The existence of bidirectional form-meaning associations can be questioned on the ground that there exist production/comprehension dissociations. In particular, when multiple forms are competing to express a meaning, the form most likely to be chosen to express the meaning in production may not be the form that would best transmit the meaning to the listener, i.e., the form that is the best cue to that meaning in comprehension (Kapatsinski, 2012; Harmon and Kapatsinski, 2017; Koranda et al., 2018). Production-comprehension dissociations of this type can even be observed within the same individual. However, the existence of such dissociations does not necessarily imply that the connections between form and meaning are unidirectional.

The basic reason that production-comprehension dissociations are not probative regarding directionality of form-meaning connections is that there is always a reason for choosing a form i.e., not the best cue to the meaning to be expressed. Often, this reason can be incorporated into the network as an additional cue to the form, which contributes to form choice independently of the bidirectional form-meaning connection. To take an extreme example, a bilingual chooses among cognate constructions in part based on how strongly they are activated by the meaning to be expressed, but also based on the language that the listener is likely to understand.

An additional reason for dissociations is the role of form accessibility in production choice. Frequent, more accessible words can be chosen for production over less frequent alternatives even when those infrequent alternatives would be better cues to the meaning for the listener. As discussed by Harmon and Kapatsinski (2017); Harmon (2019), and Smolek (2019), this mechanism can explain regularization and paradigm leveling in language change. Harmon and Kapatsinski (2017) show experimentally that increasing the frequency of a construction in a learner's experience makes the construction's form more likely to be used to express related meanings, and yet makes the same speaker more confident that it does not map onto these meanings in comprehension. For example, learners who experience the constructions N-dan and N-sil paired with multiple large creatures a few times are equally likely to pick multiple small creatures and multiple large creatures in response to either form. However, as they keep encountering N-dan with multiple large creatures they stop selecting multiple small creatures in response to examples of N-dan. They become more confident that “large” is a necessary part of the meaning of -dan (see also Xu and Tenenbaum, 2007). However, they also become more likely to choose -dan to name multiple small creatures. Koranda et al. (2018) also demonstrate this effect in a continuous semantic domain of angles: learners use frequent terms to refer to a broader range of angles although they are more confident about what angle a frequent term actually refers to.

Accessibility-driven dissociations are easily modeled with bidirectional form-meaning connections, as shown in Figure 1. We assume that connections between forms and meanings strengthen when the form is paired with the meaning, that MANY (i.e., PLURAL) is a more salient meaning for an English speaker than LARGE, and that connections between salient cues and outcomes develop faster than connections between less salient ones. When the listener is presented with -dan, s/he knows that it means LARGE rather than SMALL: -dan activates LARGE more than SMALL because it has grown an association with the (initially low-salience LARGE feature). When presented with -sil, the listener activates MANY but has no way to pick between LARGE and SMALL. Because of the initially low salience of LARGE as a feature to an English speaker, the small number of exposures to -sil paired with LARGE has not allowed that connection to develop. As a speaker, the same participant will choose -dan over -sil when presented with MANY SMALL because there is no connection from SMALL to either form, while the MANY-dan connection is stronger than the MANY-sil connection. Thus, production-perception dissociations of this kind are actually predicted by bidirectional form-meaning associations.

A different kind of argument against bidirectionality was presented by Ramscar et al. (2010). Ramscar et al. presented participants with training trials featuring form-meaning pairings, with meanings being visual depictions of novel 3D objects. The crucial manipulation was whether the form preceded the meaning or the meaning preceded the form. The meanings were clustered into six categories, with two categories paired with each of the words wug, tob or dep. There were salient non-discriminative visual features that distinguished subcategories paired with the same form, but were shared between forms, and therefore would not allow the learner to predict the form from the object. There were also non-salient discriminative visual features that defined only one of the subcategories paired with a form but were not shared between forms, and would therefore allow the learner to predict forms. Learners in the meaning-before-form condition picked up on these low-salience discriminative features, while those in the form-before-meaning condition did not.

Ramscar et al. (2010) argue that learners acquire meaning-to-form connections following the classic Rescorla-Wagner learning rule, which uses sets of cues to predict upcoming outcomes. The Rescorla-Wagner rule updates cue-to-outcome connection weights in proportion to the unexpectedness of the outcome's occurrence, or absence (Rescorla and Wagner, 1972), as well as cue and outcome salience. The rule is unidirectional in two senses: it does not learn outcome-to-cue associations, and the roles of cues and outcomes during learning are different. The rule assumes that the learner predicts whether the outcome will occur based on the present cues. Thus, the learner has expectations about which outcomes would occur in various contexts and can learn when those outcomes are unexpectedly absent. The learner does not form expectations about the contexts in which cues will occur, and therefore learns nothing from absent cues, and cue salience is due solely to its inherent perceptual properties. Because of these asymmetries in the rule, Ramscar et al. conclude that “the relationship between symbols and the things they represent is not bidirectional” (p.912).

The results of Ramscar et al. provide an important illustration of the importance of prediction in language learning, and document the existence of cue competition between semantic cues. The results are indeed consistent with the predictions of the Rescorla-Wagner rule, and support a different role for cues and outcomes during learning. Nonetheless, learning may result in associations being formed in both directions, allowing the learner to predict an outcome based on a cue and to infer that a missed cue must have occurred based on an outcome. Bidirectionality would imply that the associations in both directions should be equal in strength. Ramscar et al.'s results are consistent with this prediction. In their experiment, participants are tested both on choosing forms given a meaning and on choosing a meaning given a form (p.930). Participants who experienced the meaning-before-form condition appear to have performed better on both tasks (accuracy within task is not reported, and no task differences are reported). It therefore appears that form-to-meaning connections benefit from the meaning-before-form order as much as meaning-to-form connections do. This result is prima facie inconsistent with participants learning meaning-to-form connections in one condition and form-to-meaning connections in the other; strong correlations between the strengths of A→B and B→A are a classic argument for bidirectionality (Kahana, 2002). Rather, the results are consistent with the alternative hypothesis that participants in the meaning-before-form condition are learning bidirectional or reciprocal associations between discriminative semantic features and the forms they predict. That is, cues that are predictive of outcomes acquire salience and are associated with those outcomes more strongly than cues that are not predictive, but the associations themselves appear to form in both directions.

Second, Ramscar et al. (2010, p.918) assume that forms do not have identifiable subparts that can compete to predict meanings (though cf. Blevins et al., 2016):

This paragraph above denies both the existence of subphonemic cues, including phonetic cues and phonological features, and the pervasiveness of coarticulation. Phonemes do of course covary with loudness or pitch; for example, pitch at the beginning of a vowel is a secondary cue to the voicing of the preceding stop, distinguishing [p] from [b], and listeners are exquisitely sensitive to such patterns of covariation (e.g., Idemaru and Holt, 2011). Likewise, it is not the case that the cues to phonemes are strictly sequential. For example, the place cues to the [p] are in the formants also identifying the height and frontness of the following vowel. Given these considerations, we should expect that phonetic cues compete with each other for predicting meanings, and indeed this effect has recently been documented by Nixon (2020).

Third, the way that children experience forms and objects is often very different from the experimental setup in Ramscar et al. (2010), where the object was presented very briefly (for 150 ms) either a second after or a second before the spoken word. Head camera data indicate that most efficacious word learning episodes involve parents naming objects that the child is already looking at, and the child continuing to look at the object during the label and for some time afterwards (Pereira et al., 2014). These experiences allow the child to both predict the form from the meaning, and to predict meaning from the form, potentially forming a connection or connections in both directions.

Finally, in conditioning experiments that have provided the motivation for the Rescorla-Wagner model, cues are predictive but devoid of inherent value whereas the outcomes are biologically relevant events like the dispensation of food or electric shock. Because of this inherent asymmetry, it is plausible that cues are used to predict outcomes and not vice versa (although research in animal learning has argued for models incorporating reciprocal cue-outcome connections; Matzel et al., 1988; Honey et al., 2020). Because wordforms and other speech sounds are not themselves biologically relevant, while the events they predict often are—especially in the early experience of an infant—it appears implausible to restrict learners to predicting forms from meanings.

In conclusion, there is no current empirical evidence against bidirectionality of form-meaning mappings. Dissociations between production and comprehension can be observed, but are predicted from simple models with bidirectional associations. There is evidence that such associations can be learned by predicting forms from meanings, but the learned associations can then be used to select meanings given forms as well as to select forms given meanings.

While bidirectionality is consistent with the behavioral evidence, it does raise questions about how it could be implemented in the brain. On the one hand, many brain areas are connected bidirectionally: there is just as much top-down activation flow (from meanings to forms) as bottom-up activation flow (see O'Reilly and Munakata, 2000, for an excellent review), a fact that has provided a motivation for interactive activation models of language processing (Dell, 1986; McClelland and Elman, 1986; O'Reilly and Munakata, 2000) and Grossberg's Adaptive Resonance Theory (Grossberg, 1987, 2013). While the top-down and bottom-up connections largely involve separate neurons, it is not impossible to imagine bidirectionality at the level of forms and meanings of constructions, which correspond to activation patterns distributed over large populations of neurons (see Allen et al., 2012, for an attempt to identify such patterns in fMRI). For example, in Grossberg's theory, constructions would be resonant brain states in which the form level and the meaning level feed activation to each other, helping maintain a construction in an activated state for the significant period of time likely necessary for constructions to guide utterance planning. Based on Pereira et al. (2014) head camera data, efficacious naming episodes tend to provide children with the opportunity to establish such a resonance as an object persists in the child's view before, during and after the referring form is heard.

The bidirectional top-down and bottom-up activation flows connect semantic representations to perceptual and (pre)motor processing areas of the brain. However, to say that the same form-meaning mappings are active in comprehension and production requires the two processing directions to share a form level. The need for a form level appears to preclude a radical exemplar account of language (e.g., Ambridge, 2019) in which there is no significant abstraction, and therefore constructions map perceptual representations onto meanings in comprehension and meanings onto motor representations in production. The question of whether there is a level of form representations shared between perception and production has been a long-standing area of debate in phonetics. A promising direction for unifying the two is represented by Bayesian analysis-by-synthesis models, in which the listener evaluates hypotheses about possible production representations that could have generated the perceived auditory signal (e.g., Bever and Poeppel, 2010). If these accounts are on the right track, then production representations could serve as the form level mediating between audition and semantics in speech perception, and bidirectional form-meaning connections could connect these production representations to meanings. Literal bidirectionality could also be maintained by models in which the production targets the speaker aims to achieve are perceptual in nature.

But what if there is no form level? What if listeners map perceptual representations directly onto meanings, while speakers map meanings directly onto articulatory representations? In this case, the mappings would not be constrained to be bidirectional by the architecture of the language system. However, I would argue, learning would nonetheless modify the weights of the unidirectional mappings to bring them in close alignment, allowing for bidirectionality in activation flow. Models that posit separate form levels for production and perception also posit mechanisms for bringing those form levels into alignment during early development (Guenther and Perkell, 2004; Davis and Redford, 2019). Through these mechanisms, which likely include both reinforcement learning and imitation, production and comprehension representations appear to be linked so closely that activating one appears to of necessity activate the other. Although there is debate regarding whether the motor cortex plays a mediating role in speech perception, there is consensus that it is activated by speech sounds. Likewise, there is recent evidence that silent speech produces activation in the auditory cortex (Okada et al., 2018). If the two form levels necessarily activate and resonate with each other in both production and comprehension, the linked representations function as a single form level i.e., both activated by and activates semantics. That is, if articulatory and perceptual representations necessarily activate each other, it is possible for a meaning to always increase activation of an articulatory representation to the same extent that the corresponding perceptual representation increases activation of the meaning, allowing for bidirectionality.

Jackendoff and Audring (2016) have argued that second-order schemas are ubiquitous, and that any two constructions that share some aspect of form or meaning are linked by a second-order schema. Furthermore, second order schemas can be posited even if they are not productive. However, from a usage-based perspective, a generalization plays a role in the grammar if it is used to understand or produce language, thus unproductive schemas are rather suspect. Dabrowska and Szczerbiński (2006) and Engelmann et al. (2019), among others, show that many speakers of highly inflected languages may not use many of the second-order schemas of their language productively, with productivity of a schema being a gradient function of its type frequency and reliability. Second-order schemas are also notoriously difficult for learners to acquire (e.g., Braine et al., 1990, cf. Audring, 2019, p.14). Learning productive second-order schemas appears to require either encountering the corresponding schemas in the same context, where one form is expected but the other occurs instead (e.g., Onnis et al., 2008), or encountering them in close temporal proximity, so that the form of one can be used to predict the form of the other (Smolek, 2019). Constructions, as form-meaning mappings appear to be easier to acquire (e.g., Braine et al., 1990; Kapatsinski, 2013).

Given the existence and easy learnability of constructions, it is reasonable to assume that second-order generalizations are learned and used only for patterns that cannot be captured with direct form-meaning mappings (Bybee, 2001; but cf. Booij and Audring, 2017a). Therefore, in order to convincingly argue for the necessity of a second-order schema, we need to show that one could not have understood or generated each of the constructions it links without reference to the other construction. This is a high bar to clear in syntax. For example, hearing The dax fribbles a wug to the frumbly swuppet, the listener does not need to activate the alternative double-object formulation to understand the sentence (Goldberg, 2002). S/he also does not need to use this specific formulation in generating the double-object alternative. Hearing the sentence, the listener could categorize the swuppet as an animal or human and perhaps assign it a gender, necessary for choosing the pronoun. When producing the sentence, the speaker would then be influenced by the inferred characteristics of the swuppet, the wug, and the action of fribbling, which do not require reference to the prepositional dative formulation—they are inherent to the inferred semantics. Choosing to use a pronoun requires knowing that the wug and/or the swuppet was mentioned, but also does not require reference to the prepositional dative formulation. The choice of the construction depends on this choice—the double object construction is strongly favored by selecting a pronoun to refer to the swuppet (Bresnan et al., 2007) and disfavored by a long noun phrase—but does not depend on anything about the double object formulation. In other words, the two constructions are not in a feeding relationship—generating one of these constructions does not require reference to anything that one could find only in a construct of the other. The closest one comes to such a relationship is when the other construction would sound awkward given a certain filler for the first NP because of that filler's phonology (?I gave the highly agitated swuppet that was zwigging all over the room a wug; see Shih, 2017, for a recent review). However, even such cases do not require the use of a second-order schema. For example, the speaker could begin to generate both formulations in parallel, and the awkward-sounding construction would simply lose the race because it is harder to formulate.

In contrast to syntax, paradigmatic morphology presents numerous examples where one does need to reference the form of one construction to generate a related one. For example, Becker and Gouskova (2016) documented the productivity of the generalization that…oCC#_Nom.Sg~…eCCa#_Gen.Sg but…CoC#_Nom.Sg~…CCa#_Gen.Sg in Russian. Here, the same form would result from vowel deletion in the Genitive in both cases (…CC#), but it is avoided when another form of the word ends in a single consonant (…oC#). Thus, generating the Genitive Singular seems to require reference to the Nominative Singular construction. It is difficult to find any comparable examples of syntactic constructions; that is, constructions whose use or form depends in an arbitrary fashion on the form of another construction.

Second-order schemas allow the speaker to enact arbitrary changes to an activated form when constructing a production plan. Evidence for this claim comes from a recent dissertation by Smolek (2019), who exposed participants to a language with second-order schemas and manipulated how easy they were to extract from the input. She then tested speakers' knowledge of the language using both judgment and production. She found that participants would produce large changes to the base only if second-order schemas were easy to notice in training. Acceptability judgments were unaffected, as was production of smaller, and more a priori likely changes.

In Smolek (2019), a subset of singulars mapped onto plurals ending in [t∫a], undergoing a stem change either when they ended in [k] or when they ended in [p], as shown in (1), where the consonants in curly brackets were presented to different participants:

Learners produced the p→t∫ change only if exemplifying singular-plural pairs were kept intact during training as in (1-2). When only faithful pairs were kept intact (3) or all words were presented in random order (4), participants did not learn to produce the stem change, retaining the [p] of the singular.

When exposed to p→t∫ using the random order in (4), participants judged singular-plural pairs exemplifying the stem change as being more acceptable than those without the change. In both judgment and production, they also did not know what stems should change and what stems should not, indicating that they had not learned paradigmatic, second-order mappings. However, they would not change any stems while judging that all stems should change. Because this was not true of the smaller change k→t∫, where judgments and production probabilities aligned, Smolek argued that second-order schemas are particularly important for making large changes. Without a second-order schema, one can still judge unexpectedly frequent constructions like t∫a~PL as being particularly characteristic of the experienced language but would not produce such outcomes from inputs that are either very different or a priori unlikely to map onto them.

Smolek's results are partially consistent with Booij and Audring's (2017a) proposal that “output-oriented, constructional schemas [i.e., form-meaning mappings that do not make reference to other forms] should be used for stating regularities that are not productive” because “these schemas have a motivational function only” (p.59). However, I would not go that far, as there is evidence that constructional schemas can be productive and can even be used in preference to second-order schemas with which they conflict (e.g., Wang and Derwing, 1994; Kapatsinski, 2013). Furthermore, in Smolek's (2019) experiments, constructional schemas could support productive generation of plurals, except when singular-plural mappings in the input involved large unexpected changes to the base.

Second-order schemas are typically depicted as bidirectional (e.g., Booij, 2010; Jackendoff and Audring, 2016), like first-order schemas/constructions mapping form and meaning. However, this appears to be a false analogy. Unlike forms and meanings, paradigmatically-linked words do not occur at the same exact time in one's experience—one or the other word occurs first and can then be used to predict the other. Being able to produce plurals from singulars also does not guarantee being able to produce singulars from plurals, and depends on the reliability of the mappings in that particular direction (e.g., Engelmann et al., 2019). Thus, paradigmatic mappings linking two forms often have different strengths in different directions.

As directed paradigmatic mappings, second-order schemas resemble rules that map surface forms onto other surface forms (as proposed by Albright and Hayes, 2003). They differ from such rules because they do not involve a split into a change and a context in which that change occurs (Kapatsinski, 2012, 2013; Jackendoff and Audring, 2016). A rule is an operation that occurs in a certain context; a second-order schema is a mapping between two constructions (or their forms). I have argued for schemas over rules by observing that mappings that involve different changes but the same output can “conspire”: as evidence for one increases the other becomes more productive alongside it, and participants who like or frequently produce one mapping also tend to like and frequently produce the other. In particular, adding pairs of words exemplifying […t∫]_SG~[…t∫i]_PL to a language in which […k]_SG~[…t∫i]_PL but […t]_SG~[…ti]_PL led participants to overgeneralize the k→t∫i change to [t] (Kapatsinski, 2012, 2013). These results suggest that learners are treating […t∫]_SG~[…t∫i]_PL and […t]_SG~[…t∫i]_PL as exemplifying the same schema even though they involve different changes (0→i vs. t→t∫i). This result rules out models such as Albright and Hayes (2003) or Becker and Gouskova (2016) that split words into changes and contexts, the ingredients of a rule, and then generalize only over the contexts in which a particular change occurs.

However, rules can be rescued if we assume that zero is not a possible (or likely) input to the change, so any change must involve at least one overt segment as the input. That is, learners presented with examples like blut∫_SG~blut∫i_PL are experiencing the change t∫→t∫i rather than 0→i. The results of Kapatsinski (2012, 2013) are then captured by assuming that learners do generalize over changes, and that they generalize over inputs more than over outputs so that all kinds of inputs initially map onto [t∫i]. Assuming that outputs are action plans to be performed, greater generalization over inputs than over outputs may be a general property of learning in a world where cues calling for a certain action can vary but actions need to be performed with some precision to be efficacious (Kapatsinski, 2018, pp.64-66).

Another way to test the difference between mappings and operations is afforded by subtraction. Pure subtraction involves removing a fixed unit regardless of what remains, in contrast with truncation, which refers to removing as much material as necessary to fit a fixed prosodic template. Truncation is easily captured by a construction in which the form has certain prosodic characteristics. Inkelas (2015) identifies a diachronic pathway from subtraction to truncation, which suggests that speakers often extract a construction from the truncated forms produced by subtraction. However, subtraction does appear to be learnable, and is not easily captured by constructions.

Learnability of subtraction was examined in Kapatsinski (2017a; 2018, pp.186-192). Native English speakers were exposed to artificial languages that could be interpreted as exemplifying either truncation or subtraction. In these languages, the final vowel of the singular was deleted to form the plural always resulting in CVCVC. These languages then could be interpreted either as using the construction [CVCVC]_PL or the rule / operation V→0/_]_PL. At test, participants were then presented with CVCV singulars, for which the two generalizations predict different choices: satisfying the construction would involve the operation of consonant addition (unattested in training), but result in an attested product (CVCVC), while following the rule would involve using the attested operation of vowel deletion to produce an unattested product, CVC. Participant choices depended on whether one of the consonants was over-represented at the ends of singulars. Participants were more likely to add a consonant if they knew which consonant to add (the overrepresented one). However, both strategies were attested, sometimes within the same individual. These results therefore seem to provide support for both constructions and rules. In the next section, I explore two ways of capturing subtraction within a constructionist framework, without the use of rules.

Subtraction is difficult to capture with a second-order schema because it involves mapping something onto nothing, and null elements are not part of the constructionist framework. How then can subtraction be incorporated into the constructionist worldview? In Kapatsinski (2017b; 2018, pp.193-199), I argue that constructions must be supplemented by an operation that there I called copying, on analogy with the copy connections of recurrent networks (Elman, 1990). To produce anything, the speaker needs to construct and execute a production plan, and constructions stored in long-term memory compete for being incorporated (“copied”) into the plan.

Subtraction involves learning not to copy a certain element of an activated form when expressing a certain meaning. Thus, it may be captured by making copying conditional on various aspects of the input (Kapatsinski, 2017b). Thus, if we assume that copy connections are gated, these gates may be closed by certain meanings and input forms. If production plans for wordforms are filled out left-to-right (Roelofs, 1999), then it may be sufficient for alternative segments to be competing for a “future” slot in the plan. Preventing copying of a final vowel into plurals would then involve learning a negative weight for a connection from the semantics of plurality to a gate on the copy connection that would make the final vowel the future: w(PL→[V#→___future]) <0.

Because copying of activation patterns from one brain area to another is biologically implausible (Grossberg, 1987), the construction of a production plan is likely implemented as establishing a resonance between parts of a control structure (e.g., “future”) and activated form units. However, it is not clear how the formation of a resonance can be conditioned, thus it is worth considering alternatives to conditioned copying. A possible avenue to accounting for both changes to the base and subtraction is to incorporate negative meaning-form associations. In current constructionist frameworks, construction forms are templates that are filled out by material from long-term memory (see Jackendoff and Audring, 2016). As such, they can only be positively associated with the meaning they express and lack a mechanism for capturing subtraction when it is independent of the resulting shape of the product. However, any computational model that learns associations between meanings and the forms that cue them also learns negative associations between forms and meanings (as stressed by Ramscar et al., 2014, and Roembke et al., 2016).

Negative form-meaning associations can account for subtraction. For example, the final vowel deletion pattern in Kapatsinski (2017a) could be described as a negative association between PL and V#. They can also account for stem changes, the meaning to be expressed inhibiting elements of the base that are dissociated from it. For example, to produce a singular from a known plural, an English speaker would inhibit the -s suffix via a negative SG→s# association. The existence of such an association receives independent support from the fact that the singular form lens is often misspelled as lense, often enough for both to be entered in dictionaries. This misspelling is motivated by the fact that an s#, and especially a Cs# indicates plurality. The intention to produce an adjective may inhibit nominalizers that distinguish adjectives from nouns (see the next section for an example). If negative associations are particularly strong for unexpectedly absent elements of form, this account may also account for stem change examples like k→s in English -ity nouns. A learner of English would expect a [k] after electri… Not hearing it would provide evidence that it is suppressed by the meaning the speaker was expressing. The element of the meaning that discriminates electricity from electric is whatever distinguishes nouns from adjectives. That element of meaning would then activate -city and suppress [k]. Similarly, it is possible that the Genitive Singular in Russian inhibits oC# as well as activating CC#, resulting in greater deletion of vowels from…oC# singulars than from…oCC# singulars in Becker and Gouskova (2016). Having heard the frequent Nominative/Accusative pu∫ok “little furball,” the speaker would expect the same form in a subsequent production of the rarer Genitive; hearing pu∫ka, s/he would then learn that the Genitive Singular disfavors the oC# as well as favoring the -a#.

Cases that would still require second-order schemas involve patterns in which the same structure can be either favored or disfavored in a certain paradigm cell depending on the corresponding form in some other cell. For example, in deriving a Russian Genitive Plural from a known Nominative Singular, /o/ can be both deleted and inserted, depending on whether the noun is Masculine or Feminine, a difference that can be predicted from Nominative Singular forms: mis-k-a→mis-ok “bowl” but kus-ok→kus-k-ov “piece.” Here,…ok# appears to be both eliminated by the Genitive Plural (for Masculines) and imposed by it (for Feminines). Unless these types of choices can be attributed entirely to semantic differences between the word classes (in this case Masculines and Feminines), they require productive second-order schemas. Interestingly, the Genitive Plural is exactly the paradigm cell that Russian speakers have a difficult time filling; with great uncertainty regarding the correct form. For example, dictionaries record both portkov and portok as the Genitive of the pluralia tantum portki “pants,” which could be either Masculine or Feminine as unambiguous forms are missing. Paradigm gaps abound, and are spreading (Daland et al., 2007). For example, there is no Genitive Plural for met∫ta “dream” even though there is one for mat∫ta “mast.” The difficulties make sense if the production of this form relies on second-order generalizations, since such generalizations are difficult to acquire.

The final suffix is the case-gender-number agreement marker and is almost regularly -yj in the dictionary (Masculine Singular Nominative) form, with the exception of bez-mater-n-ij “motherless,” which likely avoids homophony with bez-mater-n-yj “lacking taboo words,” bez-mu3-n-ij “husbandless,” which follows the same pattern, and bez-trud-ov-oj “laborless,” which shares the -ov-oj with its much more frequent bez-less pair trud-ov-oj “labor-A.” With the exception of trud-ov-oj, bez-less adjectives ending in -oj correspond to bez- adjectives ending in -yj (e.g., vyezd-n-oj “able to leave” but bez-vyezd-n-yj “unable to leave,” tsvet-n-oj “colorful” but bez-tsvet-n-yj “colorless”). The choice of suffix also comes with a choice of stress location, as -yj is unstressed, while -oj is stressed. While the number of such pairs is low (n = 4), they suggest that -yj must be activated by the meaning of the construction.

At the same time, -yj must also be strongly associated syntagmatically with the preceding adjectivizing suffix -n, as 95.5% of -n adjectives take -yj, with only 3.5% taking -oj and 1% -ij. Compare the very low rate of -oj use after -n to its rate of use after another adjectivizing suffix, -ov. While -yj is still dominant with this suffix, accounting for 74% of the adjectives, -oj accounts for 26%, which is significantly higher than the 3.5% seen with -n (p < 0.00001 by Fisher exact test). As noted earlier, the only instance of -oj use with bez- occurs after the suffix -ov. These results suggest that there are syntagmatic associations between -ov and -oj, and between -n and -yj, even though the “A” meaning generally is associated with -yj more strongly than with -oj.

The adjectivizing suffix is not fully predictable. However, 79% of bez- adjectives bear -n, and -n also accounts for the majority of bez adjectives that lack bezless counterparts (67%), i.e., pairless adjectives. This is a significantly higher percentage than for adjectives generally, where -n accounts for ~52% of types (p < 0.00001 by Fisher exact test). Therefore, -n may be considered to be part of the construction, activated by its meaning (“WITHOUT N”)⁵.

There are also many pairless adjectives without an adjectivizing suffix, as in (10)-(11). These form 23% of pairless bez-adjectives while only one suffixless bez adjective, bez-pal-yj “fingerless” has a bez-less pair in the dictionary (p < 0.00001), and that pair is now obsolete. Suffixless formations are semantically conditioned: all adjectives referring to lack of expected body parts are formed this way; animal body parts account for 20/25 such adjectives. The remaining adjectives refer to parts of non-animal “bodies,” formed from the roots verx “top,” list “leaf,” os' “axle,” and metonymic extensions, pol (“sex/gender”) and styd (“shame”). Interestingly, the body part semantics cause a suffixless formation only if the body part is in some notable state: thus, bez-kryl-yj “wingless” and ∫irok-o-kryl-yj “wide-winged” but kryl-at-yj “winged”; bez-puz-yj “belly-less,” tolst-o-puz-yj “fat-bellied” but puz-at-yj “bellied”; bez-golos-yj “having no voice” and gromk-o-golos-yj “having a loud voice,” but golos-ist-yj “having a [good] voice.” The adjectivizing suffixes that are removed from such adjectives in forming the bez- form are -at, -ist and -ast. They must be suppressed by the “remarkable state of a body part” semantics.

The suffix -(l)iv is always shared with the bez-less adjective and thus not associated with “without.” Its selection is independently semantically conditioned, in that it refers to characteristic behaviors/character traits. Thus, an o-pas-liv-yj “cautious” person operates with caution (opas-k-a), and a za-stent∫-iv-yj “shy” person lives behind a self-imposed wall (stenka), having the quality of with za-stent∫-iv-ost^j (“shyness”). A zabot-liv-yj “caring” person performs zabot-a “care” for other people. The choice of variant is syntagmatically-conditioned: -liv after coronals, /s/ and /t/, and -iv after /t∫/.

The suffix -ov is less common in bez- adjectives than in other adjectives and must therefore be inhibited by the construction's meaning: only 5 (1%) of bez- adjectives have the suffix compared to 14% of all adjectives (p < 0.00001). Interestingly, this suffix is of the same shape as the Genitive Plural Masculine inflectional suffix on nouns (kot “tomcat,” kot-ov “tomcats-GEN.PL.MASC”). The preposition bez requires a Genitive noun, but does not place requirements on number or gender. Thirty-one percentage of the nouns in PP's corresponding to bez-Adjectives take -ov in the Genitive Plural. However, all nouns corresponding to bez- Adjectives taking the suffix -ov bear the Genitive Plural suffix -ov. While there are only five such adjectives, the pattern is suggestive of -ov being copied from the noun in the corresponding prepositional phrase. The pattern is statistically robust across the class of -ov adjectives in the dictionary where 74% (1022/1373) have a corresponding noun ending in -ov, a proportion statistically greater than the 39% observed with-n adjectives (p < 0.0001). Thus, it appears that the adjectival suffix -ov often results from a genitive plural noun inflection copied into the adjective when the adjective is formed. Copying of inflectional suffixes into adjectives, where they look like derivational, adjectivizing suffixes suggests that copying operates on a fully inflected wordform rather than a stem, and that what is being copied are surface chunks from that form. At the same time -ov cannot always result from nominal inflection because not all such adjectives have nominal bases ending in -ov. In 26% of the cases, it is imposed directly by the A meaning.

Copying from the prepositional phrase is also supported by another aspect of the forms of bez- adjectives, the spelling of bez- (Kapatsinski, 2010b). Both the prefix and the preposition undergo voicing assimilation, so that bez is pronounced [bes] before voiceless obstruents. However, the spelling rules for the prefixes differ from those for prepositions: the preposition must always be spelled bez, whereas the prefix must be spelled they way it sounds, with <s> before voiceless obstruents. Kapatsinski (2010b) shows that Russian college students spell the prefix [bes] <bez> ~50% of the time in low-frequency bez- adjectives they do not know, even in a graded dictation test. The error rate is two orders of magnitude higher than the error rate for other comparable prefixes (iz- and raz-), which also end in /z/ and obey the same spelling rules. Like bez-, the errorless prefixes have homophonous free morphemes that are always spelled with <z>. In the case of iz-, as in the case of the error-prone bez-, the free morpheme is a preposition i.e., near-synonymous with the prefix and is the diachronic source of it. However, neither iz- or raz- verbs have bases that contain free morphemes that correspond to the prefix and from which its spelling can be copied. Both prefixes derive perfective verbs from imperfective ones as in (9)-(10). The low rate of spelling errors on iz- and raz- suggests that the spelling errors on bez- are due to writers copying the orthographic <z> of the base prepositional phrase into the production plan for the adjective. Frequent bez- adjectives are spelled correctly because their orthographic forms can be retrieved from the lexicon.

A parallel, associationist constructicon predicts that there should be no single base from which bez adjectives are derived (see also Burzio, 1998; Booij and Audring, 2017b). The forms blended into the plan need to meet only one criterion: they need to be associated with, and therefore recurrently activated by the intended semantics. The more strongly a form is activated, the more it is predicted to affect the blend. This hypotheses is strongly motivated by results on the diachronic phenomenon of paradigm leveling, which happens between forms that are strongly related semantically (Bybee and Brewer, 1980), and changes less frequent forms by blending in elements of more frequent ones (Tiersma, 1982). For example, Bybee and Brewer (1980) show that paradigm leveling in Provencal verbal paradigms happened between forms of the verb that share all inherent semantics, differing only in agreement. Tiersma (1982) provided evidence that Frisian nouns have leveled mostly in favor of singular forms, except for those for which the plural form is more frequent.

Note that, in any case of paradigm leveling, there is a form that would fully express the intended semantics. This form would receive more activation from the semantics if frequency were controlled, and therefore can often prevent other forms from affecting the blend, blocking/pre-empting the formation of synonyms. Leveling occurs when the form fails to block the formation of a synonym because it is not accessible enough from the intended meaning, and is replaced by something else. That something else is, furthermore, not another existing form, but a new formation that incorporates elements of the more frequent semantically similar form into the form that matched the intended semantics fully. The existence of this process strongly implicates parallel activation of competing forms and a blending process that can combine them into a novel production plan. In the case of bez- adjectives, semantic similarity explains copying from the corresponding prepositional phrases that can express most of the meaning of the bez- adjective. Because these phrases contain Genitive nouns, this also explains why it is the Genitive i.e., copied.

The proposal that words are formed by blending forms activated in parallel by the intended meaning contrasts with the hypothesis that there is a single base for any particular type of morphologically complex word (Albright, 2002). We have already seen evidence that bez adjectives are motivated by both bez-less adjectives and prepositional phrases, contradicting the single base hypothesis. However, until now we could maintain that there is always a prepositional phrase base, suggesting that we could claim that there is one particular base i.e., necessary for deriving a bez adjective. However, the problems go deeper: first, it is not possible to claim that the forms of the nouns in the base prepositional phrases always come from the same paradigm cell; second, there are bez adjectives that do not have corresponding prepositional phrases.

Some Russian nouns have different stem forms in Singular and Plural Genitives. The examples in (11)-(13) show that it is not: some adjectives copy the plural form (11) while others copy the singular (12). Sometimes, different bez adjectives can even be derived from the forms in different paradigm cells, as in (12)-(13). Thus, a single base paradigm cell cannot be identified: whatever forms match the intended semantics best are the ones copied.

A single⁶ base is also ruled out by the fact that the base noun can lack an acceptable Genitive Plural form (the Genitive Plural is the nominal form in which paradigm gaps are common in Russian), be uncountable and thus lack plural forms altogether or, conversely, be a pluralia tantum that lacks singular forms. In such cases, the available form of the noun must be used to produce the adjective. For example, bez-vred-n-yj “harmless” cannot be formed from a plural form of vred “harm” because it is not countable and lacks plural forms. Conversely, bez-∫tan-n-yj “pants-less” must be formed from the plural (∫tan-ov) because it lacks a singular form.

There are also cases of variation, as in (14). Note that retention of the Vn is consistent with the adjectives being motivated by prepositional phrases, as it is not present in the singular Nominative or Accusative forms but is present in the Genitives requires by bez:

While the vast majority of bez- adjectives have a corresponding prepositional phrase, some do not, indicating that bez- adjectives cannot always be derived from prepositional phrase bases. Thus, the adjective in (15) appears to be formed directly from a verb.

Other adjectives formed from verbs can often be identified because they retain the infinitival inflection from the base verb, and add the sequence -el^j-n-yj (16-18). The -el^j is the agentive marker (cognate with English -er), as in stroit^j “to build” ~ stroit^jel^j “builder.” However, these adjectives are not derived from such nouns: the nouns are often missing, and retaining the semantics of the -er would require adding a different adjectivizing suffix, thus stroit^jel^j-n-yj musor “building garbage” (i.e., garbage associated with building something), vs. stroit^jel^j-sk-yj musor “builder garbage” (garbage associated with a builder or builders generally). The adjectives can usually be related to “deadjectival” nouns ending in -stv-o or -ost^j (stroit^jel^jstvo “the process of building”). The examples in (16) and (17) are difficult to explain without reference to such a noun. However, the example in (18) is difficult to relate to the corresponding noun: the corresponding PP is awkward and not interpretable as synonymous with the adjective. Once again, bez- adjective forms are produced using whatever semantically close words are available, as one would expect from a lexicon i.e., structured as a parallel, associative network.

This section provides an informal illustration of what production looks like in this framework⁷. The example shows the process of generating a novel adjective the meaning “tax-free,” an adjectival equivalent of “without tax(es).” This adjective is not in the dictionary but can be found on the web, with the two possible forms beznalogovyj and beznalo3nyj. The former is much more common, with 418 vs. 56 Google hits, and intuitively appears more acceptable. I take the grammar to be responsible for generating both forms and explaining why the former is more common. Figure 2 shows some of the schematic and syntagmatic associations involved in producing a novel bez adjective, including only morphemic chunks. Figure 3 illustrates the role of paradigmatic associations in enacting changes to the base, and the role of the base in the orthography, showing that chunks larger than the morpheme also play a role in production. Figure 4 illustrates how blending of these larger forms would result in the most common form produced. Note that Figures 2, 4 should not be seen as two different “routes” for producing the new adjective: there is instead a near-infinite number of routes because all meaning-to-form associations activated by as semantic feature are activated in parallel.

The top of the diagram in Figure 2, [WITHOUT TAX]_A represent the intended meaning, which I assume to be a distributed representation, as symbolized by the gradients below it. The top gradient represents the unique aspects of the meaning of the bez-A construction, which distinguish that construction from all other constructions and make its representation more than the sum of its parts. The next gradient down is the meaning “without,” which strongly cues and is cued by bez, as shown by the thick bidirectional arrow. The next one down is the meaning of “relating to taxes,” or [tax]_A, for which there is an established adjective, nalogovyj. The gradients for “tax” and the Adjective category follow.

The meaning “without” is consistent with both adjectives and prepositional phrases and therefore activates both Genitive case markers appropriate for the prepositional phrase and the adjectivizing suffix -n i.e., favored over others by this construction. The Genitive suffixes activated include -a and -ov appropriate for a noun like nalog and suffixes from other declension classes (not shown here). The activation of nalog from the meaning “tax” boosts the Genitive suffixes appropriate to its over their competitors from other declensions. This is shown by the arrows from nalog to the two suffixes -a and -ov. Because the two suffixes are incompatible with each other, I assume an inhibitory connection between them.

We have seen evidence that the suffix -ov occurs in bez Adjectives primarily when the corresponding noun selects it as a Genitive Plural suffix. Thus, -ov in prepositional phrases and adjectives with bez appears to be the same form, associated with the meaning “without,” which is the meaning of bez and one meaning of the Genitive. Because -ov can serve as an adjectivizing suffix, it must also be activated by the Adjective category. Interestingly, however, -ov is disfavored by bez-Adjectives compared to other adjectives. It must therefore be inhibited by the meaning of the construction as a whole even though it is favored by all of the parts of that meaning (“without,” “tax,” and “A”). Figure 2 therefore includes an inhibitory connection from the top gradient (unique features of the construction) to -ov.

The adjectivizing suffixes are syntagmatically associated with the case-number suffixes that follow them. As shown above, -yj is more common than -oj across the board but is particularly rare after -n. For this reason, the top-down connection from A to -yj is stronger than the one to -oj and -oj is syntagmatically boosted by -ov while-yj is boosted by -n. In addition, -ov and -yj are both activated by the “[tax]_A” meaning because nalogovyj is an existing adjective.

Figure 2 predicts rapid activation of bez- and nalog, which are not inhibited by anything. At this point, the speaker's intended production is the same whether or not it resolves into a prepositional phrase or an adjective, because both constructions are compatible with most of the meaning intended. This partial overlap results in competition between the two constructions in usage. According to Figure 2, which construction ends up being produced depends on resolution of two competitions: between -a, -ov, and -n and between -oj and -yj. The first competition will resolve mostly in favor of -n because the intended meaning inhibits the other competitors. The second competition will be resolved in favor of -yj, which receives more activation from the intended meaning and from the preceding element, and is also favored by the more likely preceding element. Because all processing happens in parallel, it is possible for the competition between -yj and -oj to resolve before the competition between -ov and -n, in which case -yj is expected to help select -n using a backward syntagmatic association (not shown), rather than -n helping select -yj.

Figure 3 shows additional aspects of form generation, specifying phonology and orthography. Because the suffix -n does not allow a velar to precede it, it inhibits the final [g] of naloga and nalogov if selected, and activates [3], alongside other consonants. The specific consonant, [3], however, is selected because it is also activated paradigmatically by the [g] of nalog (dashed arrow). Finally, the orthographic form activated most strongly by bez is <bez>, its most common spelling and the only one allowed in prepositional phrases. The strength of this connection could explain why Russian speakers would often spell bez with an <s> even when it is a prefix and pronounced with an [s]. However, it does not explain why these errors do not similarly afflict iz-, for whom the prepositional spelling is even more common relatively to the prefixal spelling. Thus, the errors must be boosted by the fact that the intended semantics for a bez Adjective activate prepositional phrases, while the intended semantics for an iz verb do not. This is shown by the connection between bez in the prepositional phrase and <bez > in the orthography. Accurate spelling requires the A category to weaken the activation of <z>, allowing the phonological context (here, the [n] of nalog) to select the right spelling syntagmatically.

The representation in Figure 2 therefore oversimplifies the network structure because it omits the larger units like bez naloga that are also activated by the intended semantics. Indeed, these units may well be activated by the semantics more strongly than their smaller or less context-bound counterparts: even though smaller units are favored by their greater frequency, larger units match the intended semantics better. This is what allows established forms to outcompete synonymous innovations most of the time. For example, irregular forms like went can block/pre-empt the creation of synonymous regulars because went is activated by both GO and PAST, whereas each part of goed is activated by only one of these cues (Kapatsinski, 2018, p.278). Of course, because frequency also plays a role, blocking can fail, allowing regularization and paradigm leveling to occur.

Figure 4 shows the larger units for the case of beznalogovyj. Only units activated by the intended meaning are shown. The block arrow shows that the activated forms are blended into the production plan, by copying and aligning them to maximize overlap. The most likely production, beznalogovyj, is predicted. However, blending these larger units will not produce any other variant: the nalo3nyj part of beznalo3nyj is blocked by the existence of nalogovyj. Thus, generating beznalo3nyj is possible only using smaller, sublexical units, explaining its lower frequency. Its existence therefore also provides support for the existence of the sublexical route.