights into the process are added by incremental learning algorithms, while classification models highlight the end result. Furthermore, and different from a statistical classifier, our error-correction simulations reveal what happens for each individual article: rather than averaging the importance of a variable for all outcomes, our learning algorithm lets us observe how individual variable values relate to individual articles. This resolves the challenges that (multi)-collinearity so often poses in linguistics since language is redundant by design. Widrow-Hoff and related algorithms are particularly resilient to these issues (for details see Widrow 1959; Widrow and Hoff 1960). In addition, the learning algorithm shows how the relationship between a variable value and an article develops over time, as more examples are encountered. The opportunity to observe the development of a cue-outcome association and the speed or rate with which it develops is a distinct advantage.

6.1 Articles as a hierarchically structured, learnable grammatical system

Based on the five dimensions, Hearer Knowledge, Referent Specificity, Number, Countability and Elaboration, a statistical classifier achieved a correct prediction rate of over 94 %. Crucially, to achieve this result, the core dimensions need to be seen as hierarchically ordered rather than being of equal importance and Hearer Knowledge needs to be promoted to first position in that hierarchy: Hearer Knowledge is the variable that, on its own, achieves the highest classification accuracy. It distinguishes reliably between the which is the default in the case of HK+, and a which is the default in the case of HK−. To understand how these defaults are overridden to make way for the zero article, other variables need to be brought into play, i.e., Referent Specificity, Countability and Number. These variables hold different degrees of importance depending on whether hearer knowledge is assumed or not: in the case of HK+, the next important variable is Referent Specificity, followed by Countability and Number. But in the case of HK−, the order is reversed. Interestingly, the historical emergence of the article system remains visible: the default for HK− is a, but a requires singular countables; other cases are handled by zero. Elaboration plays only a minor, fine-tuning role in our model.

Simulations with a computational algorithm that implements how humans learn from data show how the English article system would be learned using these key variables or cues. The simulations reveal the intricate relationships between the dimensions that govern usage of the different articles and point in the direction of different profiles: different subsets of variables and different variables values act as positive or negative cues for different articles. While the use of the is largely determined by Hearer Knowledge, the use of a hinges additionally on referent non-specificity and entity countability. The zero article, however, requires a different subset of variables, i.e., plurality, uncountability and non-specificity of reference. Crucially, not all outcomes are learned from equally good cues: while the is characterized by one strong cue for and against, a relies on three cues for and against, while zero additionally adds a large number of weakly associated cues into the mix. Interestingly, both the classification and simulation analyses show that usage of the zero article is the hardest to capture. This is unsurprising given its historical origins: the zero article does not stem from an older, specific form but instead appears to have collected any contexts a and the could not lay claim to.

Based on these findings, we argue for the grammatical category of articles to be considered a hierarchically structured, hearer-focused communicative device: the category presents itself as a grammaticalized referent tracking system that catalogs knowledge for the benefit of the hearer. This is not all surprising since, as argued by Hopper and Traugott (2003: 231), grammaticalization is motivated by the interaction between speaker and hearer where the speaker aims to make communication as informative as possible for the hearer (cf. also Sommerer 2018: 258). Fascinatingly, the historical origins of the English articles shine through in this hierarchy: the grammatical constraints appear lower down the hierarchy, supporting the now dominant discourse functions, the further the articles have grammaticalized, while the unmarked article soaks up what does not fit with the historical origins of a/the. We will unpack this proposal in the following sections.

6.2 A hearer-focused referent tracking system

It has been suggested that, in Germanic, articles started to emerge in response to the erosion of the case system (Leiss 2000), which offers different, and more limited, ways of expressing definiteness. Yet, the article system in English, as we currently know it, differs from the case systems we still observe in the Slavonic languages: while cases encode relations between participants in an event, articles (now) appear to encode the relation between the information shared by participants in a discourse situation. The system that falls out from our data is guided by Hearer Knowledge: each value of the HK variable has a default value, with HK+ characterized by the use of the and HK− typified by the presence of a. Each default value competes with zero, and any overrides of the default rely on specific values of Referent Specificity, Countability and Number.

Rather than seeing the use of the definite article as speaker centered (Epstein 2002: 371), we see the article category in its entirety as a hearer-focused system, powered by the speaker. Being a referential grammatical category, the article is obligatorily expressed with every noun and allows the referents of nouns to be tracked in discourse. According to our data, it is the speaker’s task to mark the status of the referent of each noun they use for the hearer: for every noun, the speaker reminds the hearer of whether or not the speaker assumes the referent of that noun to be known to the hearer.

Reference tracking, a procedure whereby languages allow participants to be tracked from clause to clause, is well-attested across languages (Comrie 1999; Foley and Van Valin 1984, 1985, 1985; Haiman and Munro 1983; Stirling 1993), yet has mostly been studied for languages with predominantly oral traditions. Often, the reference marker is a free or bound morpheme. An example is possessive suffixes that are used as subject trackers in some Siberian dialects: in spontaneous narratives, the referents can have been mentioned 6–7 speech turns earlier, which translates into 10–15 s of memory time (Florian Siegl, personal communication, January 2017). These numbers are reminiscent of known limits on working memory. Despite the controversy, there is agreement that working memory is a short time memory system with limited capacity: information is held for somewhere between 15 and 30 s unless it is continually refreshed (rehearsed). Information is lost due to interference, i.e., new information that enters working memory displaces the information that was present. By renewing any relevant short-term memory representations, the speaker reduces the processing burden posed on the hearer.

A grammatical article category that marks referent status obligatorily would also facilitate a more efficient memory search. Recall that DuBois (1980: 168) and Heim (1983: 210) talked about “filing cards” with indefinites requiring “a new card”, and definites requiring updating of “an old card”. Givón (1992) proposed that the grammar of referential coherence is about retracing information from episodic memory. The article system could indeed be seen as a signal to the hearer to retrieve information from memory and more specifically, to specify whether they should retrieve the entity from semantic or episodic memory. Semantic and episodic memory are two types of long-term memory systems that differ according to the information type they hold: semantic memory stores general facts while episodic memory contains memory for personal facts. If the entity is marked as known to the hearer, the hearer knows they have experience with that particular entity and can rely on episodic memory for more detailed information. If the entity is marked as unknown to the hearer, the hearer knows they can only retrieve a generic placeholder from semantic memory, that is, a noun phrase that refers to a concept or a general representation of the entity.

Our proposal shares some similarities with earlier proposals that have put discourse central. Epstein (2002: 371) sees the use of the definite article as speaker centered in that the speaker determines how the hearer should interpret the upcoming NP: the is used to “guide addressees in establishing mental spaces and appropriate connections between the elements in those spaces”. However, our data suggest that this account overestimates the power the speaker has. In our sample, HK (and SR) were annotated with reference to the context, i.e., the values of these variables were checked against the preceding discourse. We found very few “mismatched” occurrences, where the is used although the entity is clearly unknown to the hearer (8 cases) or where assumed hearer knowledge gives rise to the usage of a (2 cases). It appears rather difficult to override the expectations raised by the context, i.e., to choose an article to signal that a nominal referent needs to be interpreted as known or unknown to the hearer if the context does not support this interpretation.

This redundancy of encoding also provides an explanation for the finding that article errors rarely cause communication problems (Master 1997: 216). A series of studies conducted between the 1970s and 1990s explored the gravity (or severity) of various types of grammatical errors (e.g., Ensz 1982; Johnson and Jenks 1994; Magnan 1982; Vann et al. 1984). Strikingly, article errors were perceived as among the least irritating, in both French and English, and across spoken and written forms of the language. During reading, too, the article is frequently skipped, arguably because it is short, frequent and predictable (Angele and Rayner 2013: 649). In fact, articles are skipped 16 % more often than other equally short words (Drieghe et al. 2008) even when they are not predictable from the context, i.e., when they are syntactically unlicensed (Gautier et al. 2000) and regardless of whether they are used felicitously or infelicitously (Angele and Rayner 2013: 654, 656).

It should be noted that even though Hearer Knowledge is crucial in the choice of article and typically encoded in the context, in some cases the context allows both options and the choice of the article indicates the assumptions the speaker makes. Recall Example (1) and compare the use of the in (19) with the use of a in (20). In (19), the indicates that the speaker assumes that the addressee will assume or know both that there is a local estate agency and which one is being referred to (HK+, SR+). If we were to swap the for a, as in (20) the assumption is different, with the agency introduced as a new referent, potentially one of many, in the discourse.

Romain et al. (in press) present results from a 3-alternative forced choice task with 181 L1 speakers of English to determine the bounds on article variability. Their analysis of the properties of the contexts in which alternative construals are allowed versus inhibited reveals that only contexts classified as SR+ restrict construal, with most respondents selecting the same article for usage if the referent is specific.

6.3 Learning to master a hearer-focused referent tracking system

The rebranding of the article category as a hearer-focused system of referent tracking highlights that the challenge of mastering the system not only lies in detecting the relevant dimensions for the use of articles in input; it also requires a specific mindset on the part of the speaker. In essence, using articles correctly requires the speaker to learn to take the hearer’s perspective, to track a referent for their hearer from that perspective, and, at every mention, to express whether that referent has previously been mentioned in or can be inferred from discourse. Which cognitive demands does such a system pose on the speaker?

L1 children have been found to overgeneralize the definite article for use in contexts that cannot be assumed known to the hearer (see Cziko 1986 for an overview). This tendency has been interpreted as evidence for the assumption that children would initially associate the with Specificity of Referent, and stronger even, for the hypothesis that Specificity would be the primary concept, with children long unaware that the article system has anything to do with the hearer (Cziko 1986: 896). In fact, generative linguists have taken the issues children experience with HK, or Presupposedness as they label it, as evidence for the innateness of the category of specificity. It has been hypothesized that the ability to take an interlocutor’s perspective would need cognitive maturation, out of the Piagetian egocentric phase, a phase of “non-differentiation between one’s own and other possible points of view” (Piaget 1951; for an overview see Kesselring and Müller 2011); this starts to happen around the age of 2. Children appear very sensitive to the information they have shared with their interlocutors in discourse from that age onwards, indeed. Matthews et al. (2006) found that children respond to prior mention in discourse as an indicator of referent accessibility from age 2, but it takes them until they are 3 to respond to perceptual availability as an indicator of referent accessibility.

The requirement to track and mark referential status for the hearer may also go a long way toward explaining the challenge the article system poses for L2 learners whose L1 does not include an obligatory article category. As with spatial referential systems (Levinson 1996), the learner needs to figure out that the system is about a speaker marking information for their hearer from the hearer’s perspective. In a sense, the article category represents a grammaticalized version of “audience design” (Bell 1984). Yet rather than it being about how speakers voluntarily tailor utterances for addressees from a stylistic point of view, it is about how the grammatical system forces speakers to tailor reference to their hearer. To do this right, speakers need to inhabit the same discourse reality or knowledge space as (they assume exists on the part of) their hearer and tailor reference from the hearer’s vantage point.

Butler (2002: 472–473) confirmed that adult Japanese learners of English found the concept of Hearer Knowledge the most difficult to grasp. Yet, mastering this concept improves article usage considerably. Hinenoya and Lyster (2015) tested Epstein’s (2002) processing instruction hypothesis in the classroom and found that students who had been trained to engage themselves as speakers in a situation outperformed students who had received explicit instruction of article use in terms of identifiability, familiarity and uniqueness. The typical introduction of HK as definiteness does not sufficiently highlight the importance of the hearer. Master’s (1990) model is the only one that promotes the primacy of hearer knowledge over specificity for pedagogic purposes, but in his terminology too, hearer knowledge is called definiteness, which is typically explained in terms of identifiability, familiarity and uniqueness: the is there to identify, pick out, or individuate the referent so that the hearer can identify what is being discussed (Lyons 1999). Unfortunately, so explained, hearer knowledge is not very different from referent specificity; it comes as no surprise then that L2 learners, too, consider referent specificity as the conceptual driver of the article category and overgeneralize the definite article to first mention contexts because they initially associate the with the specificity of the referent (Huebner 1985; Thomas 1989: 351).

Our corpus study also showed that the information articles convey is retrievable from the context. L2 learners whose L1 lacks articles are used to tracking the referential status of an entity as hearers by relying on contextual information. Moving from an L1 that lacks articles to an L2 that expresses them overtly thus requires shifting perspective from being the hearer who needs to track this information implicitly to the speaker who needs to mark this information explicitly for their hearer. Work on learning helps us understand why this might be difficult: in situations in which a cue is already associated with an outcome, learning to associate a new (and informative) cue with that same outcome is difficult. Overshadowing and blocking explain this phenomenon (originally: Pavlov 1927 and Kamin 1969; for more recent discussions see, for example, Mackintosh [1971], Kruschke [2001]) and Ellis (2006b) has argued compellingly that similar “forces” are at work in L2 learning.

Of course, to some extent, learning to track reference from the perspective of the hearer may require learning the implicit cultural view of what can be assumed as known. This, again, links to the argument that learning, in general, is always contextualized (see, for example, Boddez et al. [2011] regarding the context-dependency of the blocking effect). For language learning, more specifically, the context seems to hold particular importance (for initial discussion see Anđel et al. 2015). Ultimately, proper (cultural) contextualization might turn out to be crucial for the efficient adaptation to a new system and for grasping its fixed and variable parts.

6.4 Reconciling discourse concerns with historical restrictions

So far, we have focused on the article system as a speaker-driven, hearer-focused system of referent tracking. But, of course, Hearer Knowledge is not the only variable at play. The hierarchical system is multivariate, and at least three further variables are needed to guarantee accurate usage, i.e., Referent Specificity, Countability and Number. Yet, the relative importance of these variables depends on whether Hearer Knowledge is presupposed or not. And interestingly, some of these variables encode grammatical properties that link back to the origins of the articles in the demonstrative pronoun or the numeral one.

Once the value of Hearer Knowledge has been established there are two other variables that play a major role. In the case of HK+ this is Referent Specificity, where most instances are the. This is not entirely surprising, as the combination of HK+ SR+ conspires towards an easily retrievable referent, which is close to the origin of the as the demonstrative se (cf. also Langacker [1991:103] for a comparison of the and demonstratives). Specific referents, by definition, can be identified specifically and they could potentially be pointed at: they are one specific entity or a set of entities that are uniquely recognizable.

In the case of HK−, the second most important variable in line is Number. At this end of the spectrum, we typically have something that is unknown to the hearer and plural (or uncountable). This aligns with the potential vagueness of the zero article, which is reserved for plurals or uncountable nouns. When these conditions are not met, and we are dealing with a singular countable item, then a becomes the article of choice. As noted above (Section 2.1), restrictions on using a follow straightforwardly from a having developed from the numeral one: one can only be used with singular, countable nouns. The only instances where an uncountable noun takes a is when the noun is modified (e.g., a willing and prompt obedience), thus singling out a particular type of the concept denoted by the noun.

A note is in order concerning Countability and Number. Both Master (1997) and Butler (2002: 472–473) found that L2 speakers have problems deciding on the countability status of a referent (which, in their view, in turn, affects their judgment of HK). Countability is heavily context dependent, indeed, and many uncountable nouns are sometimes used countably (e.g., That little boy’s having a long sleep, isn’t he?) while mostly countable nouns can also be used uncountably (e.g., It just tastes of ø banana). Number is not necessarily straightforward either. Even for uncountable nouns we find both singular and plural nouns, e.g., clothes is a plural uncountable noun. These may be difficult to identify for learners as they are rather rare, but usually plural uncountable nouns take the plural marking –s. They do require a quantifier to be used as individual referents, e.g., a pair of scissors.

In sum, our findings highlight the need to present the article system as a hierarchical system, governed by Hearer Knowledge. As is typical of many grammaticalized categories, usage is governed by a range of variables, in this case a combination of newer discourse concerns and older morphological restrictions. Correct use of the article system as it currently exists requires the cognitive ability to present information from the interlocutor’s point of view; this discourse demand needs to be reconciled with grammatical restrictions which are found lower down the hierarchy. A comprehensive view of a system exhibiting this level of complexity was made possible by the application of machine learning techniques: while standard statistical classifiers reveal the major trends in the system, algorithms based on insights from learning unveil that not all outcomes are learned from the same cues and that some outcomes need to be learned from amalgams of less stable and interdependent individual cues.