UNINTERPRETABLE FEATURES AND AGREEMENT* Akira Watanabe University of Tokyo 1. Introduction Recent work exploring the evolution of human language (Berwick and Chomsky 2011; Chomsky 2005, 2007, 2010) presents the view that it is a one-time event that yielded unbounded Merge, with externalization of language as a subsequent secondary process that does not involve a genomic change. This hypothesis is embedded in the following version of the strong minimalist thesis (SMT) formulated by Chomsky (2010), slightly modifying the title of Sauerland and Gärtner (2007): (1) Interfaces + Merge = Language where language is understood to mean the faculty of language in the narrow sense (FLN) in the wording of Hauser, Chomsky, and Fitch (2002). Left out of this scenario is the status of Agree, which defines one of the two syntactic relations in a rather parsimonious computational system posited in the Minimalist Program (Chomsky 2004, 2008), the other one being set-membership given by Merge. What I would like to do in this article is to clarify how Agree fits the Merge-centered picture of language evolution. An obvious step is to link it to the process of externalization, but the problem is that externalization is regarded as a secondary process under the hypothesis summarized above. Is the emergence of Agree also a secondary process? My proposal is that Merge itself lays the foundation for the major players in the operation of Agree, namely, uninterpretable features, opening the door for externalization at the same time. In relation to this, I will also put forward a new conception of the Agree operation and pursue some of its consequences. As an initial step in pursuing the idea, I begin in section 2 by summarizing the key properties that the Transfer operation must deal with in handing over the output of narrow syntax to the system that leads to the sensorimotor (SM) interface, called externalization above, focusing on uninterpretable features that drive the operation of Agree. A new conception of the Agree operation is presented next. The inventory of uninterpretable features and their theoretical status are also discussed. Section 3 applies the new conception of Agree to a rather rich empirical domain involving complex nominal morphology found in Jemez and Kiowa, reworking Harbour’s (2011) account. The result is a unified treatment of inverse in the two languages, which Harbour’s original account fails to achieve. 2. Agree and Externalizartion of LOT FLN is a computational system that connects the conceptual-intentional (CI) interface to the SM interface, with narrow syntax sitting in its center. Lexical items are atomic units of narrow syntax computation, combined by the operation of Merge to form complex structure. * I would like to thank the audience at GLOW in Asia IX for helpful discussion. The research reported here was supported by Grant-in-Aid for Scientific Research (C) 22520492 from the Japan Society for the Promotion of Science. The Proceedings of GLOW in Asia IX Semantic and phonological features are packed together in lexical items, to be used in the CI and SM systems, respectively. FLN must therefore include an operation of Transfer, which teases apart semantic and phonological information, sending the former to the CI interface and the latter to the SM interface. It is not just phonological features that are handed over to the so-called PF branch of FLN, however. Narrow syntax contains an operation of Agree, which gives a value to originally value-less uninterpretable features by matching them with valued interpretable counterparts (Chomsky 2001). Once valued, uninterpretable features may be realized phonologically, a rather interesting property of natural language. This means that Transfer also picks out uninterpretable features that have undergone Agree and sends them to the morphological computational system that assigns to them phonological forms as in the theory of Distributed Morphology (Halle and Marantz 1993 and subsequent work). Thus, there are two sources of phonological information, namely, phonological features of lexical items and uninterpretable features valued by Agree. What would be the form of FLN if we adopt the view put forth by Berwick and Chomsky (2011) and Chomsky (2005, 2007, 2010) that the system of externalization came later in the evolution of human language? They claim that FLN functioned as a system for a language of thought (LOT) at the earliest stage when human language emerged. This consequence is innocuous as far as lexical items are concerned. The research in the 1980’s emphasized the significance of empty categories, which are not realized phonetically, as strong evidence for the working of universal principles. Functional categories also often come without phonological content, perhaps reflecting the LOT nature of FLN. So it is perfectly natural to have a structure building system that dispenses with the link to the SM interface. The computational system without externalization, however, cannot retain the operation of Agree in the form currently assumed. Agree outputs valued uninterpretable features that need to be taken care of by morphology. Without externalization, such features cannot exist. One might imagine handling them by brute-force deletion, but then, there is no point in throwing them into the computational system in the first place. Only with the potential of phonetic realization do uninterpretable features serve the purpose of establishing a link between the CI and SM interfaces through Agree, which matches interpretable features (CI entities) with their uninterpretable counterparts (see Watanabe 2008). There are only two logical possibilities: the initial computational system of FLN is equipped with the Agree operation together with uninterpretable features, or it isn’t. I lean toward the affirmative answer here. At the same time, evidence for the primacy of the CI interface is considered to be robust, including the design optimization keyed to the CI interface and the lack of substantial differences between spoken and sign languages. How can one reconcile the CI primacy of FLN with the eventual linkage of Agree to the SM interface? I am not prepared to give a full story in this article, but hope to provide a plausible outline. I will concentrate on elucidating the nature of uninterpretable features by developing the suggestion made in Watanabe (2009) that they are recruited from semantic features. This suggestion locates the origin of uninterpretable features in the CI systems. I would like to elaborate it in this section. 2.1. Formal Features, Semantic Interpretation, and Agree Uninterpretable features that drive the operation of Agree are classified as formal features in the typology of features proposed by Chomsky (1995), according to which there are two kinds of features that contribute to semantic interpretation in the CI systems. One is called semantic features, and the other interpretable formal features. The difference between the two is that semantic features are inert during narrow syntax whereas formal features enter into agreement when interpretable ones are matched with their uninterpretable counterparts Uninterpretable Features and Agreement (A. Watanabe) under appropriate locality conditions. The proposal of Chomsky (2001), mentioned above, views this process as valuation. Crucially, there are no formal features like [±consonantal]. For this reason, Watanabe (2009) argues that formal features are recruited from resources on the CI side even though there are uninterpretable versions of them. Furthermore, comparative study of different stages of English suggests that there is a parameter concerning feature classification allowing the definiteness feature to act as formal in some languages and as semantic in others, reinforcing the case for the idea that formal and semantic features share a common evolutionary origin. Then, precisely how are uninterpretable formal features created out of CI resources? To answer this question, we need to sharpen the notion of uninterpretable features that receive a value through the Agree operation. For this purpose, we can make use of Harbour’s (2007, 2011) proposal that uninterpretable features are characterized by the presence of both the plus and minus values, as in [+F, –F] for the feature F. This specification is uninterpretable because it gives contradictory instructions. Now, observe that it is a small step from this conception of uninterpretability to identification of the evolutionary process that derives it: binary Merge. Harbour himself (2011: note 5) comments that given a combinatorial system such as syntax, the existence of [+F] and [–F] can automatically give rise to [–F, +F] unless a further stipulation blocks cooccurrence of the two. Since Merge forms a set, the uninterpretable version of F is {+F, –F}, strictly speaking.1 The prerequisite for this hypothesis is that conceptual resources for formal features must come in pairs. Harbour (2011) indeed argues for the bivalent nature of number features on the basis of the analysis of Kiowa and Jemez, which will be revisited in section 3. See also Watanabe (2010) for the same conclusion from different empirical material and Watanabe (to appear) for the binarity of the person feature system. Quite generally, the strictly privative feature system is incompatible with the use of valuation for agreement, as Adger and Svenonius (2011) point out, since valuation presupposes two distinct states of a feature. After the privative system is ruled out, there remain various logical possibilities for multi-valued features. Only the binary system, however, is compatible with the idea that Merge creates uninterpretable formal features. Once uninterpretable features are made available for the FLN computation and are actually thrown into the derivation together with lexical items, the need to get rid of them immediately arises. The outlet must be the SM systems. Thus, we can conclude that the motivation for externalization comes from exploitation of the CI resources by the operation of Merge. One may say that this is another respect in which the CI interface enjoys the primary status. FLN is destined to develop the mechanism of externalization even though it is an instrument for LOT. This reasoning also suggests that the distinction between semantic features and interpretable formal features is superfluous and derivative. Uninterpretable features are created out of interpretable ones and therefore can always be matched with them (with one important exception that will be taken up in section 2.3). It is an open empirical question whether the earliest stage of FLN already possessed the system for externalization. The availability of uninterpretable features could be only latent at the beginning. The question needs to be addressed together with whether the earliest stage of FLN already possessed the operation of Agree. One relevant consideration has to do with the fact that Agree serves as a search mechanism for the proper operation of Internal Merge. It is not clear whether Internal Merge can work in an optimal way without the help of Agree. Did 1 I am not saying that Merge forms uninterpretable features as part of derivation. I assume that they are given for each individual language, with the precise inventory parametrized. My claim is that binary set formation is responsible for the phylogenetic origin of uninterpretable features. Let me add that recursion is not needed for the creation of uninterpretable features. It would only give rise to monsters that the externalization system cannot handle. The Proceedings of GLOW in Asia IX the earliest stage of FLN lack Internal Merge, even though this mode of Merge is given for free (Chomsky 2004)? I will not resolve the issue here. Instead, I now turn to the formulation of Agree. 2.2. A New Theory of Agree The idea that uninterpretable features come in the form of {+F, –F} allows us to reconsider the valuation mechanism of the Agree operation. Harbour (2007, 2011) takes the view that values matched with those of the interpretable counterpart are retained and become visible at PF, whereas unmatched values get deleted (or simply become invisible at PF). Under this conception, retention of the matched values is the core process of valuation. I would like to propose instead that valuation is indeed deletion. The traditional intuition tells us that what happens in agreement is something like (2). (2) a. Valuation of {+F, –F} with +F means deletion of –F, producing {+F}. b. Valuation of {+F, –F} with –F means deletion of +F, producing {–F}. But if valuation deletes one of the two values, there is no logical necessity that things should work as in (2). Agreement can operate in the opposite direction, as in (3). (3) a. Valuation of {+F, –F} with +F means deletion of +F, producing {–F}. b. Valuation of {+F, –F} with –F means deletion of –F, producing {+F}. In other words, matching of {+F, –F} with +F (or with –F) itself does not dictate which value should go as a result of valuation. No matter which value is deleted, it is a stipulation made arbitrarily. And as long as valuation always involves deletion, this arbitrary choice must be made for each case of agreement, a locus of parametrization. Is there any evidence that the option in (3) is needed? Actually, a mundane fact about English subject-verb agreement seems to require it. Commenting on data like (4), Chomsky (1975:234) remarks that the singular form of the verb is matched with the plural subject and vice versa, viewing the suffix -s as a marker of [–singular] both in (4a) and in (4b). (4) a. The boys like apples. b. The boy likes apples. The conventional treatment leaves the two -s suffixes in (4a, b) as completely unrelated. The new conception of agreement allows us to accommodate data patterns like (4) in a uniform account of what looks like a single morphological piece. Option (2) is also needed, in view of the following Spanish data from Harris (1991:34): (5) a. Mi sobrino es alto. my nephew is tall.m b. Mi sobrina es alta. my niece is tall.f Here, the feminine subject forces the feminine form of the adjective, and the masculine subject the masculine form.2 Given the conventional treatment of agreement, one may be led to think that option (2) is the unmarked choice. But the matter is entirely empirical. Future research should examine the distribution of options (2) and (3). Anders Holmberg pointed out to me that the mechanism of valuation in terms of deletion 2 See Watanabe (2011) for an account of agreeing predicative adjectives in terms of Multiple Agree. Uninterpretable Features and Agreement (A. Watanabe) finds an analogue in pairing of yes-no questions and answers. Yes-no questions denote a set of propositions of the form {p, ¬p}, from which the answer is formed through deleting one of the propositions. Note the striking formal similarity. Valuation may have been designed on the model of the CI system that lies behind yes-no questions and answers. 2.3. CI Resources Let us examine next whether the conceptual resources for the φ-feature system were available at the birth of FLN. To start with the number features, Hauser, Barner, and O’Donnel (2007) report that rhesus monkeys exhibit the sensitivity to the singular-plural distinction. There does not seem to be any obstacle to the assumption that [±singular] was recruited from pre-linguistic conceptual resources. For [±augmented], on the other hand, there is no comparative study, as far as I am aware. Watanabe (2010) suggests that [±augmented] is involved in licensing of numerals, linked to the natural number system. If the notion of natural numbers was made possible by the emergence of Merge along the lines suggested by Chomsky (2008), [±augmented] could not have existed prior to the appearance of FLN, at least in the form linked to natural numbers. The notion behind [±augmented], though, is simply the contrast between minimal and non-minimal, informally speaking. It is conceivable without assuming language. The rationale connecting [±augmented] to natural numbers in Watanabe’s (2010) discussion is that the hierarchical specification in the shape of [–augmented] ([+augmented]) serves as the successor function by yielding the minimal element of the non-minimal part. It is possible that only the linkage to natural numbers (and hence numerals) was established by the emergence of FLN. We also need to address whether the contrast between minimal and non- minimal is a notion available for non-human animals. The singular-plural distinction, which rhesus monkeys are sensitive to, may be due to [±augmented]. Turning now to the person features, a naïve reaction would be to say that notions like speaker and hearer are impossible without language. But person distinctions are deictic in nature. A member of a species facing another member is a commonplace event, especially for animals living in groups. The notions of speaker and hearer were probably transposed from situations of such social interactions. One may even talk about non-verbal communication. Only the verbal part is an innovation, then. The interpretability of gender features itself is debatable in the first place, but Percus (2011) suggests that the problem can be sidestepped by providing an explicit interpretation procedure that specifically mentions the irrelevance of the masculine/feminine contrast for inanimate entities. He takes up Italian as the simplest case, which only has two classes of nouns. Though there does not seem to be any consensus on what are the possible noun classification systems for natural language, one can adopt a strategy similar to Percus’s for any classification system as long as it employs semantic notions as its basis. In principle, then, features of noun classification can be recruited from the CI systems. The real task is to identify and enumerate semantic notions that define possible noun classification systems. Chomsky (2007, 2010) stresses that concepts realized as lexical items are radically different in nature from those entering into representational systems of other animals.3 If any one of these concepts turns out to be crucially involved, that must be treated as an innovation. Much work remains to be done. To sum up so far, at least some of the φ-features can be attributed to pre-linguistic conceptual resources. One can therefore construct a primitive agreement system on that basis. The account of φ-feature agreement cannot be complete without taking up the status of case, however. And here, we face a real difficulty. Structural case has been considered to be a 3 For detailed discussion of various examples, see Chomsky (2000b). The Proceedings of GLOW in Asia IX quintessential example of uninterpretable entities in FLN. Even if one can point to some abstract semantic correlates of structural case (see Svenonius 2007), it is simply impossible to organize relevant concepts into binary features. In a way, this status of structural case is reflected in the valuation system of Chomsky (2001), where case is simply assigned a value as a by-product of φ-feature agreement, depending on the type of the probe, without being matched with an interpretable counterpart. Binarity requirements on conceptual resources put rather severe constraints on possible avenues for exploration. In this connection, inherent case, which is linked to thematic role interpretation (Chomsky 1986), must also be taken into account, because it is on a par with structural case in being reflected in morphological realization, at least in some languages. Important hints might be sought in the way externalization works. As shown by Hiraiwa (2010), realization of case is regulated by the OCP in a cyclic fashion.4 Given the theoretical origin of the OCP (Leben 1973), it might be fruitful to compare case with tone, though only future research can tell whether this promissory note can be cashed.5 3. Inverse in Jemez and Kiowa In the rest of this article, I would like to show how the new theory of agreement treats inverse marking in Jemez and Kiowa. One of the great achievements in Harbour’s (2011) work is to identify nearly identical sets of noun classes in Jemez and Kiowa. Previous work on Jemez such as Noyer (1997) classifies Jemez nouns somewhat differently, failing to recognize the unity of noun classification in Jemez and Kiowa. Harbour accomplishes a nearly complete unification by pointing to the special status of dual in Jemez. My account will inherit this insight. On the other hand, inverse is still characterized separately for Jemez and Kiowa under Harbour’s analysis, the difference between the two languages being treated as nothing but an arbitrary stipulation. I will show that the new theory of agreement allows us to capture the fact that inverse works in exactly the same way in Jemez and Kiowa, enabling us to make progress in this respect as well. The fact remains, though, that there is a difference between Jemez and Kiowa. The last key element in my proposal is the treatment of the special status of dual in Jemez pointed out by Harbour, which finds an independent cross-linguistic motivation, unlike the way Harbour handles it. Once the special status of dual in Jemez is correctly pinned down, the difference between the two languages follows. The discussion proceeds in the following way. Section 3.1 reviews Harbour’s (2011) account, introducing at the same time the empirical material to be explained. Section 3.2 compares the new theory of agreement with Harbour’s execution of agreement. Section 3.3 presents a novel uniform analysis of inverse in Jemez and Kiowa, attributing the difference between Jemez and Kiowa to something other than inverse. 3.1. Harbour’s (2011) Account of Noun Classes in Jemez and Kiowa A very intriguing characteristic of Jemez and Kiowa is that the majority of nouns have an inherent number value and that when the actual number interpretation differs from the one expected from the inherent value, a special marker called inverse is suffixed to the noun. In this section, I will review how Harbour (2011) handles this phenomenon. Jemez and Kiowa make a tripartite distinction of singular, dual, and plural in number. These number categories are defined in terms of elementary features as follows: 4 Let me add that regulation is intended to cover even those cases where multiple instances of identically case-marked phrases are tolerated by the OCP in a local domain, as in the Japanese nominative case. 5 See Maling, Yip, and Jackendoff (1987) in this connection. Uninterpretable Features and Agreement (A. Watanabe) (6) a. Singular: [+singular, –augmented] b. Dual: [–singular, –augmented] c. Plural: [–singular, +augmented] Informally speaking, [+augmented] designates non-minimal entities. Since [±augmented] is interpreted relative to [±singular], the combination [–singular, –augmented] picks out minimal elements in the [–singular] entities, namely, dual. Similarly, [+singular, +augmented] is a contradictory specification for the purposes of semantic interpretation and therefore is impossible. For a model-theoretic definition of these features, see Harbour (2011). The function of inverse marking can be observed in the following Kiowa examples: (7) a. Tógúl Ø-dɔ́ɔ́. (Harbour 2007: 26) young.man 3sg-be ‘It’s a young man.’ b. Tógúl ę-dɔ́ɔ́. young.man 3du-be ‘It’s two young men.’ c. Tógúúdɔ́ e-dɔ́ɔ́. young.man.inv 3inv-be ‘They’re young men.’ (8) a. Kútaadɔ e-dɔ́ɔ́. (Harbour 2007: 26) pencil.inv 3inv-be ‘It’s a pencil.’ b. Kútaa ę-dɔ́ɔ́. pencil 3du-be ‘It’s two pencils.’ c. Kútaa gya-dɔ́ɔ́. pencil 3pl-be ‘They’re pencils.’ The suffixed noun in (7c) is interpreted as plural, whereas the bare form in (7a, b) means either singular or dual, depending on the verbal inflection. In (8), on the other hand, the suffixed form corresponds to singular, and the bare form either to dual or to plural. Note also that inverse-marked nouns trigger inverse agreement on the verb in (7c) and (8a). Harbour calls nouns like tógúl SDI nouns, and nouns like kútaa IDP nouns, to indicate the agreement type of each noun class for the singular-dual-plural triad in this order, where S is singular, D dual, P plural, and I inverse. The inherent number of SDI nouns is [–augmented], and that of IDP nouns [–singular]. Thus, noun classes are defined in terms of number features. Inverse marking is used when the intended interpretation refers to the opposite value: [+augmented] for SDI nouns and [+singular] for IDP nouns. The Kiowa inverse can express dual, too, as illustrated in (9). (9) a. Nɔ́ɔ́ a-dɔ́ɔ́. (Harbour 2007: 32) I 1sg-be ‘It’s me.’ b. Nɔ́ɔ́ e-dɔ́ɔ́. I 1inv-be ‘It’s me and him/her.’ or ‘It’s me and them.’ According to Harbour, the first person pronoun is the only item whose inherent number is The Proceedings of GLOW in Asia IX characterized as [+singular]. It exhibits the SII behavior. (9b), where the verb shows inverse agreement, is ambiguous between dual and plural for that reason.6 Kiowa also has nouns whose cardinality is expressed transparently by the verbal agreement marker. (10) a. X!óú Ø-dɔ́ɔ́. (Harbour 2011: 563) stone 3sg-be ‘It’s a stone.’ b. X!óú ę-dɔ́ɔ́. stone 3du-be ‘It’s two stones.’ c. X!óú gya-dɔ́ɔ́. stone 3pl-be ‘They’re stones.’ This type of noun does not have an inherent number specification and lacks inverse marking. Nouns of this type belong to the SDP class. Harbour (2011) presents (11) as the list of noun classes attested in Kiowa. (11) Kiowa noun classes (Harbour 2011: 578) class class features semantic characteristics SDP Ø default SII [+singular] first person only SDI [–augmented] independently mobile objects IDP [–singular] vegetation; most non-SDI implements; most non-SDI body parts IDI [–singular, –augmented] hair types; midsize fruit growing in clusters SDS [+group] non-shape-inductive objects IDS [–singular, +group] vegetation occurring in natural collections; implements that may act collectively SSS [+augmented, +group] nongranular mass nouns PPP [+augmented, –group] pluralia tantum nouns; granular mass nouns (for some speakers) I will not bother the reader with further examples of each noun class. These are amply discussed in Harbour’s (2007) book. Our major concern in this article is how the inherent feature specification of each noun class is combined with the precise characterization of inverse to yield the attested agreement pattern. For this particular purpose, (11) suffices. The list in (11) includes a feature [±group] that I have not explained yet. It plays a special role in agreement within DP in Harbour’s account. Its function will be taken up when Harbour’s featural characterization of inverse is reviewed below. Let me just say at this moment that the active role of [±group] is limited to pluralities (hence [+augmented]), where the presence ([–group]) or absence ([+group]) of salient subparts matters. For Jemez, Harbour (2011) claims that its noun classification system can be summarized as in (12). 6 The first person pronoun is not suffixed with an inverse marker (Harbour 2007: 88). Kiowa has a null inverse suffix that is used for nouns ending in /p/ or /t/ (Harbour 2007: 55), but the first person pronoun does not fall under this generalization. This fact may be due to the different morphological status of the D head associated with pronouns. As will be explained below, the inverse marker is considered to be located at D. Note also that Kiowa distinguishes between exclusive and inclusive. (9b) exemplifies exclusive dual and plural. Inclusive dual and plural also trigger inverse agreement (Harbour 2007: 82). Uninterpretable Features and Agreement (A. Watanabe) (12) Jemez noun classes (Harbour 2011: 580) class class features semantic characteristics SIP Ø default SII [–augmented] animates IIP [–singular] vegetation; artifacts; body parts III [–singular, –augmented] weakly granular mass nouns SIS [+group] collective counterpart of SIP IIS [–singular, +group] collective counterpart of IIP SSS [+augmented, +group] nongranular mass nouns PPP [+augmented, –group] granular mass nouns The behavior of a noun from the IIP class is illustrated below. (13) a. Nı́·̨-tɁæ tyê·tɨbæ-š nı́·̨ ɨ-̨l-kɁɑ́. (Yumitani 1998: 126) that-inv box-inv I 1sg-3inv-lie.sg/du ‘That box is mine.’ ‘Those [two] boxes are mine.’ b. Nî·̨ tyê·tɨbɑ nı́·̨ ɨ-̨Ø-gyó·. that box I 1sg-Ø-lie.pl ‘Those [several] boxes are mine.’ The suffixed form in (13a) is ambiguous between the singular and dual readings here. Some more Jemez examples will be presented later on when I propose a new analysis. It is quite remarkable that the set of noun classes in Jemez is featurally almost identical to the Kiowa counterpart.7 The only difference is the absence of the [+singular] class from (12). This near identity is not a coincidence. Both Jemez and Kiowa are members of the Kiowa- Tanoan family. Another observation to be made is that when inverse marking is available for a class, dual is always marked with inverse in Jemez, unlike in Kiowa. In fact, nouns with the same inherent number specification display different agreement profiles in the two languages. The Jemez noun tyê·tɨbɑ in (13), a member of the IIP class, is inherently marked with [–singular]. Kiowa nouns with the same inherent number specification, however, belong to the IDP class. Harbour (2011) attributes this difference to parametrization of the way inverse is characterized in terms of number features, a topic to which I will turn next. Harbour (2011) posits the following structure for DPs: (14) DP NumberP D Class (Noun) Number Class is the locus of inherent number specification, hosting a subset of {±singular, ±augmented, ±group}. These features are chosen according to the conceptual content of the noun in question and do not contribute to model-theoretic interpretation. The semantic characteristics associated with each class in (11) and (12), which do not concern us here, are regarded as relevant to inherent number specification. Number consists of [±singular, ±augmented], determining the number interpretation of DPs as in (6). Inverse marking is associated with the D head, which hosts [±singular, ±augmented] as uninterpretable features 7 Membership of each class differs slightly, too. Yumitani (1998) also notes speaker variation for Jemez. The Proceedings of GLOW in Asia IX that need valuation. Crucially, Class and Number are assumed to jointly value D. According to Harbour’s analysis, inverse marking arises under the following conditions: (15) Inverse a. Inv ⇔ [–F, +F] (Kiowa) b. Inv ⇔ [αF, αG] (Jemez)8 As discussed by Harbour (2007) and Yumitani (1998), the inverse marker within DP has allomorphs, including zero mentioned in note 6. Thus, Inv in (15a) and (15b) is nothing other than a cover term for various morphologically realized forms, as noted by Harbour (2011). (15a) and (15b) should be taken as abbreviations for actual Vocabulary items in the framework of Distributed Morphology (Halle and Marantz 1993, Embick 2010). Let us now turn to the mechanism of valuation that can yield the feature specifications in (15). Chomsky (2001) hypothesizes that uninterpretable features lack values and therefore need valuation. Harbour (2007, 2011) proposes instead that uninterpretable features take the form of [–F, +F], as we have already seen, and that they undergo valuation as described in (16). (16) Valuation in agreement a. An uninterpretable feature is valued if and only if it is matched with an interpretable counterpart in the appropriate domain. b. A feature that has been matched is visible at PF. (Unmatched uninterpretable features are invisible.) In other words, valuation functions as retention of the matched feature under this view. To see how this mechanism works, consider the Jemez IIP noun tyê·tɨbɑ in (13), which is [–singular]. The input to agreement has the following options, where uF is used as a shorthand notation for [–F, +F] to save space: (17) a. [[[ –singular] [ +singular, –augmented]] [ usingular, uaugmented]] Class Number D b. [[[ –singular] [ –singular, –augmented]] [ usingular, uaugmented]] Class Number D c. [[[ –singular] [ –singular, +augmented]] [ usingular, uaugmented]] Class Number D The fact that both Class and Number value D means that the result of valuation is the union of the two sets of features. The resulting content of D is shown below. (18) a. [ +singular, –singular, –augmented] <= (17a) D b. [ –singular, –augmented] <= (17b) D c. [ –singular, +augmented] <= (17c) D (15b) predicts that (18a) and (18b) lead to inverse marking while (18c) does not. This is the correct result, as can be seen from (13) or the class label of the noun, which is IIP. All the other Jemez nouns that do not involve [±group] are also accounted for correctly. Since dual is [–singular, –augmented], the retention view of valuation makes sure that dual nouns will always be marked with inverse, given (15b), as long as there is no other interfering factor. The presence of [±group] can constitute such an interfering factor. Harbour (2011: 572) posits special provisions in (19). 8 Since the features in question are [±singular] and [±augmented], a more accurate specification of the Jemez inverse under Harbour’s account should be [αsingular, αaugmented].