Projecting Grammatical Features in Nominals: Cognitive Theory and Computational Model

A localist theory of the representation and projection of grammatical features in nominals is presented in which words and phrases functioning as specifiers and modifiers—in addition to heads—project grammatical features to encompassing nominals. Grammatical features may be redundantly encoded in words and phrases fulfilling different grammatical functions. At the level of the nominal, the projected grammatical features are collected into a set without duplicates. Redundantly encoded grammatical features may occasionally conflict or a grammatical feature may be unspecified—without the expression being ungrammatical— necessitating mechanisms for handling conflicts and accommodating unspecified features. An incremental, serial, pseudo-deterministic system for processing nominals which operates over an interactive (context-sensitive), parallel, probabilistic, constraint-based substrate is presented and motivated. Within this overall processing capability, non-monotonic mechanisms of blocking and overriding of grammatical features, without backtracking, are presented for handling conflicts. These non-monotonic mechanisms are part and parcel of normal processing and are not viewed as exceptional. Construal mechanisms for handling unspecified features are also needed. In the simplest case, the referent of the referring expression provides the (semantic) basis for construal of unspecified features. The processing of nominals within a computational cognitive model of language processing implemented in the ACT-R cognitive architecture is used to demonstrate and support various representational and processing claims. Representational Considerations The current linguistic standard as exemplified in X-Bar Theory (Chomsky, 1970; Jackendoff, 1977), Generative Grammar more generally (cf. Radford, 1997, 2004), and HPSG (Sag & Wasow, 1999; Sag, Wasow & Bender, 2003) is that heads project the category of the phrases they head. In the case of a noun phrase, it is assumed that a noun head projects the category of the noun phrase. It is also typically assumed that heads project various grammatical features to the phrases they head (or that grammatical categories are really just collections of grammatical features). For example, the noun head of a noun phrase may project grammatical features like person, number and gender to the noun phrase. More specifically, if the noun phrase is ―the man‖, the noun head ―man‖ may project the grammatical features third-person, singular, and male. The person and number features are assumed to be needed for determining agreement in expressions like ―the man runs‖ and the number and gender features are needed for binding pronouns and reflexives appropriately as in ―the meni like themselvesi‖ or ―the mani believes hei is smart‖. Projection of features is especially important to localist theories in which there is no non-local access to grammatical features (cf. Sag 2009). For example, on localist principles, in ―the man runs‖, only grammatical features associated with the noun phrase ―the man‖ are accessible to satisfy agreement with the verb ―runs‖ (or its projection). There is no non-local access to the agreement features of ―man‖ which have not been projected to the noun phrase. It is sometimes also assumed that only heads project grammatical features. For example, the head feature principle (HFP) of HPSG is (largely) based on this assumption (Sag & Wasow, 1999), and in the Minimalist Program as described in Radford (1997) only semantically interpretable head features are retained in LF representations. However, this assumption leads to a system of linguistic representation in which most of the subcomponents of a phrase must be heads in order to project the needed grammatical features to the headed phrase, or to a system in which heads must redundantly encode features marked on non-heads. Consider the simple expression ―the man‖. If the grammatical feature definite which is part of the grammatical behavior of ―the‖ needs to be projected to the encompassing phrase and the grammatical features of ―man‖ also need to be projected, then the following options are apparent: 1) ―the‖ is the unique head (cf. Abney, 1987) and we must somehow mark the grammatical features of ―man‖ on ―the‖; 2) ―man‖ is the unique head and we must somehow mark the definiteness feature of ―the‖ on the head ―man‖, 3) both ―the‖ and ―man‖ are heads and project grammatical features, or 4) we must relax the assumption that only heads project grammatical features (the approach adopted herein). In the first approach—the functional head approach—since ―the‖ is the unique head, ―man‖ is typically treated as a complement of ―the‖ (complement being the best available place in the X-Bar schema for the non-head noun given a functional head). How then do the grammatical features of ―man‖ get projected to the encompassing phrase (typically called a determiner phrase or DP)? Grimshaw (2000) introduces the notion of extended projections in which a noun complement can project grammatical features without violating basic notions of endocentricity (Bloomfield, 1933) by assuming that the noun complement and functional head are of essentially the same syntactic category with respect to grammatical feature projection. In fact, Grimshaw treats the noun complement as an extended head. However, treating the noun as both a complement and an extended head distorts the basic notion of complement (which we take to be largely synonymous with argument). The basic function of complements is to describe distinct objects that are related to the head of an expression. The description of these distinct objects requires its own grammatical features. In order to accommodate functional heads, Grimshaw is forced to adopt a distinction between complements of lexical heads and complements of functional heads, since complements of lexical heads do not project features, whereas complements of functional heads do. Radford (1997) presents an alternative approach in which the grammatical features normally associated with nouns are redundantly encoded on the determiner. This approach leads Radford (1997, p. 188) to suggest that ―the‖ in ―the students take themselves too seriously‖ has the features third-person, plural and nominative—since ―the‖ is the head of the subject! Worse, in an expression like ―the man‖, ―the‖ would presumably encode the gender feature male as well (although Radford does not discuss this possibility). Besides the fact that there is no grammatical evidence that ―the‖ encodes these features, note the tremendous ambiguity that such an approach introduces: ―the‖ will have multiple sets of grammatical features which can only be resolved by the overall context in which it occurs. The second approach is simply the reverse of the first approach with ―man‖ functioning as the ―head‖ and the grammatical features of ―the‖ needing to be redundantly encoded on ―man‖ or handled via something like extended projections. The grammatical evidence suggests that singular count nouns are not marked for definiteness (in English), and insisting that they carry a definiteness feature adds ambiguity that cannot be resolved by the noun. For example, to handle ―a man‖ vs. ―the man‖, ―man‖ would need to be coded as either indefinite or definite, depending on the determiner. At least the determiner ―the‖ or ―a‖ is available when ―man‖ is processed and can influence the selection of the appropriate grammatical features for ―man‖. This is not the case in the first approach. In the third approach, both ―the‖ and ―man‖ are treated as heads (on the same level) and can project grammatical features to the encompassing phrase. For example, in Cann (2001), ―the‖—which functions as a specifier—is treated as a secondary head. The primary problem with this approach is the positing of two heads to capture the fact that both the determiner and noun need to be able to project grammatical features to the encompassing phrase. As will be argued below, modifiers (but not complements) can also project grammatical features. Rather than proposing a three-headed monster to allow modifiers and specifiers to project grammatical features as well as heads, we will relax the assumption that only heads project grammatical features. In the fourth approach—which is adopted and motivated in this paper—if we allow nonheads to project grammatical features to encompassing phrases, then in the example ―the man‖, the determiner ―the‖ can project the feature definite and the noun ―man‖ can project the features third-person, singular and male. We will further assume that ―man‖ is the head of the expression based on semantic evidence that the expression ―the man‖ can be used to refer to an object of type man—assuming a semantic motivation for the functional category head (see Ball 2007a for further details). If ―man‖ is functioning as the head, what is the functional status of ―the‖? A traditionally suggested candidate is modifier (cf. McCawley in Cheng & Sybesma, 1998), but a better candidate is specifier— we agree with Cann (2001) and Chomsky (1970), in this respect. To the extent that the functional categories modifier and specifier are distinct, determiners are better treated as specifiers since they combine with nouns to form complete noun phrases (e.g., ―the man‖) whereas modifiers often combine with nouns to form incomplete noun phrases (e.g., ―old man‖). (For arguments against the distinction between specifiers and modifiers, see van Eynde, 2006.) This is an original insight behind the idea put forward in Chomsky (1970) that specifiers combine with heads to form maximal projections. Ball (2007a) adapts Chomsky’s formalism in positing four phrase internal (or sub-maximal projection) functional categories: specifier, head, modifier (called adjunct by Chomsky) and complement. HPSG (cf. Sag & Wasow, 1999) adopts the same set of basic phrase internal functional categories. Huddleston & Pullum (2002) adopt the sub-phrasal functional categories determiner (where determiner is a functional category and determinative is the part of speech of words like ―the‖), head, modifier and complement. Biber, Conrad & Leech (2002) adopt the same functional categories as Huddleston & Pullum, but do not make a distinction between determiner as a functional category and determiner as a part of speech. In this paper, determiner will be used as the part of speech of words like ―the‖ and specifier as the grammatical function that is typical of determiners. Allowing for specifiers to project grammatical features (which is also assumed by Grimshaw, 2000, in the case of possessive nominals), one can ask if modifiers and complements can also project grammatical features. If ―two‖ in ―the two books‖ is functioning as a modifier, then the modifier ―two‖ can project the number feature plural. Since ―books‖ also projects the feature plural, projection of this feature by ―two‖ is redundant. However, in an expression like ―the two on the counter are ready‖, the grammatical evidence suggests that ―two‖ projects the feature plural as indicated by the plural agreement with ―are‖. In this example, is ―two‖ functioning as a modifier or head? On the assumption that the head is empty, it is functioning as a modifier. Further support for the existence of empty heads in noun phrases (which are henceforth called nominals since a noun head need not occur) is provided below. With respect to complements, to the extent that ―of books‖ is functioning as a complement in ―a pile of books are on the table‖, it appears that complements can also project grammatical features—at least the number feature. However, I do not believe that ―of books‖ is functioning as a complement (i.e., to the extent that nouns take complements, it is the combination of the noun—in this case ―pile‖—with the nonoptional preposition ―of‖ that licenses the complement, not the noun by itself), and if there is a phrase internal functional category that does not project grammatical features it is the complement category. Complements describe objects that are related to heads. The elements of the complement project grammatical features to the complement phrase, which requires its own set of grammatical features, but complements do not contribute to the grammatical description of the head per se. Given the basic function of complements (which has unfortunately been clouded with the introduction of functional heads), it would be surprising if they projected features to the encompassing phrase. If ―of books‖ is not functioning as a complement in ―a pile of books‖, what is its grammatical function? ―Of books‖ may be functioning as a modifier of ―pile‖, with ―pile‖ functioning as the head (in which case ―a pile of books is on the table‖ would be expected), or ―books‖ may be functioning as the head of ―a pile of books‖ with ―a pile of‖ functioning as a phrasal specifier (or ―pile of‖ functioning as a modifier). Note that in the latter case, the plural feature of ―books‖ overrides the singular feature of both ―a‖ and ―pile‖ and yet ―a pile of books are on the table‖ is grammatical for many speakers of English. It is also the case that the closer proximity of a non-head noun to a main verb, relative to the head noun of the subject which normally determines verb agreement, can influence verb agreement in ways that are not discussed in this paper, but which could explain the plural agreement between ―books‖ and ―are‖ without assuming ―books‖ is the head of ―a pile of books‖ (cf. Quirk et at., 1985). More generally, if a non-head noun (i.e., preor post-head modifier) is more cognitively salient than the head noun as in ―a pile of books‖ or ―the airspeed and altitude setting are unchanged‖, the non-head noun, or conjunction of nouns, may block or override the number feature of the head noun. Definiteness, Person and Number What the determiner does when functioning as a specifier is provide the primary indication of the definiteness of the nominal in which it is embedded. I use the term ―primary‖ since not all nominals contain a determiner and yet they nonetheless provide an indication of definiteness. For example, the nominal ―books‖ in ―books are fun to read‖ is indefinite. Since the nominal only contains the plural noun ―books‖, ―books‖— and more generally plural nouns—must be capable of providing an indication of definiteness. An alternative is to assume a zero determiner (cf. Biber, Conrad & Leech, 2002) that projects the definiteness feature. But that leaves unexplained why ―books‖ but not ―book‖ can occur alone as a nominal. If we allow both specifiers and heads to project grammatical features, there is the possibility of conflict between the grammatical features that each projects. For example, the nominal ―the books‖ contains both a determiner and a plural noun. On the assumption that ―the‖ projects the feature definite and ―books‖ projects the feature indefinite there is a conflict. This conflict can be resolved if we assume that the definiteness feature of the specifier is primary and blocks the definiteness feature of the head. Thus, ―the books‖ refers to a definite, but plural quantity of books. Note that ―books‖ may still project the features third-person and plural which are not blocked by ―the‖. On the other hand, the determiner ―a‖, unlike ―the‖ projects the number feature singular and blocks the number feature plural making ―a books‖ ungrammatical. Within this formulation, why ―a books‖ is ungrammatical, whereas ―the books‖ is grammatical is an interesting and as yet unanswered question. This question is complicated by the fact that ―a few books are on the table‖ is grammatical, suggesting that at least under some circumstances the singular number feature of ―a‖ can be overridden. An assumption worth exploring is that for a nominal to be grammatical it needs to encode a set of grammatical features which, as a minimum, might include definiteness, person and number—regardless of whether these features come from the specifier, modifier or head. Adopting this assumption (for now), the ungrammaticality of ―the‖ and ―a‖ used by themselves as nominals can be explained if they do not encode for one or more of these grammatical features. In the case of ―a‖, the person feature may not be encoded, and in the case of ―the‖ both person and number are not encoded. Similarly, singular count nouns like ―dog‖—unlike plural and mass nouns—fail to encode the definiteness feature and do not normally occur alone as nominals. On the other hand, the fact that ―that‖ and ―these‖ can occur alone as full nominals suggests that they do encode for these grammatical features. ―That‖ is definite, third-person, singular, and ―these‖ is definite, third-person, plural.