Keywords

1 Introduction

1.1 Data of Interest

The goal of this paper is to present a novel account of additive particles like too and either, with a special focus on their Romanian counterparts şi and nici. We first begin with an overview of their distribution and interpretation when acting as additive particles. The positive additive marker şi, like English too, appears predominantly in positive contexts where it makes the additive contribution that the predication holds of at least one other alternative to its associate. In the second sentence in (1), the additive component is that Maria drinks something else besides beer, namely wine.Footnote 1

figure a

Note that the use of şi in the second sentence would not have been felicitous in the absence of an antecedent proposition such as the one provided by the first sentence specifying what else Maria drank.Footnote 2 For this reason, the additive component, which is generally argued to be a presupposition, is more specifically referred to as the antecedent requirement since the felicity conditions on the use of such additive particles is dependent on there being an antecedent in the discourse.

Şi can also occur with negation, but when it does, it is usually as a negative answer in response to a possibly implicit question such as (2). This is the case regardless of the locality of negation, as shown by the lack of contrast between the two sentences in (2a-b). Note that here too, as in the case in (1), the antecedent proposition must be positive, namely that Maria wants wine.

figure b

Contrast this with the negative marker nici, which, like the English additive either, must co-occur with negation and requires a negative antecedent.Footnote 3 The use of nici in (3) conveys that Paul drank neither beer, nor another salient alternative to beer, wine in the case below.

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1.2 The Goal of This Paper

In a recent analysis that aims to account for the distribution of English too and either [4], Ahn takes too to denote an anaphoric conjunction and either an anaphoric disjunction. By taking either to denote a disjunction, she argues that its restricted distribution can be explained by the same mechanism deriving the restricted distribution of other elements with disjunctive/existential semantics, e.g. the English negative polarity item (NPI) any. While this analysis captures the data, it is arguably not well suited for the Romanian data for the following reason. The morphology of the Romanian particles suggests a common core to the positive and negative particles, and this generalization persists cross-linguistically, with other examples including Italian anche and neanche and Serbian i and ni. Given that the positive additive marker is commonly also employed as a conjunctive marker cross-linguistically, offering an additive, and thus a conjunctive semantics to both the positive and negative markers is desirable.

The goal of this paper is to present such an analysis, one which takes both markers to make the same additive contribution. I will propose that both şi and nici contribute additivity, with the negative marker furthermore carrying an additional component that delivers the negative restriction; in this way I will depart from Ahn’s proposal which takes only the positive particle to contribute additivity. This analysis will be shown to parallel that of other duals in the QP domain, such as positive existential quantifiers and NPIs, like some and any.

The paper is organized as follows. Section 2 lays out the analysis of the positive additive marker, accounting for its distribution and interpretation in both positive and negative contexts, as well as the antecedent requirement. Section 3 presents the analysis of the negative additive marker and shows how this analysis can account for its interpretation and its restricted distribution. Section 4 concludes with a number of open questions and directions for future research.

2 The Positive Additive Marker

2.1 Deriving the Additive Meaning

Szabolcsi in [46] claims that “too is a functional element whose only mission is to induce an additive presupposition.” I follow her and previous authors [6, 34, 35] and assume that the additive marker is semantically vacuous but signals that an alternative proposition where the additive too is replaced by the exclusive particle only is not true. I will implement this intuition within an exhaustification framework by arguing that additive markers trigger obligatory exhaustification with respect to an alternative proposition containing a silent exhaustification operator. Before turning to the details of this analysis, I provide a very quick overview of how exhaustification operators work.

The exhaustification framework takes certain inferences, in particular scalar implicatures, to be derived in the grammar via silent operators [12]. Implicatures are claimed to arise as the result of a syntactic ambiguity resolution in favor of an LF which contains a covert exhaustivity operator exh (building on work in [9, 16, 25, 44], among others). Scalar elements (e.g. the disjunction and conjunction particles) activate alternatives and the grammar integrates these alternatives within the meaning of the utterance by means of this exhaustification operator which is similar to overt only in that it negates all stronger alternatives. There are two important differences however: (i) unlike only, this operator also asserts its prejacent, and (ii) stronger alternatives are negated as long as no contradiction results when their negation is conjoined with the assertion.Footnote 4 These two points are encoded in its semantics below where ie\((p,{Alt }(p))\) is meant to pick out those alternatives which are innocently excludable, that is, whose negation does not lead to a contradiction:

figure d

Let us consider how the scalar implicature associated with disjunction is generated. The first question to ask is what the alternatives to the disjunction are. Besides the conjunctive alternative, the individual disjuncts are also taken to be relevant, following Sauerland’s proposal in [42]. Applying exh delivers the strengthened exclusive interpretation that only one of the disjuncts is true by negating the one innocently excludable alternative, the conjunctive alternative. Note that negating either of the disjuncts would result in a contradiction.

figure e

Returning to the case at hand, I will argue that the alternative to şi p is exh p, as in (6a). I assume going forward that the additive particle spells out add. Since the alternative exh p, which amounts to p and nothing else, is stronger than p itself, it gets negated, as in (6b). The result is the expected conjunctive meaning that both the host proposition p and an alternative are true: p and not only p.Footnote 5 The intuition should be clear: the use of the additive particle is meant to mark that an exclusive interpretation was not intended. This is also entirely consistent with the observation that the use of additive markers is obligatory when the additive presupposition is satisfied [6, 41].

figure f

It’s been noted that additive particles have an anaphoric component by Heim and Kripke in [26, 32], which amounts to the requirement that the alternative of which the predication holds needs to have been mentioned recently or be part of the “active context.” In other words, a sentence like John is having dinner right now too. is not acceptable out of the blue even though we all know that somebody other than John is surely having dinner right now as well. One way to think of this requirement is in terms of what alternatives are relevant (or active, depending on your terminology) in the context. For the alternative proposition exh p to be distinct from the prejacent, p, there needs to be an alternative proposition q relevant in the discourse. Assuming that only relevant alternatives are considered in the calculation of implicatures, this anaphoric component falls out naturally.

Why should additive markers induce obligatory exhaustification? While I cannot provide a fully satisfying answer to that question here, it is worth noting that additive particles involve association with focus [31, 40, 41]. Assuming focus activates alternatives and alternatives need to be integrated into the overall meaning, the fact that silent exhaustification is invoked is not that surprising since we see something similar at play in cases like (7a) and (7b) which appear to involve exhaustification by exh and covert even, respectively, with respect to other relevant individuals.

figure g

In his work on the topic, Krifka has argued in [31] that the prosodic stress pattern encountered with additive particles is more similar to contrastive topic association rather than to focus association. Along these lines, note that additive particles and the use of contrastive topic intonation impose a similar requirement on the context, namely that the predication hold of somebody else (taking the contribution of focused constituent in (8a) to be that of an existential quantifier).

figure h

To what extent this parallel plays a role in the nature of the alternative (pre-exhaustified versus distinct) is going to remain an open issue here but surely one that deserves further discussion (see [28] and [39] for some recent discussion on these parallels).

2.2 The Positive Antecedent Requirement

As per the discussion in the introduction, the additive component is commonly referred to as the antecedent requirement, in light of the fact that it behaves more like a felicity condition. At first sight, this might seem to pose a problem for the current way of deriving the additive component since the semantics provided in (6) has the additivity be part of the entailed component. In her work on presupposition triggering, Abrusán has argued that any information conveyed by the sentence that is not about the main point of the sentence ends up being presupposed [1, 3].Footnote 6 She uses this triggering mechanism in [2] to argue that the additive component becomes presupposed by virtue of not being about the main point described by the sentence. One way to identify the main point(s) is by looking at the sentence’s entailments and whether they are about the event time of the matrix predicate. If they are not, or they are but only accidentally so, they must not be the main point of the sentence and thus can be presupposed. To tell if an entailment is only accidentally about the main event time, one can check whether the temporal-alternatives (T-alts below) are well-formed, with such an alternative being obtained by replacing the temporal arguments of the matrix and embedded predicates with different ones. She provides the nice minimal pair in (9) to illustrate the difference between know and manage with respect to their factivity: know presupposes its prejacent by virtue of the well-formedness of its T-alternative, while manage does not.

figure i

Returning to the additive component, Abrusán shows in [2] that the additive entailment is not necessarily about the main event time with the example below (her examples (20–21)). Observe that the temporal alternative where the tense in the matrix clause and the tense in the additive component differ is well-formed.

figure j

Given the acceptability of the T-alternative, Abrusán concludes that the additive component is temporally insensitive and thus presupposed. We adopt her proposal throughout.

2.3 Positive Additives Under Negation

Recall that when şi co-occurs with negation, as in (11), the salient interpretation is that Maria doesn’t want to drink beer, and the fact that she wants something else becomes accommodated. As mentioned in the introduction, such a construction is usually employed as part of a negative answer in response to a (possibly implicit) question involving the additive particle itself.

figure k

How is the additive component q = Maria wants water derived in this example? First observe that wide scope for the additive particle, per the LF in (12), would yield the wrong interpretation, namely that Maria doesn’t want either water or beer, so we can rule this out straight away. A discussion of why this LF should be ruled out is postponed to the penultimate section.

figure l

Assuming then that the additive particle takes scope under the negation, since şi calls for obligatory exhaustification, it follows that the exhaustification must also scope under the negation, as in (13). Here we implicitly assume a mechanism of embedded exhaustivity operators as a means to derive embedded implicatures, a result which has received substantial empirical support [8, 9, 42, 43].

figure m

Note that the result in (13b) does not derive q as an entailment, so how does it end up being presupposed given the mechanism put forth by Abrusán? I propose that the additive implication, which is derived below the negation, can be turned into a presupposition at that embedded level, hence its projection out of the scope of negation. It is crucial and in fact necessary to allow this triggering mechanism to apply at embedded levels. I assume this obligatoriness is governed by a principle which calls for maximizing the amount of information presupposed.

The careful reader will have noticed that the use of exh in (13) results in weakening at the matrix level; in other words, the use of şi under negation does not give rise to a stronger conjunctive meaning but rather to a weaker disjunctive one. General principles of economy argue that covert operators, such as exh, should not be used if their insertion leads to a weaker or equivalent interpretation. A more recent discussion of such an economy condition governing the distribution of exh, particularly as it pertains to its embeddability, can be found in [18, 19]. The basic idea behind the proposal is the following: an instance of exh is considered vacuous if its overall contribution leads to weakening or an equivalent interpretation. Note that in the case above, however, the insertion of exh is not weakening if we consider its contribution more broadly, i.e., in conjunction with the mechanism for presupposition derivation. Without the insertion of exh no additive component would have been generated, and in turn no presupposition would have been triggered. So while the initial contribution of exh may seem weakening, when we take the presupposition generated into account, a stronger meaning can be said to be derived.Footnote 7

Finally, note that there is another context which would facilitate the use of şi under negation, namely one where şi contrasts with overt only.

figure n

This interpretation can be derived if we assume the LF representation in (15). If we assume the relevant alternative is one without the additive particle, (15a), we derive the intuitively correct interpretation that only p is the case. This is precisely the same derivation employed to derive the “metalinguistic” use of disjunction under negation: I didn’t eat cake OR ice cream, I ate both. in [19].

figure o

We now turn our attention to the negative additive particle nici which, unlike şi, is restricted to negative environments.

3 The Negative Additive Marker

Observe that the NPI/neg-word prefix in Romanian is ni, (16). We see it in nimeni ‘nobody,’ nimic ‘nothing,’ and nicăieri ‘nowhere.’Footnote 8

figure p

Similarly to the negative additive particle nici, the neg-words in (16) are restricted to strictly negative environments, such as sentential negation and the scope of fără ‘without,’ suggesting that their restricted distribution has the same source. I propose the following analysis for nici:

figure q

The analysis I present in this section will take the distribution and interpretation of the negative additive nici to be the result of the types of alternatives \(\textsc {exh}^\textsc {n}\) and \(\textsc {exh}^\textsc {add}\) act on and the interaction of these two exhaustification operators with other elements in the clause.

Before turning to the analysis, I will offer a brief overview of the current approaches to deriving polarity restrictions within the exhaustification framework, as proposed in [11, 14, 15, 20, 21, 45] and [37, 38] among many other works.

3.1 Polarity Restrictions as Constraints on Obligatory Exhaustification

There are three main lines of approaches to deriving the restriction on the distribution of negative polarity items. One line, first presented by Chierchia in [9, 10], argues that the analyses of polarity phenomena and scalar implicatures should converge in light of the fact that NPIs are acceptable in precisely those contexts where an existential quantifier does not give rise to a scalar implicature, namely under negation and other logical operators which reverse the direction of entailment. To this end, he takes negative polarity items like any to be existential quantifiers with active sub-domain alternatives which require obligatory exhaustification. This exhaustification is performed by a covert operator O, which conjoins the assertion with the negation of all logically non-weaker alternatives. The meaning of O is similar to that of the exclusive particle only, and is crucially distinct from the operator exh presented earlier in that it allows contradictions to arise. It is precisely this possibility that [10] builds on to explain why NPIs like any are unacceptable in upward entailing environments. Analyzing any as an existential quantifier means that the alternative propositions obtained by replacing the domain with each of its sub-domains are stronger than the assertion since entailments hold from subsets to supersets. Since the alternatives entail the assertion in upward entailing environments, the application of O will result in the negation of each of the alternatives, which will amount to a contradiction since it will express that something holds of a set but it does not hold of any of its subsets. Assuming that logical contradictions of this type always lead to ungrammaticality, following Gajewski’s work in [22], the unacceptability of NPIs in upward entailing contexts falls out. As for their acceptability in downward entailing environments, [10] argues that this falls out straight away because the application of O is vacuous in the presence of entailment-reversing operators since the alternatives are all weaker and thus O has nothing to negate. Note that O, in the context of NPI licensing, must furthermore be immune to the restriction against vacuous exhaustification.

Another exhaustification-based account of NPIs builds on the analyses proposed by Krifka and Lahiri in [30] and [33]. Based on the morphological make-up of Hindi NPIs, which are built out of the scalar particle bhii ‘even’ and an indefinite NP, [33] argues that the distribution of such NPIs falls out straightforwardly once we assume that the contribution of bhii, as with even, is to impose on its prejacent that it be less likely than any relevant alternative. Assuming that the indefinite NP activates scalar alternatives that differ only in terms of what integer is used, the requirement imposed by even will only be satisfied in the presence of entailment-reversing operators since only there will the alternatives be weaker, and thus more likely (e.g., not a/one boy came to the party is entailed by not two boys came to the party). Crnič in [14, 15] has extended this analysis even to NPIs which lack an overt even counterpart by proposing that all NPIs involve association with a covert even-like operator. Note that within this family of proposals, the derivation of scalar and free choice implicatures is still achieved via exhaustification via exh.

Lastly, we turn to positive polarity elements, whose restricted distribution has been explained within the exhaustification framework as well.Footnote 9 Spector and Nicolae, in [45] and [37, 38], have argued that the positive polarity character of disjunction should be analyzed as an interplay between a lexical requirement for obligatory exhaustification imposed by the polarity item and an economy condition which prevents vacuous exhaustification, following work by Fox and Spector in [18, 19]. Crucially, the relevant exhaustification operator in this case is exh, as presented earlier in the paper, which only pays attention to innocently excludable alternatives and cannot lead to contradictions. As an example, consider the complex disjunction soit soit in French. [45] takes this disjunction to require obligatory exhaustification with respect to an alternative proposition where the disjunction is replaced with the conjunction. In upward entailing contexts, the result of exhaustification is the strengthened exclusive interpretation. In downward entailing environments, however, the contribution of exh is vacuous since the conjunctive alternative is weaker when negated. Since vacuous exhaustification is ruled out, the PPI-like behavior of the disjunction soit soit falls out. Observe that this restriction against vacuous instances of exh is crucial to the account and in this way, stands in stark contrast with the first family of analyses proposed above, which deliver the acceptability of NPIs in downward entailing contexts precisely because the exhaustification is vacuous. A simple way to reconcile these proposals is to assume that there are indeed a number of covert exhaustification operators which perform similar tasks but are subject to different constraints, O and exh.

In the following sections I will provide an analysis of the NPI status of nici by taking it to associate not with O or even, but with exh, a novel approach as far as NPI licensing is concerned.

3.2 Nici in Upward Entailing Contexts

As already mentioned, I propose a decompositional analysis of nici:

  • Nici spells out the negative marker and the additive particle: n-add.

  • Each particle carries an inherent focal feature indicating active alternatives which must be used up by a corresponding operator: \(\textsc {exh}^\textsc {n}\) & \(\textsc {exh}^\textsc {add}\).

  • \(\textsc {exh}^\textsc {n}\) & \(\textsc {exh}^\textsc {add}\) differ in terms of what alternatives they operate on.

We already know what alternative \(\textsc {exh}^\textsc {add}\) acts on, namely one where the additive particle is replaced by the exclusive particle exh, which in turn is evaluated with respect to an alternative obtained via lexical item replacement (of p with q), repeated in (17a)Footnote 10. The alternatives considered by \(\textsc {exh}^\textsc {n}\) are derived via (i) lexical item replacement of p with q, and (ii) deletion, whereby constituents are replaced with their sub-constituents, e.g. nici p with p, as shown in (17c). Going through the composition step by step, we see that the first level of exhaustification will result in the additive meaning, (17b), while the application of \(\textsc {exh}^\textsc {n}\) in (17d) will be vacuous since there are no stronger alternatives to negate. Assuming exh is subject to a constraint against vacuous occurrences, the unacceptability of nici in UE contexts falls out.

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3.3 Nici in Downward Entailing Contexts

For ease of presentation, I repeat the relevant example below:

figure s

We need to explain the following two facts:

  • The interpretation of the sentence hosting nici is that of a conjunction of two negated propositions (\(\lnot \)p\(\wedge \lnot \)q).

  • The use of nici carries a negative presupposition, which amounts to the second conjunct (\(\lnot \)q).

Given the presence of an additional operator, namely the negation, \(\textsc {exh}^\textsc {n}\) has two possible adjunction positions. If it adjoins below the negation, the contribution of \(\textsc {exh}^\textsc {n}\) will be vacuous as before given the nature of the alternatives.

figure t

If \(\textsc {exh}^\textsc {n}\) adjoins above the negation, its prejacent will denote the disjunction of two negated propositions, so the result should be similar to what happens when exh applies to a disjunction. Let’s begin by reviewing how free choice inferences with disjunctive sentences come about within the exhaustification framework as proposed by Fox in [16]. The basic idea is that the relevant alternatives are not the disjuncts themselves, but rather their pre-exhaustified variants. One way to implement this is by assuming exhaustification can happen recursively, via two instances of the exh operator, as in (20).Footnote 11 The first instance of exh will be vacuous, (20b), since the alternatives are stronger but not innocently excludable, (20a). The second level of exh will look at the pre-exhaustified alternatives in (20c) and the result will be the conjunctive interpretation in (20d). This conjunctive interpretation comes about as follows: the disjunction of A and B is possible, but it’s not possible that only A is true and it’s not possible that only B is true, so the conjunction itself must be possible.Footnote 12

figure u

Carrying this over to the case at hand, invoking recursive exhaustification on the disjunction of two negated propositions will deliver precisely the right interpretation, namely the conjunction of two negated propositions. Below I go through each step of the derivation. In (21c) I list the alternatives considered by \(\textsc {exh}^\textsc {n}\). The first application of \(\textsc {exh}^\textsc {n}\) will be vacuous, (21d), as the alternatives are symmetric and neither can be negated innocently. By the second application of \(\textsc {exh}^\textsc {n}\), the result will no longer be vacuous as the alternatives in (21e) are no longer symmetric – they can both be negated without contradiction, as shown in (21f). The resulting meaning will be stronger, taking us from the disjunction of two negated propositions to their conjunction.Footnote 13\(^{,}\)Footnote 14

figure v

We’ve thus shown why nici must co-occur with negation, and that is because the presence of negation allows \(\textsc {exh}^\textsc {n}\) to scope above it and access stronger alternatives which can be innocently excluded. Since the overall contribution of \(\textsc {exh}^\textsc {n}\) leads to a strengthened interpretation, the acceptability of nici in entailment-reversal environments, more generally, falls out, as does its contribution to the overall meaning, that of an additive.

Before we conclude, it deserves pointing out that ni neg-words as well as the additive nici, have a very restricted distribution, being allowed to appear only under negation and without, as well as in fragment answers, as per the distribution of neg-words in strict negative concord languages. I will not discuss how to derive this restricted distribution, but I point the interested reader to the work of Fălăuş and Nicolae in [21] for details on how to derive this distribution within an exhaustification-based framework.

3.4 The Negative Antecedent Requirement

Having shown how the additive interpretation and the restricted distribution are derived, we next turn to the antecedent requirement. Like şi, nici requires an antecedent, but unlike with şi, the antecedent needs to be negative. At which point does the presupposition triggering mechanism apply? There are two options, either below or above the negation. If it applies below the negation, the material presupposed, namely q, would end up contradicting the resulting interpretation in (21f). If, on the other hand, the triggering mechanism is postponed until the matrix level, the negative additive implication \(\lnot q\) will end up being presupposed, as desired.

3.5 Carving Out the Space of Possibilities: şi or nici?

There is one potential concern that still needs to be addressed, namely why the positive particle şi cannot be used with negation and have the LF in (21). I argue that this relates to the morphological point made in the beginning of this section, namely that nici spells out two particles, each of which associates with a distinct exh operator. I argue that each instance of exhaustification (assuming recursive exhaustification counts as a single instance) corresponds to a focus feature on its associate. In the case of nici, which spells out n-add, there are two such features. On the other hand, şi can host only one focus feature, meaning that there can only be one instance of exh associating with it.

On a separate but related note, one might wonder why şi cannot take wide scope with respect to negation. Recall from Sect. 2.3 that if it did, the resulting interpretation would be the same as what we derive with nici, yet şi and nici never overlap in their interpretation. There are languages, e.g. Japanese, where the same particle, namely mo, can be used in both positive and negative contexts; in fact, in Japanese mo is the only way to express additivity. For such particles we would surely want to argue that they have the option of scoping above the negation, unlike şi, thereby deriving an interpretation akin to that contributed by nici. This seems like a deeper problem which will have remain an open issue for now. What seems to be at play is some type of competition between the two particles, şi and nici: while in the presence of negation şi is ambiguous, nici is not, so of the two possible interpretations of şi, only the one not shared with nici can ultimately survive. How to best formalize this remains an open problem, but interestingly one we see in other cases of ambiguity resolution.

4 Summary and Open Issues

In this paper I presented a new analysis for pairs of additive particles like Romanian şi and nici which, I argued, captures their additive interpretation and distribution. While Ahn’s 2015 recent analysis is similarly able to capture the distribution of these particles, it is conceptually not as well suited for pairs of particles such as the Romanian ones which very clearly share a morphological and presumably semantic core with conjunctive rather than disjunctive particles; recall that her analysis takes the negative particle either to be a disjunction at its core. That is not to say that an analysis such as Ahn’s is not viable and possibly even better suited for other additive particles, such as English either, which also doubles as a disjunction (either A or B) and free choice determiner (either boy), although note that her analysis cannot immediately be extended to account for these other uses.

The study of additive particles, especially in the context of polarity, is a very fertile area cross-linguistically. There is ample variation both in terms of the possible interpretations of these elements, as well as in the different roles they may play within a language. Not only has this variation not received a proper theoretical analysis, it has not even been fully mapped out yet (see for example [23] and [13]). Take for example the negative additive particle. As mentioned above, English either can also double as a positive disjunction and a free choice determiner. This is not the case in Romanian, where instead it can be used to form negative words by attaching to an indefinite NP (nicio fată ‘no girl’), something we also see in, e.g., Hindi [33]. The creation of NPIs based on additive particles like nici and indefinite NPs is in fact cross-linguistically common. The common analyses of these elements attribute, however, a scalar semantics to the additive particles, whereby they contribute an even-like interpretation. This is not surprising since additive particles are cross-linguistically known to double as scalar particles. There is variation within this area as well, however. While Spanish ni must express a scalar meaning, Romanian nici can express it, while English either cannot.

Nici can also appear in complex coordinations, e.g. nici A nici B ‘neither A nor B’ to convey the conjunction of two negated propositions. French ni can also function as a negative additive particle as in Romanian, as well as a negative connective A ni B ‘neither A nor B’ and can be doubled, as in Romanian, ni A ni B ‘neither A nor B.’ The distribution and interpretation of these particles is so varied and multi-faceted that many authors have argued that a unified account is not possible for all their different uses (see e.g. recent work particularly on French ni by [24]). Clearly much is left to be understood.