CQ belongs to the Quechua II branch of the Quechua language family (Cusihuaman 2001: 29). It is spoken in the southern parts of Peru, the particular variety studied here in the department of Cusco.3 Its morphological type is agglutinative and exclusively suffixing. Its basic word order is SOV but other orders are possible. It has a nominative-accusative case marking system and cross-references both subjects and objects on the verb. Pro-drop is frequently used.

CQ possesses a large number of enclitics that mark information structural notions (topic, focus, contrastiveness), evidentiality, modality, aspectual notions, and, most relevant for the current paper, additivity and exclusivity. (2) exemplifies some of them.

With the exception of the evidential focus enclitics (Weber 1986; Muysken 1995; Floyd 1999; Faller 2002) (and to a lesser extent topic enclitics (Grzech 2016)), the semantics of enclitics have not received a lot of attention beyond grammars. One notable exception is the work by Tellings (2012; 2014) on the exclusive enclitic =lla in Ecuadorian Quichua. Many enclitics are multifunctional and their combinations are not always transparently compositional. For example, the combination of the exclusive =lla4 and the contrastive -taq in (2) indicates that the described event is a continuation or repetition of a previous event (see also Tellings (2012) for Quichua). The combination of additive =pas and exclusive =lla expresses scalar additivity in negative sentences (section 2.2).

Additives quantify over a set of propositional alternatives to their prejacent. This set is obtained by replacing the denotation of the focus constituent ([…]_F) the additive associates with (Rooth 1992), with contextually relevant alternatives (Kay 1990; Gast & van der Auwera 2011). They assert their prejacent and presuppose that at least one of the alternatives is true (König 1991; Gast 2013; Forker 2016). For example, the additive too in the second conjunct in (3), associates with the NP his brother. The relevant set of alternative propositions is the set obtained by assigning different values to x in the open proposition x was there, that is, {Fred’s brother was there, Fred was there, Mona was there, Sara was there, … }. In (3), the first conjunct verifies that Fred was there, and therefore the entire utterance is felicitous.

The principal marker of simple additivity in CQ is the enclitic =pas (allomorph =pis). Cusihuaman (2001: 237) labels it aditivo ‘additive’, suggesting that he thought this to be its primary function. As an enclitic, =pas can attach to constituents of all major types: NPs in (1a) and (4), a nominalized adverbial clause in (5), and the verb in (6). The constituent it attaches to contains its associate.5

Forker’s (2016) sample includes the Huallaga Quechua additive =pis (allomorph =si), illustrated in (7).6

The two varieties are substantially different, and it cannot be assumed that their additives have the same set of functions. I will discuss cases of potential differences in the following sections.

If additives presuppose the existence of an alternative, they should only be felicitous in contexts in which this presupposition is satisfied. This is the case for =pas: it is felicitous in contexts that establish such an alternative such as (8), but not in contexts that do not, (9). That is, =pas imposes a Strong Contextual Felicity constraint in the sense of Tonhauser et al. (2013).7

The following examples moreover show that the additive presupposition projects. Despite being in the scope the question operator, =pas is only felicitous in (10), which satisfies its additive presupposition.

These tests confirm the additive implication as a presupposition.

Additives may be specified for additional semantic features such as scalarity, polarity or scope (König 1991). Section 2.2 argues that =pas is not scalar. It is also not marked for polarity and freely occurs in negative sentences such as (12).

English either, illustrated in (13a), is only felicitous in negative polarity contexts, and can only have wide scope over negation, that is, it is the negated proposition that is asserted and that is used to calculate the alternatives (König 1991: 31). In contrast, too can occur in both positive and negative clauses and may have narrow scope (13b), that is, the alternatives are calculated without the negation.

=pas is to my knowledge not restricted with respect to scope. (12) presupposes that there are other things that the alcadevaras did not give to the runas; =pas therefore has wide scope. While I have not come across any naturally occurring examples of =pas having narrow scope, (14) is an elicited example.

The main aim of this paper is to establish the various functions of =pas as the basis for the discussion of the consequences for the map of additivity in section 7, not to provide a fully fledged semantic account. Nevertheless, it is useful to introduce some basic semantic representations to facilitate comparison. I adopt a version of Rooth’s (1992) focus semantics for characterizing the set of alternatives =pas quantifies over. In this approach, a sentence S not only denotes its ordinary semantic value ⟦S⟧^o, the proposition expressed p, but also has a focus semantic value ⟦S⟧^f, which is the set of propositions denoted by sentences S′ that are obtained from S by replacing the focus constituent with a contextually salient alternative of the same type (see also Guerzoni & Lim (2007), Gast & van der Auwera (2011: 10), Gast (2013), among many others).

For example, the focus value for Pilar speaks Aymara is (15a) when Pilar is the focus, and (15b) when Aymara is the focus. The ordinary semantic value (15c) is the same for both.8

I use F-Alt as a short-hand to refer to the set of focus alternatives in the following. The semantic contribution of additive =pas can then be schematically represented as in (16).

=pas does not contribute to the asserted content p, but contributes the presuppositon that there is at least one true alternative proposition in F-Alt that is distinct from p. Moreover, Strong Contextual Felicity requires this proposition to be salient and established in the common ground (Tonhauser et al. 2013: 100).9

(17) applies this to (17a) (repeated from (1a)). Assume that Ana is the speaker and the salient alternative individuals are Mario and Pilar.

Following Gast (2013), I also make use of a set of parameters to capture the variation in meaning between different types of additives and their other uses. To his parameters of quantificational force (existential/universal), informational status of the prejacent P and the quantificational statement Q (asserted/presupposed), and scalarity, I add the type of alternatives quantified over, the polarity of the sentence (pos(itive)/neg(ative)), and the scope of the marker with respect to other scope-bearing markers (wide w, narrow n). Table 1 presents these parameters for the additives discussed so far (scalarity will become relevant only in the next section).

The exclusive only is included for comparison. As shown in (18), only also quantifies over the set of focus alternatives, but the quantificational force is a negated existential, and it is the quantificational statement Q that is asserted, while the prejacent P is presupposed (Gast 2013).

The scope parameter is omitted in what follows, as I currently lack data on scope interactions for the non-additive uses of =pas.

To conclude this section, note that while =pas is the main marker for additivity, in the sense that native speakers typically use it to translate Spanish sentences with tambien ‘also’, the instrumental-comitative suffix -(pu)wan also has an additive function, as shown in (19) (Cusihuaman 2001).10

Additive -(pu)wan differs from =pas in requiring the referent to be part of a group with the presupposed alternative(s). (19) is not felicitous in a context in which the speaker goes to sow on their own, while the presupposed alternatives go separately. This will be relevant for the discussion of the coordinative use of =pas in section 2.4.

Scalar additives such as English even or German sogar interact with a pragmatic scale that orders the alternatives in terms of informativeness or strength (Kay 1990; Gast & van der Auwera 2011).11 They presuppose that their prejacent is stronger/more informative than its alternatives. Often, the overall effect is one of unexpectedness (König 1991: 38). For example, in addition to the additive presupposition that Pilar speaks another language, (20a) and (20b) presuppose that the proposition that Pilar speaks Aymara is more informative than its alternatives, that she speaks Quechua or Spanish according to the scale in (20e) (ordered from most to least informative). If Pilar was born and lives in Cusco, where Aymara is not commonly spoken, the fact that she speaks Aymara is unexpected.

Gast & van der Auwera (2011) illustrate scalar additives from different languages with, amongst other things, translations of Bible verse Luke 8:25. (21a) is the English translation in the New International Version and (21b) the German one from the Einheitsübersetzung 2017 (both last accessed on the bibleserver.com on 5 April 2019).

CQ does not have a dedicated scalar additive, and the translation of this verse in (22) uses the additive =pas.12

(23) gives two further examples (which are not translations) with a scalar interpretation.13

Forker (2016) classifies 30 out of 42 additives in her sample as also having a function as scalar additives. This amounts to an ambiguity claim: as simple additives, they contribute an additive presupposition; as scalar additives, they contribute an additive and a scalar presupposition. I argue that CQ =pas is not ambiguous in this way, and that the scalar interpretation in these examples arises from contextual assumptions.14 First note that even though the German version of Luke 8:25 in (21b) uses the scalar additive sogar, in other versions of the Bible, the simple additive auch is used instead, as shown in (24).

The reason we do not need to encode scalarity linguistically in this example is that our world-knowledge tells us that humans can not command the winds and the water. It is therefore entirely unexpected to see Jesus calm the storm in this way. The translators of (21b) decided to make this explicit by using sogar, while those of (24) rely on the reader’s world knowledge. The same holds for the CQ example in (22). If we were to change the context to one that is not inherently scalar, such as a world of supernatural heroes with powers to control the natural elements, the simple additive sentences (in contrast to the scalar additive ones in (21)) would no longer be interpreted as scalar.

Similar observations apply to the examples in (23): the town in (23a) was built in a valley. We know that it is easier to build houses on the flat than on steep mountain sides. Thus, the proposition that the mountain sides are full of houses is surprising. The speaker of (23b) used to be mayor and preside over meetings. He no longer is mayor, but given his previous involvement in local government, one would expect him to still attend meetings. The proposition that he does not is therefore unexpected. Thus, the scalar interpretation of these examples is not triggered by =pas but part of the wider context.

A second way in which sentences with =pas can have a scalar interpretation is if other expressions in the sentence reference a scale. For example, in negative polarity sentences, the combination of =pas with the exclusive enclitic =lla results in a scalar additive reading, as illustrated in (25).15

Exclusives are commonly assumed to contribute a scalar presupposition to the effect that their prejacent is the least noteworthy or informative amongst the alternatives (König 1991; Guerzoni 2003). Combining this with the additive presupposition of =pas results in an overall scalar interpretation. In (25a), the thing that is most expected to be given, and therefore the least remarkable, is corn, and they didn’t give that, in addition to any less expected thing not being given. In (25b), one animal being killed would be the least remarkable, and this didn’t happen in addition to more animals not being killed.

Guerzoni (2003: 189ff) develops a compositional analysis along these lines for German auch nur and similar constructions in other languages (see also Gast & van der Auwera 2011).16 I expect her analysis also to be applicable to CQ =lla=pas, but will have to leave the details for future work. The point for current purposes is that the scalarity in these examples is contributed by =lla and not by =pas.

In sum, then, =pas does not have a separate function as a scalar additive. Since Forker (2016) classifies the Huallaga Quechua additive =pis as having such a function, I briefly review the relevant examples from Weber (1989) in (26).

While the scalar interpretation of (26a) can easily be attributed to world knowledge, this is not obviously the case for (26b). We can imagine a context in which meat is rarely eaten in the speaker’s community, in which case the scalar interpretation of (26b) would arise from this contextual assumption. But for all we know (26b) may also be felicitous in contexts that do not contain any such assumption. More research is needed to ascertain whether this is a genuine difference between Huallaga Quechua =pis and CQ =pas.

Both König (1991) and Forker (2016) identify conjunctional adverb as a separate use. Around one fourth in Forker’s sample have this use, illustrated in (27) for German auch and English also.

Since not all additives that have this use are adverbs, I will use the term discourse connective (Schiffrin 1987) instead. This use is still very much additive in the sense that it requires an antecedent that is distinct from its prejacent. In this case though, the associate is the entire prejacent, and so the relevant alternatives do not necessarily share any material. The set of alternatives is nevertheless restricted, namely to those propositions that contribute the same discourse topic (Zeevat & Jasinskaja 2007; Forker 2016). Additive discourse connectives often express “a continuation or a consequence of the situation referred to in the first clause,” and are then translatable with “and then, moreover, therefore [italics added], etc.” (Forker 2016: 81f).

CQ =pas also has this use, as shown in (28). On its own, =pas seems to be closer in meaning to the discourse connective and, as reflected in the translation with Spanish y in the original. Translations of (28) with the additive also/moreover (Spanish tambien/además) would not render a coherent discourse. Nevertheless, (28) still presupposes relevant prior discourse.

=pas also combines with other discourse connectives such as hinaspa ‘and then’, and then has a more strongly additive flavour, as shown in (29).

No additional semantic components are needed to account for this use, except the requirement that the set of alternative propositions have to address the same overall discourse topic. Zeevat & Jasinskaja (2007) argue that this is in fact a general feature of additives, not just when they are used as discourse connectives. There is then no distinction between the standard additive and the discourse connective use.

CQ has a number of strategies for coordinating constituents, including juxtaposition, the instrumental/comitative suffix -wan, the contrastive enclitic =taq and two independent particles, ima ‘and’ and utaq ‘or’ (Cusihuaman 2001: 141–143). (30) illustrates juxtaposition.

Of interest for current purposes is that the additive =pas can also be used for constituent coordination. This is a cross-linguistically frequent extension of additives, occurring with more than half of the languages in Forker’s (2016) sample.

The constituents coordinated with =pas can be of any type, though impressionistically, the coordination of NPs (including nominalized clauses) as in (31) is most common. Coordinating =pas tends to occur on all conjuncts (Cusihuaman 2001: 142), though there are cases of =pas only appearing on the last conjunct.

(32a) and (32b) are examples of VP and clause coordination respectively.

Given that juxtaposition is already interpreted as conjunction (see (30)), the question arises whether =pas simply makes this meaning overt or whether it narrows down the interpretive possibilities. Forker (2016: 83) (see also Szabolcsi 2015: 181) observes that additives tend to force a distributive interpretation, and this is also the case for =pas: (33) can only mean that Tomás and Alicia each met other people, not each other.

Even with inherently distributive predicates such as eat, =pas coordination adds a further meaning element of separation. Thus, (34) is interpreted as Tomás and Alicia eating separately. In this respect, =pas contrasts with the additive use of the comitative marker -(pu)wan in (19), which, recall, requires accompaniment.

To what extent can the constituent coordination function of =pas be assimilated to its additive function? According to König (1991: 66), both “link separate but parallel information to the preceding discourse.” However, coordination differs from additivity in that the two pieces of parallel information are part of the same constituent, and on the face of it, does therefore not carry an additive presupposition. I suggest, however, that =pas can also in this use still be analyzed as involving a presupposition of sort. Consider again (35a) (repeated from (31a)). Each instance of =pas refers to the set of focus alternatives F-Alt calculated from its associate. Given that these are of the same type and occur in the same sentence, there is in effect only one F-Alt, as shown in (35c). (35a) asserts that there are paqays and avocados in the valley. The predicted presuppositions of the two instances of =pas are indicated in (35d). As can be seen, each presupposition is satisfied by the other conjunct. They do therefore not project beyond the sentence, that is, (35a) can be uttered out of the blue.

Presupposition satisfaction is usually assumed to proceed incrementally (Rothschild 2011; Chemla & Schlenker 2012), so the assumption that the first conjunct’s additive presupposition is satisfied by the second may seem problematic. However, following Szabolcsi (2015: 168), who analyzes similar data with quantifier particles such as Japanese mo ‘too/and/every’, we can appeal here to Brasoveanu’s (2013) notion of post-suppositions. Post-suppositions are constraints that need “to be satisfied relative to the context that results after the at-issue meaning is evaluated” (p. 158) [his emphasis], within a specified domain. Thus, the post-supposition of the first =pas can be satisfied within a larger domain that includes the second conjunct.17

Such an additive semantics for the coordinative use of =pas also goes some way towards explaining why it can not be interpreted collectively (see above, examples (33) and (34)): as an additive, =pas presupposes the existence of a distinct propositional alternative, not just an individual, and therefore also of a distinct event. While, in principle, this is compatible with the summation of the relevant individuals and events into a collection, the fact that =pas highlights their distinctness puts it in pragmatic competition with the non-additive strategies of coordination, including juxtaposition, resulting in an implicature of non-collectivity for coordinative =pas. While this account needs to be fleshed out, these considerations suffice to highlight the similarity between the additive and coordinative uses.

The sketched analysis is also compatible with the fact that additive markers can be the diachronic source of constituent coordinators (Mithun 1992). Constituent coordinators like and have in turn been claimed to evolve into discourse connectives (Koops & Lohmann 2015). In section 7.3 I will therefore suggest to put these three functions on the same path in Forker’s map.

To summarize, Table 2 shows the shared features between the discourse connective, the coordinative and additive uses of =pas. Their differences result from the type of associate selected.

Forker’s semantic map predicts that additives that can be used as discourse connectives can also be used for marking contrastive topic (CT). Cusihuaman (2001) describes neither topic nor contrast marking for =pas and there are dedicated markers for both, namely =qa for topic (Cusihuaman 2001: 227) and =taq for contrast (Cusihuaman 2001: 240). There is then no a priori reason to think that =pas has this use. This section presents evidence to confirm that =pas does indeed not mark contrastive topics.

CTs may informally be defined as providing a partial answer to a question with at least two sub-questions (Krifka 1999; Büring 2003; Constant 2014). For example, Fred in (36b) partially answers the question in (36a), in particular, it answers the subquestion What did Fred eat? Thus, beans in (36b) is the focus and Fred is contrasted with the relevant alternatives (Büring 2003: 520).18 The sequence in (36c) is a (more) complete answer to (36a), with both Fred and Mary being CTs.

Typically, different CTs combine with different foci, as in (36c), but this distinctiveness condition (Krifka 1999: 122) is only an implicature which can be canceled with an additive. This is shown in (37).19

In such cases, the associate of the additive is a CT, but this is not sufficient to conclude that the additive marks CT. That also and too do not mark contrastive topic is confirmed by the fact that they cannot be added to the second sentence in (36c) (unless there is someone other than Mary or Fred in the context who ate eggplant).

The same pattern obtains for CQ =pas. =pas is fine in (38b) in response to (38a), where the speaker’s mother and father both went to the field. But in (38c), where they went to different places, the contrastive =taq has to be used instead. Replacing =taq with =pas would result in the interpretation that a third person went to the field, which within the confines of the given context would result in infelicity.

Examples of additives that do have contrastive topic marking as a distinct function are Sheko =k’əra, illustrated in (39a) and Udihe =de, illustrated in (39b).

Equivalent examples in CQ, for example, (40a) and (40b), require the contrastive enclitic =taq. Attempts at substituting it with =pas are rejected by the CQ speakers consulted.

In conclusion, while CQ =pas can associate with a CT, it cannot be claimed to have CT marking as a distinct function.

Since Huallaga Quechua is classified as having this function by Forker (2016), let me point out that Weber (1989), which is given as Forker’s (2016) only source for HQ, does not use the term contrast(ive) in describing the different uses of =pis, nor does he discuss =pis in his chapter on topic. There are also no examples like (39) with =pis in these sections. Just as in CQ, it is possible that the associate of =pis happens to be a contrastive topic, as in (41), but as discussed above, this is not sufficient to conclude that it marks CT.

Since Forker does not include any HQ examples, it is not clear on what basis she classifies HQ =pis as a CT marker.

In the epistemic modal use, =pas typically co-occurs with the conjectural enclitic =chá, (47a), and/or the conditional mood -waq (2nd person) as in (47b) or -man (1st and 3rd person). According to my consultants, adding =pas to the conjectural =chá weakens the epistemic force from being almost certainly true to being only possibly true. I argue below that this is due to the additive presupposition requiring that the speaker entertain at least two epistemic possibilities.

Epistemic =pas is also found in questions, as for example in (48a), and with the future tense, as in (48b).

Epistemic =pas is not found in past or present tense declarative sentences without another epistemic operator, suggesting that it does not mark epistemic modality by itself. Rather, I propose that it operates on a set of alternatives introduced by a modal. I focus here on non-future declaratives like (47) with an epistemic possibility modal.

Following Aloni (2007), I assume that modals quantify over sets of propositional alternatives. With an epistemic possibility modal, all alternatives in this set Epist-Alt are live epistemic possibilities. =pas then quantifies over this set, requiring there to be at least one epistemic possibility in Epist-Alt that is distinct from the asserted one.

As in the simple additive use, focus contributes to the determination of the relevant alternatives: in (49), =pas attaches to the negation particle and the relevant alternatives Epist-Alt are the prejacent and its negation.

In (50),24 =pas attaches to the subject NP, and the alternatives are constructed by replacing it with relevant alternatives.25

We need to be careful to formulate the epistemic additive presupposition in such a way that (50) is not given the meaning This may happen to me in addition to something else happening to me. This would simply be the regular additive reading of =pas. While this might be a possible reading of (49),27 we are aiming to capture the epistemic meaning There is a possibility that this may happen to me in addition to there being a possibility that something else may happen to me. This can be achieved by adding the requirement that the presupposed alternative be true at a world v distinct from the world w′ at which the prejacent is true. The epistemic use of =pas can then be represented as in (51).28

(51a) represents the assertion that the prejacent p is an epistemic possibility, that is, it is true at at least one epistemically accessible world w′. The epistemic additive presupposition in (51c) requires there to be a distinct epistemically accessible world v, at which a distinct proposition q from the set of epistemic alternatives Epist-Alt is true.

This analysis captures the observation by native speakers mentioned above, that =pas weakens an epistemic modal sentence. The epistemic assertion and additive presupposition together entail that the speaker entertains at least two propositions as live epistemic possibilities. Without the additive presupposition, the assertion would be compatible with the prejacent being the only epistemic possibility.29

In addition to the simple epistemic possibility use, =pas participates in constructions with the conditional mood to produce as if and wish clauses, neither of which have to my knowledge been described in the previous literature. The first construction typically also involves the adverb hina ‘like, same’, and the second the exclusive marker =lla. The as-if construction is exemplified in (52).30

The wish-construction is exemplified in (53). (53a) was volunteered by one of my consultants as a further example of the combination of the exclusive =lla with =pas, before I was aware of this use, and, when prompted, offered (53b) as a further example of this sort.

In both sets of examples, the conditional =man again references a set of epistemic possibilities, which are here understood as counterfactual. =pas in turn presupposes the existence of an alternative distinct from the one denoted by the prejacent, which can be assumed to be the way the world is known to be, that is, the speaker of (52a) not having been drunk and the speaker of (53a) not being Paula. The particle hina ‘like’ explicitly marks the comparison in the hypothetical comparison clauses, whereas the role of =lla in the wish construction is perhaps comparable to English only in If only I was a member of congress …. A full analysis of such examples is left for future research, though I hope to have shown that =pas can, in principle, be analyzed as an additive operator over epistemic possibilities also in these constructions.

There is then a clear connection between this and the simple additive use of =pas. As summarized in Table 4, the main difference between the two uses is again the type of alternatives quantified over.

The nodes on a semantic map are often taken to be functions of linguistic expressions, a cover term for both its senses as well as its uses, that is, both its conventional meanings and its contextual meanings (van der Auwera & Plungian 1998; Haspelmath 2003). The main advantage of this approach is that it avoids having to commit “to a particular claim about which functions are part of the conventionalized linguistic knowledge […] and which functions only arise in different utterances depending on the pragmatic context” (Haspelmath 2003: 213). Typologists often do not have the relevant data to make this distinction and from a diachronic perspective, this approach can deal with expressions that are in the process of conventionalizing previously pragmatic meanings.

With semantic maps based on functions, an expression is taken to have the functions represented by the nodes it covers. This becomes problematic, however, when we include subtypes, as discussed in section 7.2.

Another notion that has been used to define the nodes of semantic maps is that of generalized utterance meanings, GUMs. GUMs take account not only of the relevant properties of individual expressions but also of the utterance they occur in. They “can be thought of as utterance types that are stripped of their lexical content” and represent “properties of sentences such as the illocutionary force of the corresponding utterance, the (non-)veridicality of the proposition expressed, the (non-)instantiation of an event, TAM-features, etc.” (Gast & van der Auwera 2013: 132). To give a non-additive example, Gast & van der Auwera (2013: 137ff) show that the distribution of impersonal pronouns such as they is constrained by properties of the pronouns themselves, for example, their quantificational force, as well as by properties of the state of affairs described, for example, whether it is episodic or generic. Whether a linguistic expression covers a node on a GUM-based map is determined by its ability to occur in diagnostic sentences that unambiguously exhibit the relevant properties such as (60a) and (60b).

Since they can occur in both (60a) and (60b) it maps onto the respective nodes in the semantic map of impersonal pronouns. In contrast, Italian si can occur in (60b), but not in (60a) (Gast & van der Auwera 2013: 146), and so will only map onto the node corresponding to (60b).

Crucially, the fact that an expression can be used in a diagnostic sentence does not, at least not in and of itself, constitute evidence that it has the function of expressing the particular features associated with that node.34 Thus, impersonal they does not have the function of expressing episodicity, despite being able to be used in all episodic diagnostic sentences. Replacing they with a personal pronoun, for example, She is knocking on the door, only removes the impersonal feature, not episodicity.

Replacing functions with GUMs on a semantic map affects the nature of the implicational universals it encapsulates, which now take the form in (61).

Such universals are weaker than function-based ones because, again, compatibility with a GUM does not equate to an expression marking a particular feature of that GUM. Of course, in many cases, we are in a position to make this stronger claim, but such a claim must be argued for on the basis of evidence other than mere compatibility with the corresponding GUM. I will in the following adopt GUM-based maps precisely because their claims are weaker to start with.

Scalar additivity is often treated as a subtype of additivity with an additional scalar presupposition (König 1991; Gast & van der Auwera 2011; Forker 2016), but this is not reflected in Figure 2, which represents it as an independent node on an equal footing with additivity. In order to formally capture that some GUMs are subtypes of others, I adopt Gast & van der Auwera’s (2013) feature-based approach. Restricting ourselves to binary features F, there are three possible value specifications for any F:

The values are interpreted relative to a context, including the linguistic co-text as well as the wider context of utterance. A positive specification requires F to be present, a negative specification indicates incompatibility with a context exhibiting F, and underspecification (+/–) means that there is no constraint one way or another.

A GUM is defined as a set of feature-value pairs. (63) shows the feature structures for simple and scalar additivity. The feature [ADD +] is to be understood as short-hand for the set of features identified in section 2, namely, presupposition of the existence of a distinct alternative to the prejacent in the set of focus alternatives.35

The feature [SCAL +] requires a context in which these alternatives are ordered.

Subtypes can be defined as follows. GUM G₁ is a subtype of G₂, iff it agrees on all feature values for which G₂ is specified, and has a specified value for at least one feature for which G₂ is underspecified. Thus, scalar additivity is a subtype of additivity. The relevant part of the additive map in Figure 3 captures that scalar additivity is a subtype of additivity by representing it as a subset (van der Auwera & Plungian 1998).

GUMs, recall, are generalizations over utterance tokens that share the same set of features. Some of these features are contributed by the expression that is being mapped, while others are not. Simple additives like CQ =pas, German auch or English also, too contribute [ADD +], scalar additives such as even in addition contribute the feature [SCAL +]. We know that these feature values are contributed by these expressions because removing them also removes the features. Thus, Pilar even speaks Aymara requires a context in which Pilar speaks a language other than Spanish and in which her speaking Spanish is less expected than her speaking that other language, whereas Pilar speaks Aymara has no such requirements.

(64) presents the features for some of the additives we have encountered:36

Leaving the SCAL feature underspecified for the simple additives in (64b) predicts that they should be able to occur in non-scalar as well as scalar contexts. This prediction is borne out for CQ =pas and German auch, as argued in sections 2.1 and 2.2. (65a) is an example of =pas in a scalar context (repeated from (22)).

(65a), recall, is interpreted as scalar due to background knowledge that people cannot control the natural elements, and is, in English, translated with even. GUMs, as defined above, do not directly capture features of contexts, but linguistic features of utterance types. Since there is no linguistic expression that specifies a value for SCAL, this example instantiates a [SCAL +/–] GUM as shown in (65b).

A further prediction of underspecifying =pas and auch for scalarity is that they should be able to occur with scalar GUMs, that is, in utterances that contain other expressions that are specified [SCAL +]. This prediction is also borne out, as discussed in section 2.2 for sentences containing the exclusive =lla. As mentioned in section 2.2, the German construction auch nur ‘also only’ also has scalar additive uses (Guerzoni 2003; Gast & van der Auwera 2011). (66a) is repeated from (25a), and (66b) represents the relevant features of the GUM instantiated by it.

We are now in a position to justify more fully the use of GUMs instead of functions as nodes. Mapping CQ =pas (or German auch) onto the partial map in Figure 3, we grey in the simple additivity node. With scalar additivity a subtype, this node automatically also becomes grey. A function-based map would commit us to the claim that all simple additives have a function as scalar additives, which, as argued for CQ =pas, is too strong. Moreover, since anti-scalarity, [SCAL –], is its logical sister subtype,37 we would also be committed to the claim that all simple additives have a function as anti-scalars. This is clearly wrong. A GUM-based map allows us to capture the irrelevance of the SCAL feature as underspecification and only commits us to the claim that =pas is compatible with both scalar and non-scalar utterances and contexts, which is the case.

We do of course still want to be able to say that an expression E has the function of expressing a particular set of features F. I propose that this requires that we can trace the respective features to the presence of E, in other words, that E is causally implicated in bringing them about.38 The CQ and German additives have the function of marking additivity, but not scalar additivity.

As mentioned, the adoption of GUMs instead of functions affects the implicational universals that can be read off a semantic map. Consider (67) (repeated from (59a)) in relation to Figure 3.

Assuming that Forker (2016) uses reading synonymously with function, the CQ =pas constitutes a counterexample to (67).39 =pas is however not a counterexample if we rephrase (67) in terms of GUMs:

Note though that (68) does not make interesting predictions. Any additive that is underspecified for scalarity validates it. Such an additive would equally validate it, if the conclusion referred to anti-scalar GUMs instead. Moreover, (68) makes no useful predictions for scalar additives, because they are able to be used with scalar GUMs by definition. In general then, connections between subtypes and their supertypes should not form the basis for implicational universals.40

The last issue to be addressed with respect to subtypes is Connectivity, the requirement that the region that any particular expression maps onto must form a connected graph. We saw in section 3 that both non-scalar additives like =pas and auch as well as scalar additives like even can be used in concessive conditionals. In Figure 3, additivity is directly linked to concessivity, which ensures that Connectivity holds for the simple additives. In addition, I suggest that subtypes are understood as being connected to another node if their supertype is connected to that node. That is, Figure 3 satisfies Connectivity for even by virtue of it being an additive.

In sum, adopting GUMs as the nodes of the semantic map for additivity allows us to capture that scalar additivity is a subtype of additivity. The revised map in Figure 3 satisfies Connectivity for CQ =pas and German auch without having to claim that these additives have a separate function as scalar additives.

Recall from section 2.5 that CQ =pas does not mark contrastive topic or topic switch and therefore falsifies the universal in (59b). Given that I argued that both the conjunctive and the discourse connective use can still be analyzed in terms of additivity, it seems natural to put these three GUMs on the same path, as in Figure 4. As can be seen, =pas (grey nodes) no longer violates Connectivity. The revised map in Figure 4 now encapsulates the implicational universal in (69).

Forker does not explicitly discuss this, but the reason that she did not opt for this arrangement herself is presumably that there are two languages in her sample that appear to be counterexamples, namely, Laz and Karbi. These languages have additives that can function as discourse connectives but which are marked by Forker as not having a function as constituent coordinators. A closer look reveals, however, that it is not entirely clear that they do not. Konnerth (2012) explicitly states that Karbi disallows NP coordination with the additive marker =tā, but she also describes uses of this marker as a bisyndetic coordinator for verb phrases and clauses. Thus, if we include constituents other than NPs, Karbi conforms to (69).

Regarding Laz, Lacroix (2009: 79) includes French et ‘and’ as a possible translation for the additive =ti. Some of his examples appear to be coordinations of verb phrases or clauses, e.g., (70).41

While I cannot commit to the claim that -ti here is definitely used as a constituent coordinator, it also seems too strong to claim that it is not. Therefore, I would also not consider it a counterexample to (69) at this point, though further research may prove otherwise. If it turns out to be a counterexample, the only way to accommodate it as well as CQ =pas would be to add a link between Constituent Coordination and Discourse Connectivity on Forker’s original map. The disadvantage of adding links, however, is that it reduces the predictive power of the map (Gast & van der Auwera 2013).

Our last task is to incorporate the epistemic use of =pas into the map. Semantic maps for modality link epistemic possibility to concessivity (van der Auwera & Plungian 1998; van der Auwera et al. 2009), based on the fact that possibility modals often have concessive uses as well. This is illustrated for English may in (71).

This suggests that the map of additivity can be connected to that of modality via concessivity. There is however some disagreement as to how epistemic possibility and concessivity relate to each other: van der Auwera & Plungian (1998) treat them as two separate, connected, nodes, while van der Auwera et al. (2009) take concessivity to be a subtype of epistemic possibility.

Müller (2016) argues that genuine concessives with German obwohl ‘although’ imply that the actual world does not comply with normal expectations. As argued in section 3, this also holds for concessive conditionals with non-scalar additives. That is, concessives express a slight possibility in Kratzer’s (1981) terminology. I therefore adopt here the approach that analyzes concessivity as a subtype of epistemic modality.

The final map in Figure 5 incorporates this proposal and the other modifications to Forker’s (2016) map discussed in sections 7.2 and 7.3.

The nodes that the CQ additive =pas maps onto (grey shaded) form a connected region without gaps. Figure 5, unlike Forker’s (2016) original map in Figure 2, therefore satisfies Connectivity also for this marker. Recall that the fact that scalar additivity and concessivity are also grey shaded due to them being subtypes of additivity and epistemic possibility respectively does not commit us to the claim that =pas marks these notions. Since the nodes are understood as GUMs, not as functions, the only requirement is that =pas be compatible with scalar additive and concessive contexts, which is the case.