Generalization and discrimination

From the standpoint of a classical WP model, the challenges that arise in describing Georgian are intrinsic to a strategy that encapsulates the patterns exhibited by a set of forms in a set of rules that apply to a natural class of cells. Unlike morphemic accounts, realizational analyses do not need to impose a biunique correspondence between features and forms. However, if a rule spells out feature specifications in the realization of one cell, it will in general spell out the same specifications when they occur in other cells. For the most part, this is a good thing; it is the mechanism that permits realizational analyses to express consistent patterns of exponence within a system. But if there are deviations from a uniform pattern, the expected rule must somehowbe inhibited. In Georgian, the rule realizing 3sg subject features as -s does not apply to cells that contain 2pl object features.[1] The rule realizing 1p subject features as v- does not apply to cells that contain 2p object features. At the point that these patterns arose in the development of the Georgian verbal system, there may have been principled explanations for the fact that -t and g- prevailed. But whatever their origins, both patterns are now established in Georgian and are part of what a speaker needs to learn when they acquire the language.

One might ask then why a realizational model would seek to ‘derive’ this outcome in a synchronic analysis. It is instructive to contrast a realizational account with the discriminative treatments of these patterns outlined in Chapter 8. To account for the contexts in which the prefixes v- andg- occur, realizational models introduce a pair of rules, one that spells out 1p subject features by v- and a second that spells out 2p object features byg-. In cells that contain 1p subject features and 2p object features, the requirements of both rules are met. Given that only g- actually occurs in such cases, a realizational model must somehow assign priority to the rule that spells out 2p features. However, Georgian prefixal competition does not fall straightforwardly within the scope of a specificity-based condition, given that 2p object features are in no obvious way more specific than 1p subject features. Solutions to this problem have of course been explored in different realizational frameworks, but it is the logical structure of the challenge that is particularly relevant here. Because they interpret feature specifications, realization rules apply to the natural classes of cells characterized by those specifications. As noted above, patterns of form variation that are associated with a non-natural class of cells are attributed to the interaction of rules, each of which applies to a natural class of cells, but which overlap in a way that creates a distribution over a non-natural class. In a realizational analysis of the paradigm in Table 3.4, the rule that spells out 1p subject features by v- is applicable to the natural class of cells with 1p subject features but only applies to those with 3p objects because it is preempted by the rule that spells out 2p object features.

From a discriminative perspective, the problem faced by realizational analyses of slot competition is symptomatic of initial overgeneralization. Speakers of Georgian would be expected to learn from exposure to the patterns in the language that v- does not appear in forms that realize 2p object features. The knowledge that such a speaker acquires about the distribution of v- is not accurately represented by a rule that introduces v- as the realization of 1p subject features everywhere. Within a realizational model, overgeneralization is endemic to the rule format and cannot readily be corrected by adding specifications. For example, the rule introducing v- could be revised so that it applies to cells with 1p subject features and ‘non- 2p’ (or 3p) objects. This refinement would have the desired effect for transitive verbs. Yet this solution creates the need for a separate rule to introduce v- in the realization of intransitive verbs, which specify no object features that ‘compete’ for the prefixal slot.

By modelling the attested, non-natural, distribution of agreement markers, a learning-based discriminative approach attempts to avoid the overgeneralization that leads to slot competition. In a realizational analysis, it is natural to associate g- with ‘2p object features’ and highly unnatural to associate g- with ‘ip subject features’. Yet within transitive verb paradigms, g- is in fact a more reliable cue for ip subject features than the ip subject prefix v-. Conversely, it would be natural within a realizational analysis to identify the spell-out of ‘2p object features’ as just the prefix g-. However, the complementary distribution of 2p object features and v- also forms part of the dynamics of the system. A discriminative learning model, like the human learner, will come to recognize that ‘2p object features’ and v- exhibit perfect complementarity. But this pattern does not conform to the model of a feature-form spell-out.

Any account must specify the deviations from a fully uniform distribution of agreement markers in Georgian. The cases in which motivated markers fail to occur do not become any more natural if they are attributed to a gerrymandered feature system or to ad hoc extensions of disjunctive ordering. A classical WP analysis also does not make the distribution any more natural. It merely avoids the need for unnatural restrictions by not abstracting an overgeneralized distribution in the first place. An analysis that takes the paradigm in Table 6.5 as an analogical base for proportional analogies would not motivate the presence of -s in a form realizing 3sg features and 2pl object features. The marker v- would likewise not be motivated in forms containing 2p object features. As these examples illustrate, the distributional patterns that can be projected analogically from this paradigm do not invariably correspond to exponence rules. But an analogical analysis has the advantage of avoiding the overgeneralization that is intrinsic to approaches in which rules must apply to natural classes of feature bundles. Consider again the distribution of the marker -s in Table 6.5. A realizational model can fail to generalize altogether and introduce a separate rule for each cell in which -s occurs. However, a more general description must attribute the distribution of -s to the interaction of rules that apply to natural classes of cells. The rules can either treat the distribution in Table 6.5 as the result of a rule blocking a more general rule, as in Anderson’s analysis, or as the union of multiple, natural classes of outputs. The first analysis rests on an ad- hoc notion of ‘specificity’ and the second on a purely expedient classification of occurrences of -s.

Implementing a classical WP analysis in terms of a discriminative learner (as outlined in Chapter 8) again does not make the distribution of prefixes seem more natural or explain why the prefixes have the distribution that they do. However, the brief illustration above suggests how a learning-based account is designed to avoid inducing an overgeneralized distribution and the problems that arise from that distribution. Furthermore, this illustration also suggests how overgeneralization is itself a symptom of a general realizational strategy of isolating single contrasts from within larger systems of contrasts.

This final point can be clarified with reference again to the competition between v- andg-. From a realizational perspective, it may seem that the contrast in meaning between the isg subject form davxatav and the 2sg subject form daxatav can be directly associated with the presence or absence of v-, ignoring object features altogether in transitive paradigms. Yet the contrast between davxatav and dagxatav shows that 3p object features facilitate—whereas 2p object features inhibit—the association between isg subject features and v-. Hence the overgeneralization expressed by a rule that spells out isg subject features as v- results from a strategy of isolating individual form-feature contrasts from the larger system in which those contrasts operate.

  • [1] In contrast, the rule realizing 3sg subject features as -a does apply, before the rule that realizes 2plobject features, as illustrated, e.g., by dagexatat in Figure 6.8.
 
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