The Marking and Morphing Model

The MARKING AND MORPHING MODEL is embedded in a two stage model of syntactic encoding as described above (cf. Bock and Levelt, 1994; Bock, 1995b;

Bock et al., 1992; Levelt, 1989; a comprehensive overview is given in Ferreira and Engelhardt, 2006). In accordance with the two levels of grammatical en-coding the Marking and Morphing Model assumes two distinct processes for the specification of number and in particular the production of number markers on agreement targets. NUMBER MARKING relates to syntactic function assignment and is determined by notional number, whereas NUMBER MORPHING applies at the positional level and is predominately determined by grammatical number.

Number morphing is a bunch of operations that are related to each other. Number morphing binds morphological information to structural positions, compromises syntactic number values (resulting from number marking) and lexically specified number values, and transfers number features to agreement targets (e.g., verbs).

Marking and morphing differ in their sensitivity to notional factors. While no-tional number affects number marking directly, it has no direct impact on number morphing. The later process is exclusively controlled by syntactic factors, that is grammatical number. Notional number comes only indirectly into play, namely via the number marking of the particular noun phrase.

The Marking and Morphing Model was first proposed for verb agreement (Bock et al., 2001) and later extended to pronoun agreement (Bock et al., 2004;

Eberhard et al., 2005). It provides an elegant account for similarities and differ-ences between the two kinds of agreement relations. Since verbs do not have any inherent number value, they get their number specification via agreement which is computed through syntactic processes transferring the number morphing of the subject noun phrase to the verb. Pronouns, on the other hand, have a lexically specified number value. This difference explains why pronouns are more sensi-tive to notional number than verbs.

Attraction is assumed to occur during number morphing. As noted above, number morphing involves the transfer of number features to agreement targets.

Usually, the grammatical number of the subject noun phrase controls the number specification of a corresponding verb. But a distractor can interfere in this rela-tion. The details of number marking and number morphing and in particular the occurrence of attraction will be discussed in turn.

3.4.3.1 Three Types of Number

The Marking and Morphing Model distinguishes three different types of number which are represented at different levels. Notional number is a property of dis-course referents whereas grammatical number is a property of lexical items (both lexical and grammatical morphemes) and syntactic words. Finally, morphological number is the morphological instantiation of grammatical number.

Notional number is represented at the message level and transferred into syn-tax via the process of number marking. Grammatical number is associated with morphemes in the lexicon and applies to phrases at the positional level. Number morphing mediates between notional number of syntactic functions and grammat-ical number features contributed by words and morphemes.

For noun phrases, grammatical number is a compromise between the notional number marking of the corresponding syntactic function and the grammatical number values contributed by the lexical items. In the absence of lexically spec-ified number values, notional number prevails; singular nouns can show plural agreement when the corresponding message element is perceived as a plurality (e.g., collective nouns like faculty or distributive readings of phrases like the label on the bottles). In the presence of a lexically specified number value, grammatical number dominates number morphing; plural nouns show plural agreement even when notionally perceived as singletons as in the case of summation plurals like scissors. Notice that the term ‘specified number value’ refers to plural specifica-tion, that is the marked opposition.

While Bock and her colleagues do not make any specific claim regarding the mental representation of number in their original proposal, they seem to follow their previous assumptions about an asymmetric representation of number: Plu-ral is explicitly represented, singular is not (Eberhard, 1997). Evidence for this assumption comes from the asymmetric attraction pattern observed in a series of experiments. The rationale is the one presented above: Singular nouns are usu-ally not specified for number whereas plural nouns are specified for plural - either inherently or due to the contribution of the plural morpheme.

Eberhard et al. (2005) provide a model in which number is represented by a continuously valuated number feature, the so-called SINGULAR-AND-PLURAL FEATURE (‘SAP feature’ for short). The basic idea is that the number valuation underlying the discrete singular–plural distinction at the morphosyntactic level is actually gradient. In a nutshell, the more positive the value the more plural-like the corresponding item, the more negative the value the more singular-like the item.

The SAP-feature ranges from −1 (unambiguously singular) to +1 (unambigu-ously plural). Plural NPs have a positive SAP-feature value, singular NPs have a near zero value (or negative value when a singleton is explicitly individuated, e.g., by means of a proper name or a singular quantifier like one etc.).

Lexical number specifications vary according to the noun class (count nouns, collective nouns, pronouns etc.) and the contrastive frequency (C_{f requ} in equation 3.1). The later is estimated by the ratio of singular frequency and plural frequency (for details of the equation see Eberhard et al., 2005). This frequency adjustment is motivated by the finding that a singular controller that has a contrasting plural counterpart is more vulnerable to attraction than a singular tantum.

S(m) =speci f ication×C_{f requ} (3.1) Determiners contribute their own lexically specified value: zero for ambiguous determiners like the, a negative value for singular quantifiers like one or each, and a positive value for plural quantifiers like many. The probability of a plural verb is lower when a singular quantifier accompanies the singular distractor. A singular quantifier contributes a negative value and therefore diminishes the SAP value for the entire NP. This explains why phrases like the keys to one cabinet cause attraction errors while phrases like the keys to the cabinet do not.

3.4.3.2 Number Marking

Number marking is based on the notional valuation of discourse referents with regard to numerosity and results in an abstract number specification of syntactic functions. The whole process of number agreement starts at the message level where the valuation of discourse referents with regard to numerosity takes place.

During functional processing, grammatical functions are number marked in such way that their grammatical number value fits the numerosity valuation at the mes-sage level. Basically, the notional number of event participants determines the number marking of the corresponding noun phrase. Thus, when the message ele-ment that will later be mapped onto the subject function is valuated as a singleton, the subject is marked as being singular; if the message element is a plurality, the subject is marked as being plural. Note that number marking does not apply to nouns, that is bare words, but rather to noun phrases or actually grammatical func-tions (remember that subject and object etc. are syntactic primitives).

Furthermore, functional processing involves lexical selection. Lemma re-trieval must be consistent with the conceptual features in the message including notional number valuation. For pronoun selection, the task is straightforward:

Pronouns are lexically specified for number. Thus, if the corresponding message element is valuated as being notionally plural, a grammatically plural pronoun has to be chosen, if the message element is notionally singular, a singular pronoun has to be retrieved. The same logic applies for further categories like animacy, person and gender.

Noun selection is harder, for two reasons. First, a message element can cor-respond to more than one noun (e.g., ham and eggs or the man with the hat).

Second, lexical entries for nouns are often not specified for number. To satisfy notional plurality, it might be necessary to select the entry for a count noun to-gether with the entry for the plural morpheme. Alternatively, the speaker might chose a noun inherently specified for plural such as parents.

The number marking of the subject NP (and any other NP) is calculated by a spreading activation process involving two sources: the notional number of the intended referent and the lexical number specification contributed by the mor-phemes contained in the NP. The resulting SAP-feature value is the sum of the notional number value plus the weighted sum of the lexical feature specifications on the nouns and determiners contained within the NP. The equation in 3.2 gives the details of the calculation. The reconciled number valuation of the subject NP is represented as S(r), notional number is represented as S(n)and the morpheme number valuations are symbolized by S(m). The index j indicates that several morphemes might contribute their number values, wj represents the correspond-ing weights.

S(r) =S(n) +

∑

j

(3.2) S(n)is directly determined by the message level number information. Pluralities have a positive value, singletons have a zero value. Notionally number ambiguous entities (e.g., masses, collections and distributions) are represented with a value of about 0.5. In case of specific individuation, S(n)is−1.

3.4.3.3 Number Morphing

While number marking applies at the functional level, number morphing applies at the positional level. At this point, grammatical agreement features are determined on the basis of the morphological specifications of words. Although the process of number morphing is mainly determined by grammatical number, notional number has a chance to prevail, in particular in the absence of lexically specified number features. Number morphing has three functions: (i) the binding of morphological information to structural position, (ii) the alignment of number information from number marking and lexical specifications and (iii) the transfer of the resulting number feature to dependent elements such as verbs.

For noun phrases, number morphing has two sources: the lexical number fea-tures of the lexical items and the number marking of the corresponding syntactic function. Simple count nouns are assumed to be unspecified or only weakly speci-fied for number. When accompanied by a plural morpheme, however, the resulting number morphing is plural because the plural morpheme contributes a lexically specified grammatical number value. In the absence of any number information at the lexical items, number morphing instantiates the abstract notional number

marking. Collective nouns, for instance, are not lexically specified for number.

As a consequence, notional number marking is the only determinant for number morphing. Since the semantics of a collective noun is compatible with both a sin-gle referent (which is further structured) and a plurality, grammatical number can be singular or plural. When the speaker conceptualizes the referent as a singleton, number marking is singular and number morphing transfers this notional number value to the grammatical number value singular. When the speaker focuses on the individual members of that unit, number marking is plural as is the grammatical number value. This explains why the gang on the motorcycles is more likely to take a plural verb than the gang near the motorcycles (cf. Humphreys and Bock, 2005). In other words, grammatical number of collective nouns depends on the number valuation of the discourse referent.

In case of conflicting information, number morphing has to solve the conflict.

Take for instance summation plurals like scissors. Due to the plural morpheme, summation plurals are lexically specified for plural. Nevertheless, the number marking of the corresponding syntactic function might be singular, because the corresponding object is perceived as a singleton. We end up with a mismatch between grammatical number and number marking. In this case, grammatical number overrides notionally determined number marking.

For verbs, number morphing results from a transfer process. Verbs are neither intrinsically specified for grammatical number nor marked for notional number at the functional level. Number morphing of verbs is controlled by the number specification of the subject noun phrase. Contrary to Vigliocco, Butterworth and Garrett (1996), the marking and morphing model does not assume a direct relation between the message level and the number specification of verbs. Instead, the model assumes that the number value of a verb is controlled by the subject noun phrase and computed via number morphing.

3.4.3.4 The Emergence of Attraction

Attraction errors arise during number morphing. They reflect conflicts between notional number of the subject and morphological number of words and mor-phemes. When a singular subject contains a plural distractor (e.g., a modifier as in the key to the cabinets), the resulting number morphing is still singular. But when the number value of the modifier interferes during number morphing, occasionally the subject will end up with a plural specification which will then be transferred to the verb. Since number morphing is mainly determined by lexically specified number values, a plural distractor has a chance to interfere because of its inherent plural specification or its plural morpheme. In the reverse constellation, a singular distractor can affect number morphing only when lexically specified for singular.

Thus, attraction can only occur with a marked singular distractor (e.g., the keys to

one cabinet, cf. Eberhard, 1997).

Under the assumption of a Singular-and-Plural feature, the asymmetry is de-rived as follows: A plural head NP contributes a positive value, while a singular distractor contributes a zero value. The sum of both is greater than zero and as a consequence most probably a plural verb is produced. In the reverse configu-ration, the singular head NP contributes zero and the plural distractor contributes some positive value, resulting in a sum that is slightly greater than zero. As a con-sequence, the probability of producing a plural verb is higher than in the match condition in which the zero value of the singular head NP and the zero value of the singular distractor NP sum up to zero for the whole NP.

Because verb agreement, respectively attraction errors, results from number morphing, the notional number value of a potential distractor does not play a role.

Being notionally plural is neither necessary nor sufficient for causing attraction.

The crucial factor is grammatical number. This explains why attractions occur with grammatical plurals (independent of their notional number, compare razors and scissors), but not with notionally plurals which are not also grammatically plural, e.g., collective nouns like team (for details see section 3.3.4). Although notional number is more or less irrelevant for attraction, it has still some impact on agreement. As pointed out above, the whole process of agreement computation starts at the message level where the numerosity of discourse referents is valuated.

Agreement computation proceeds with number marking which is sensitive to mes-sage features. Furthermore, notional number prevails in number morphing when the lexical item either contribute the same number value or no number value at all. Beyond this indirect influence, notional number does not affect subject–verb agreement. In its essence, verb agreement is determined by grammatical number only.