Towards a refined usage- / exemplar-based definition of construction

In Goldberg (1995: 4), constructions were defined as a form-meaning pair with at least one unpredictable property. In Goldberg (2006: 5), a different definition is proposed: Something unpredictable is no longer a necessary condition something can also be a construction by virtue of "sufficient frequency." In usage-/ exemplar-based models, linguistic/constructional knowledge is conceived of as a high-dimensional space with formal (phonetic, phonological, morphological, syntactic, ...) and functional (semantic, pragmatic, discoursal, contextual, ...) dimensions. In such a space, exemplars are stored in positions representing their values on these dimensions, and clouds of exemplars with high densities (compared to the space surrounding them) are what corresponds to categories. If a speaker encounters a linguistic token with a particular function in a particular context, then this token is categorized according to its position in the high-dimensional space and will be categorized as a member of the category (point cloud) to which it is most similar (closest).

The above discussion of the cline of co-occurrence complexity and entropy gives rise to a different kind of definition of construction. I view a construction as an entropy-reducing spike of a distribution in an area in multidimensional space where formal and functional dimensions intersect. That is, when a point cloud is particularly dense compared to its environment, that means that particular combinations of features (the densest center of the cloud) are more frequent than many others, giving rise to the peak in a Zipfian distribution. An example will help to clarify this rather abstract notion. Consider a child's growing linguistic knowledge as a multidimensional space of formal and functional characteristics before that child has begun to acquire a ditransitive construction. As part of his input, the child hears words such as give, tell, show, hand, etc. as verbs in the ditransitive construction, but also in other formal contexts (give up, the show on TV, my hand hurts, ...) with different meanings (i.e., functional characteristics). According to the above proposal, the child may begin to form a ditransitive construction when he 'realizes' that give does not occur randomly frequently (i.e., with high uncertainty/entropy) in different formal contexts (a.k.a. constructions) and with different meanings but that:

- the distribution of formal contexts with which give occurs features a high frequency of ditransitive constructions (plus maybe some other constructions), resulting in a low-uncertainty Zipfian distribution along this dimension;

- the distribution of meanings with which give occurs features a high-frequency of 'transfer' meanings (plus maybe some other meanings), giving rise to a low-uncertainty Zipfian distribution along this dimension.

When such an informative confluence of formal and at least one functional characteristic is noticed, an (at first) item-specific construction can emerge, which is then extended more productively as the low-frequency range of uses of the same construction is noticed the child begins to be able to handle the higher entropy/ uncertainty of this distribution and, for example via Hebbian learning, extends the category.

This perspective helps operationalize Goldberg's notion of "sufficient frequency" more precisely/meaningfully: a frequency is "sufficient" if the frequency of a confluence of one or more formal and one or more functional characteristics has become skewed/Zipfian enough to reduce the uncertainty along the dimensions characterizing the distribution. Note that this means that, for a productive category to emerge, a certain type frequency will be necessary because it is against the background of that type frequency (i.e., many low-frequency bars in any panel of Figure 9) that an entropy-reducing spike (a high-frequency bar in any panel of Figure 9) can be registered. Note also that such a 'realization' of an uncertainty-reducing confluence can of course be facilitated by the salience of the particular confluence in some context, which helps account for instances of fast-mapping and long retention, e.g. when two casual mentions of the nonce-color term chromium was sufficient for three- and four-year-old to infer and retain the word's meaning. Crucially, the casual mentions were in a contrastive context ("not blue"), which in the current account simply means that the discoursal context reduced the uncertainty of what chromium refers to in semantic space to a degree that children could make the relevant inference.

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