Intrinsic and extrinsic ordering

There are various formulations of specificity-based constraints on rule application, all reflecting a shared intuition that the rule with the most restricted application takes priority when multiple rules are applicable to a given bundle. For the most part, the relevant restrictions are taken to be determined by the feature component of a rule, and not by constraints imposed on the input form. For models that adopt this assumption, relative restrictiveness or specificity can be expressed in terms of standard set- or feature-theoretic notions.

However, many of the rule formats adopted within realizational approaches extend a basic interpretive feature-form mapping. For example, the inflectional Word Formation Rules of Anderson (1992) impose constraints on the shape of an input form as well as on the properties in a feature bundle:

An inflectional Word Formation Rule operates on a pair {S, M} consisting of a phonologically specified stem S, together with any further lexical specifications associated with that stem; and the Morphosyntactic Representation M of some (terminal or nonterminal) position in a Phrase Marker which is to be interpreted by (an inflected form of) that stem.

The Structural Description of such an inflectional Word Formation Rule thus includes two sorts of specification: conditions on S (e.g. the requirement that the rule may only apply to stems of more than two syllables), and conditions on M (e.g. the specification that the rule applies to Nouns interpreting positions bearing the feature [+ Ergative]). (Anderson 1992:185)

The “two sorts of specification” included in the structural descriptions of these types of rule will define two separate relative specificity relations, one at the level of features, and the other at the level of ‘forms’ (possibly including “lexical specifications”). Hence for rules of this type, a specificity-based ordering constraint must either explicitly regulate the interaction of the two dimensions of relative specificity or else classify the form specification as relevant for determining rule applicability but not for determining relative rule priority.

For realization rules that do just interpret properties that are associated with feature bundles, the applicability of a rule can be determined by whether a bundle contains the features specified by a rule. This notion of rule applicability generalizes over nearly all the ways that rules and bundles can be represented formally. On the simplest representational assumption, rules and feature bundles specify sets of features (or feature-value pairs). On these set-based assumptions, a rule is applicable to a bundle whenever the features specified by the rule are a subset of the features in the bundle. Alternatively, rules and bundles can both be interpreted as specifying feature structures in the sense defined in feature-based frameworks such as GPSG (Gazdar etal. 1985) and PATR-based systems (Shieber 1986). In this case a rule is applicable to a bundle whenever the structure specified by the rule subsumes the structure representing the bundle. It is also possible to interpret rules as specifying sets of features and bundles as constituting structures. In this case, a rule is applicable to a bundle if the features specified by the rule describe or are satisfied by the structure, as in model-theoretic feature-based frameworks such as LFG (Kaplan and Bresnan 1982) and HPSG (Pollard and Sag 1994).

Each of these alternatives defines a specificity order on pairs of rules R and S. On a set-based conception, R is more specific than S if the set specified by S is a proper subset of the set specified by R. On a structure-based conception, R is more specific than S if the structure specified by S properly subsumes the structure specified by R. On a description-based conception, the definition of relative specificity depends on the model theory assumed by a framework. In LFG, which allows partially specified structures, R is more specific than S if the most informative structure that satisfies S properly subsumes the most informative structure that satisfies R. In versions of HPSG that do not allow partially specified structures, R can be regarded as more specific than S if the structures that satisfy R are a proper subset of the structures that satisfy S.

Given a set of exponence rules, relative informativeness relations between their associated feature bundles define a partial order that correlates with intuitive notions of relative specificity. The relative priority of any pair of rules can simply be read off their position in the informativeness order. Referral rules will likewise occur at the points in a rule hierarchy dictated by the feature sets specified by the rules. These conceptions of rule and specificity can be formalized to any desired level of precision within a more fully-developed approach. For the most part, the differences between alternatives reflect more general assumptions of a model, and do not themselves have direct empirical consequences. On any of these alternatives, the priority determined by relative informativeness is intrinsic in the sense that it reflects the features interpreted by realization rules and does not have to be stipulated or imposed.

In contrast, the relative order in which rules apply cannot be keyed to relative informativeness of the features they interpret, since the properties at different points in a form tend to be at least partially distinct. In forms with comparatively simple morphotactics, these points are described in terms of units such as ‘roots’, ‘stems’ and ‘terminations’. These units determine a conventional ‘head-thorax- abdomen’ analysis in terms of lexical roots, derivational stems, and inflectional terminations. The traditional analysis that Matthews (1991) attributes to elelykete is represented by the structure in Figure 6.21.

Traditional stem structure of elelykete (Matthews 1991

Figure 6.21 Traditional stem structure of elelykete (Matthews 1991: 176ft.)

Table 6.3 Block stem structures for elelykete

e

le

ly

k

e

te

Linear

A

B

C

D

E

F

Nested

C

B

A

B

C

D

A realizational model does not assign morphotactic structure to a word form but transfers this organization onto the ‘derivational structure’ of an analysis. Hence the domains represented in Figure 6.21 correspond to rule blocks, or to sequences of blocks. The precise correspondence depends partly on how order is assigned to blocks, specifically whether it reflects a linear arrangement of exponents or a nested organization. On a linear account, there will be one block for the augment e-, a block each for the rules in Figures 6.5, 6.6 and 6.7, which define the perfective active stem lelyk, a rule for the past suffix -e and a final rule for the termination -te. This is a morphotactically consistent view of rule blocks, in which the exponents introduced by the rules in a block occupy a common position (e.g., are suffixal or prefixal) with respect to the input form.

A linear block organization preserves no reflex of the traditional stem structure in the analysis assigned to elelykete, adding exponents from left to right. A nested organization can, however, represent morphotactic domains in terms of blocks. Beginning with the root, which undergoes a perfectivizing shortening rule, a concentric block structure can be defined which represents the traditional domains. The first block contains the reduplicated prefix le- and -k, the second contains the augment e- and suffix -e, and the final contains the termination -te. These alternatives are set out in Table 6.3.

The paired blocks ‘B’ and ‘C’ in the nested structure [[C [B [A] B] C] D] can be interpreted either as containing sets of prefixes and suffixes, or as comprising higher-level blocks containing prefixal and suffixal blocks. Since realization rules assign no morphotactic structure to the forms they spell out, the choice between different strategies for organizing blocks hinges on whether the blocks define domains for realizational principles or constraints. Disjunctive rule ordering is the primary constraint that is taken to apply within blocks. Hence patterns in which the effects of disjunctive ordering appear to span rule blocks provide useful test cases for evaluating different conceptions of block organization. The distribution of verbal agreement markers in Georgian, as described by Anderson (1986,1992), represents a pattern of exactly this kind.

 
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