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Rules in Paradigm Function Morphology

The differences between the rule formats employed by Matthews (1991), Anderson (1992) and Aronoff (1994) are fairly superficial, and mainly reflect different ways of packaging the same information. In contrast, the rules in PFM differ more substantially. Exponence rules are the most conservative rule type in PFM, since they have the same effect as other spell-out rules. As in earlier formats, RR in (6.5) applies to an ‘input’ form-feature pair and defines an ‘output’ form.[1] However, unlike previous rules, the rule contains a variable, a, that explicitly represents the bundle to which the rule applies.

(6.5) Realization rule format in PFM (Stump 2001:44)

RR„,r>C«X, a» =def

Hence a) represents the input pair to which RR applies, and , a) a pair containing the output Yh As before, ‘X’ represents a form, whereas ‘Y7’ represents a class of forms. This class contains ‘Y’ and all of the forms obtained from ‘Y’ by “any applicable morphophonological rules” (Stump 2001:45).[2]

The most distinctive feature of this rule format is the sequence of indices subscripted to RR. The block index n identifies the rule block in which the rule occurs, the property set index т specifies thefeaturesthatare spelledoutbytherule, and the class index C indicates the class of lexemes to which the rule applies. As discussed in Section 6.3, assigning rules to ordered blocks groups together rules that apply at the same point in a structure, and imposes an extrinsic order on rules that apply at different points. The set т contains the features that are specified in the previous rule types, except for word class and morphological class features, which are segregated in C. The rule in (6.6), which again realizes 1st declension genitive plural nouns in Slovene, shows how information is distributed across pairs and indices.

(6.6) Slovene case realization rule in PFM

RR1,{NUM:plu,CASE:gen},{N,I} (<X, a )) =def <XoV, a )

The block index ‘1’ assumes that all nominal inflections are introduced in a single suffixal block. The features {NUM:plu,CASE:gen} are the attribute-value counterparts of the privative and binary features in earlier rule formats. The indices N and I likewise indicate that the rule applies to 1st declension nouns. The variable X again represents the noun stem, and XoV the result of concatenating -ov and applying any morphophonological rules.

Given that the rule in (6.6) achieves much the same effect as simpler types of exponence rules, it is worth identifying the source of additional complexity in PFM. Dividing features among the three indices in (6.6) is the most obvious source. A model that makes use of rule blocks requires some means of assigning rules to blocks and the block index merely annotates that information on the rules themselves. The use of separate property set and class indices expresses an intuitive contrast between the ‘content’ features in т and the ‘context’ features in C. However, it ultimately makes no formal difference whether properties are split across two feature sets or pooled in a single set B.

Distributing feature across separate sets and indices in turn complicates the formulationofruleapplicability, asillustrated by thecoherence’ conditions in (6.7). The condition in (6.7a) imposes the usual condition on applicability by requiring a bundle a to contain all of the features in т.

(6.7) Rule-argument coherence (Stump 2001:45)

RRn,,C((X, a)) is defined iff (a) a is an extension of т; (b) L-index(X) e C;

and (c) a is a well-formed set of morphosyntactic properties for L-index(X).

The remaining conditions illustrate the kinds of complications that arise from the scattering of feature information in PFM. Both conditions refer to the function, ‘L-index, which is described as mapping roots and other forms onto the lexemes with which they are associated. In the passage quoted on p. 63 above, Stump (2001) elucidates the notion of L-indices by suggesting:

lie ‘recline’ carries a covert index lie1 (so that L-index(lie) = lie1), while lie ‘prevaricate’ carries a covert index lie2 (so that L-index(lie) = lie2). (Stump 2001: 43f.)

However, if the value of L-index is a lexeme, then condition (6.7b) will only be satisfied if the class index set C contains lexeme indices. On this interpretation, condition (6.7c) requires that individual lexeme indices must also be typed for properties, much as structures in HPSG accounts are typed. Conditions (6.7b) and (6.7c) would both make more sense if they applied to the word class of the lexeme represented by X. But on this interpretation, it becomes even clearer that condition (6.7b) is only required because word class features have been segregated in C, rather than included in т. Moreover, although any feature-based approach must specify wellformed combinations of features, this would normally be defined for a word or inflection class as a whole, and not embedded within the definition of a particular rule format.[3]

Even if all of this can be made to work technically, it is unclear why the feature information in an exponence rule should be organized in this way. There are no obvious formal or empirical problems that are addressed by putting some features in т, others in C and treating yet others as covertly associated by form-to-index functions. Even more fundamentally, it is unclear that different ways of dividing features across sets could have any effect, given that the conditions that apply to particular classes of features can be (and are) defined to look for them in whatever sets they have been assigned to. The main effect of the conditions in

(6.7) is to restrict the applicability of exponence rules, and this can be achieved far more transparently if features are pooled in a single set B, as suggested above.

A rule RR that specifies a consolidated property set B will be applicable to bundles that extend B. Dependencies between class features and morphosyntactic features (as expressed by (6.7c)) are also completely unaffected by whether the features are in a common set or in separate sets, though the statement of these dependencies can be simplified if they are treated as co-occurrence relations within a single feature bundle (or structure).

By consolidating indices into a single set B and eliminating multiple references to the input feature bundle a, it is possible to express exponence rules in PFM in the simpler and more transparent format in (6.8).

(6.8) Simplified realization rule format in PFM RRb «X, a » =defY'

Eliminating multiple references to a is particularly beneficial, as it builds the interpretive character of realization rules into the format itself, rather than enforcing an interpretive construal of a more general format. A realization rule like (6.6) has the syntax of an IP process, which, as described in Chapter 2.3 and in (6.1a), maps entries onto entries. By convention, the property sets represented by the occurrences of a are identical, but this convention is only required because there are multiple occurrences of a. The reason that a is specified at all in (6.8) is that an analysis in PFM proceeds by passing (bundle, form) pairs between the realization rules invoked by a paradigm function.

Stump (2001) acknowledges that exponence rules do not need to make reference to a. However, he argues that such reference is necessary for referral rules and suggests that the inclusion of a permits a unified rule format:

Given any argument (X, a) to which a realization rule applies, the corresponding value (Y;, a) shares the property set a. In light of this, one might well ask why the definition of a realization rule ever needs to make explicit reference to the shared property set. As it turns out... there is a subclass of realization rules—namely rules of referral—whose application yields a value (Y', a) such that the form of Y; depends on the specific identity of a; for this subclass of realization rules, mention of the shared property set a cannot be suppressed. The need for schematization in the definition of paradigm functions makes it desirable to employ a format for the definition of realization rules which is usable for any such rule (whether or not it is a rule of referral)... (Stump 2001:280)

As discussed in Section 6.2.2, exponence and referral rules have different effects. An exponence rule spells out features by forms, whereas a referral rule relates a pair of exponence relations. Referrals cannot be formulated as simple spell-out rules. Exponence rules may be expressed as degenerate cases of referrals, but this does not necessarily express any underlying commonality between the rule types. To the extent that referrals implement the same intuition as the ‘morphological transformations’ and other devices in Section 6.2.3, they trigger the realization of one set of features in place of another. In a PFM analysis, these sets would correspond to values for the index т (or B in the simplified format), not to values for the repeated property a set, representing cells.

The final issue to consider in this brief summary of PFM rules is the form of paradigm functions and the influence that they exert on realization rules. Paradigm functions are the most innovative feature of PFM, representing a distinctive hypothesis about the organization of morphological systems. The basic conception is set out by Stump (2001) in the following terms:

A paradigm function ... is a kind of function... [that] applies to a root pairing (X, a) (where X is the root of a lexeme L and a is a complete set of morphosyntactic properties for L) to yield the a-cell (Y, a) in L’s paradigm. (Stump 2001:43)

This initial form-based format is exhibited in in (6.9).

(6.9) Root-based format for paradigm functions (Stump 2001:43)

PF((X, a)) = (Y, a)

In a subsequent revision of PFM, Stewart and Stump (2007) propose the format in

  • (6.10) , which maps lexeme-property set pairs onto paradigm cells.
  • (6.10) Lexeme-based format (Stewart and Stump 2007)

PF((L, a)) = (Y, a)

Perhaps the most original characteristic of PFM concerns the central role of paradigm functions in the control structure of a grammar. Paradigm functions do not directly modify a root X or spell out a cell a but control the application of the rules that do spell out a by modifying X. An example that Stump (2001:53) provides to describe verbal paradigms in Bulgarian is repeated in (6.11).

(6.11) Where a is a complete set of morphosyntactic properties for lexemes of category V, PF((X, a)) =def NarD(NarC(NarB(NarA((X, a))))).

The paradigm function in (6.11) defines the realization of the paradigm cell a by invoking the most specific realization rules that apply to a in the ordered rule blocks A through D. The rule in block A modifies the root X, and the rules in each successive block modify the output of the preceding block.

This example illustrates how paradigm functions explicitly control interactions that are built into the structure of other realizational models. The paradigm function in (6.11) expressly stipulates intrinsic and extrinsic ordering relations that would otherwise be incorporated into the definition of rule applicability. The nesting of rule blocks A through D in (6.11) imposes an intrinsic order that is attributed to a general block order in realizational models that assign rules to sequentially-ordered blocks. The function ‘Nar’, which picks out the narrowest rule in each of the blocks in (6.11) achieves the effect of a disjunctive ordering condition by imposing a specificity constraint on each block independently. Incorporating these ordering conditions within individual paradigm functions allows for greater flexibility. Within PFM, individual paradigm functions can freely reorder blocks or impose conditions other than relative specificity to regulate the application of rules within a block. Stump (2001, 2005a) argues that this flexibility permits an account of patterns that he attributes to ‘reversible’ rule blocks. Yet even if rule- specific ordering constraints are useful for the description of exponent reversal, it does not follow that constraints should also be stipulated on a rule-by-rule basis in languages that have a uniform block order and obey a general disjunctive ordering condition.

As this brief summary suggests, much of the complexity of PFM derives from two related design features. The first is the use of maximally uniform rule formats, so that the most complex rule type determines the complexity of the entire class to which it belongs. The second is a maximally local control structure, mostly delegated down to the level of individual rules. This again reflects a uniformity hypothesis, which dictates that if the analysis of any construction requires rule- by-rule stipulation of block and rule ordering constraints, then all analyses should stipulate these constraints at the level of individual rules.

A number of recent works, notably Spencer (2013) and Bonami and Stump (2015), propose substantial revisions to PFM, some of which bear on issues that arise within the ‘classic PFM’ model formulated in Stump (2001). Once these proposals have been integrated into a new reference model of PFM, it may be possible to evaluate the cumulative effect of the revisions and execution choices and clarify the formal and empirical claims they embody.

  • [1] As in other realizational models, rules define correspondences between features and forms, so thatreferences to ‘input’ and ‘ouput’ structures are a matter of expositional convenience and do not imputeany genuine derivational structure.
  • [2] Although this may appear to be a complication of previous formats, the classes represented by ‘Y7’are largely implicit in the phonemic representations in earlier rules.
  • [3] A separate technical problem is that ‘L-index’ cannot be a function, since no actual function canmap an ambiguous string to multiple unambiguous lexeme indices.
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