2.1 The morpheme –ish

First described by Kimenyi (Reference Kimenyi1980), the –ish morpheme has uses as both a morphological causative and an instrumental applicative. With many verbs, both causative and instrumental uses are available; there are also certain classes that prohibit particular readings. Consider the data in (8) where the causative and instrumental readings are both available with the verb kw-andika ‘to write’.

In this example, the verb marked with –ish has an additional argument compared with the bare verb in (7). In (8a), one of the objects is an instrument that is used to bring about the event; in (8b), there is a causee who is made to perform a writing event. Many transitive verbs from a variety of verb classes allow both interpretations, e.g. creation verbs such as ku-baka ‘to build’, ingestive verbs such as ku-rya ‘to eat’ and ku-nywa ‘to drink’, and caused change-of-state verbs such as ku-mena ‘to break’, ku-vuna ‘to break/snap’, and kw-ica ‘to kill’.

Both readings can also be found with unergative verbs. Consider, for example, the verb gu-kora ‘to work’ in (10).

Unaccusative verbs, such as ku-rumbura ‘bloom’, however, do not allow the instrumental reading, such as in (12a).

Other verbs, on the other hand, do not allow the causative reading. Specifically, verbs that entail the use of an instrument – such as gu-kata ‘to cut’ and gu-kubita ‘to hit’ – do not permit the causative reading.

In (14b), the causative reading cannot arise with the verb gu-kata ‘to cut’.

Thus, two questions emerge regarding –ish. First, given the two uses, what is the appropriate argument structure of –ish? To assume either a purely causative or a purely instrumental reading would fail to capture the full spectrum of uses of the morpheme, unless one proposes that the two uses correspond to two homophonous morphemes. Second, why are certain readings ruled out with specific verbs? Generally, it is assumed that causative and instrumental morphology increases valency in a monotone fashion without consideration of the meaning of the verb, but the data in this section suggest that verb meaning does in fact affect the realization of –ish. Before I present my analysis of the data in Section 4, I argue against a homophony analysis of –ish in the next section.Footnote ^[6]

3.1 Semantic vagueness

A homophony analysis assumes that there are two (or more) distinct senses that share phonological shape. On such a view, it is expected that the two uses are distinctly categorizable as causative and instrumental. In Kinyarwanda, there are readings associated with –ish that are not easily distinguishable between instrumental and causative interpretations. One such example is a dictation reading, where an animate object is manipulated to bring about an event.

In the sentence in (16), there are several possible interpretations, one of which is a typical causative reading where the teacher is commanding the student to write a story, and the student is creating the story of his or her own accord. Another available interpretation, however, is that the teacher is dictating a story to the child, and the child is writing down verbatim the story orated by the teacher. In this scenario, the child is being acted upon in a way that shows properties of both instruments and causees: although animate, the child is not acting volitionally, functioning more in line with a prototypical instrument.

Another reading that is difficult to categorize is where the intermediary causee is a machine or robot, such as the sentence in (17). In this case, a robot is used to bring about the writing of the story, and the ambiguous level of volitionality of the robot results in neither a clear causative nor instrumental reading.

While in (16) there is an animate causee that is being acted on, in (17) there is an inanimate entity that is acting autonomously. In neither case is the intermediary caused entity a prototypical causee or instrument (contra, e.g., Peterson Reference Peterson2007, who assumes that the difference between a causee and an instrument is the animacy of the caused entity). While in principle these facts are compatible with a homophony analysis, the lack of a sharp distinction puts into question the need to posit two separate forms. With a generality account of the type I propose in Section 4, on the other hand, there is no expectation that there should be categorically distinct uses, and it is natural that there are cases where the morpheme has readings that are not categorically causative or instrumental. To put it another way, the semantics of the notions of causee and instrument are not categorically distinct and there are blurred boundaries between the two (see Schlesinger Reference Schlesinger1989), and thus there is no semantic evidence for positing two homophonous forms for the different readings associated with –ish.

3.2 No syntactic distinction

Another related expectation of a homophony account is that there might be grammatical differences between the causative and instrumental uses. For example, in several languages, demoted causees of transitives are marked with oblique morphology, while applied objects are marked similarly to direct objects. As is typical of Bantu, Kinyarwanda does not have case marking on DPs (Diercks Reference Diercks2012), but one way to probe the grammatical properties of the two forms is the syntactic behavior of the causee and applied instrument, looking at whether the objects in applicative and causative sentences can appear in positions traditionally restricted to objects. Several diagnostics used in the Bantuist literature to observe the syntax of objects include pronominal object marking on the verb (Diercks Reference Diercks2010, Diercks & Sikuku Reference Diercks and Sikuku2013) and passivization (Gary & Keenan Reference Gary, Keenan, Cole and Sadock1977, Kimenyi Reference Kimenyi1980, Bresnan & Moshi Reference Bresnan and Moshi1990, Alsina & Mchombo Reference Alsina, Mchombo and Mchombo1993, Marten, Kula & Thwhala Reference Marten, Kula and Thwhala2007).Footnote ^[7] Before continuing, it is worth noting that the data in this section do not necessarily falsify the homophony analysis of –ish, since Kinyarwanda is often a symmetrical language across several applicative types (Kimenyi Reference Kimenyi1980, Wunderlich Reference Wunderlichto appear), and thus it is expected that any argument-adding morpheme will result in symmetry between the applied and thematic objects (although see Gerdts & Whaley Reference Gerdts and Whaley1993 for complexities that arise for verbs with multiple applicatives). Crucially, the goal here is to show that there is no clear-cut syntactic difference between the putatively distinct readings of –ish. In the absence of any syntactic or semantic evidence to the contrary, an analysis of underspecification is preferred in that it provides an explanation for why such a syncretism should appear at all.

First, consider the passive, which is marked morphologically after the verb stem by the suffix –w. The data in (18) show that the causee object and the thematic object licensed by the verb are both equally viable candidates for being subjects of a passive.Footnote ^[8]

The data in (19) show that the same situation holds for the instrumental reading; both the instrumental object and the thematic object can be subjects of a passive.

Another test for object status in Bantu languages is the ability for the object pronoun to incorporate onto the verb. Bantu languages vary with respect to the exact behavior of the object marker (Bresnan & Mchombo Reference Bresnan and Mchombo1987, Baker Reference Baker1988, Alsina & Mchombo Reference Alsina, Mchombo and Mchombo1993, Bax & Diercks Reference Bax and Diercks2012, Reidel Reference Reidel2007), but for many languages (including Kinyarwanda), the ability for a DP to appear as a morpheme on the verb is a sign of object status (as opposed to an oblique or secondary object which cannot, cf. Gary & Keenan Reference Gary, Keenan, Cole and Sadock1977, Kimenyi Reference Kimenyi1980, Dryer Reference Dryer and Perlmutter1983). In the causatives in (20), both the causee and the patient can be marked on the verb; similarly, both the instrument and the patient can be marked in (21).

The data from passivization and object marking are the same for both causative and instrumental uses of the morpheme, which suggests that there is no distinction in the grammatical status of the two. For some speakers, one difference between the two is the default word order (cf. Kimenyi Reference Kimenyi1980). For these speakers, the causee must come before the patient, while the instrumental object must follow it, as shown in (22) and (23).

For many Bantu languages, however, the animacy of the two objects has been cited as the crucial factor for determining word order (Morolong & Hyman Reference Morolong and Hyman1972, Hyman & Duranti Reference Hyman, Duranti, Hopper and Thompson1982, Aranovich Reference Aranovich, Butt and King2009). The preference for the animate object to precede the inanimate object suggests that the word order differences in (22) and (23) are not due to a grammatical distinction between causative and instrumental structures, but a separate restriction on the prominence of specific arguments. In the cases just mentioned, this means that the causee will precede the theme because the causee is animate.

As with semantic vagueness, the absence of any clear grammatical differences of the causative and instrumental uses is expected on an account where the two putatively distinct uses are in fact outgrowths of the same grammatical operation. While the syntactic facts are also technically compatible with the homophony approach, there is no obvious case where the causative and instrumental uses are distinct in their grammatical behavior. Furthermore, with the causative reading, there is no evidence (morphologically or syntactically) of the causee being a demoted or oblique argument; instead, it patterns exactly with the object of a monotransitive verb.

3.3 Diachronic evidence

The strongest piece of evidence against a homophony account is that there is no phonological change that can explain why the instrumental reading of the applicative *–ɪd in Proto-Bantu would change to become –ish in modern Kinyarwanda. First, it would be surprising for a phonological change to target only one reading of a particular morpheme (since *–ɪd is reconstructed as a general applicative covering various roles, although only the instrumental reading was folded under –ish). Second, there is no obvious pathway in Kinyarwanda for the phonological change from *–ɪd in Proto-Bantu to synchronic –ish.

This leaves a semantic explanation for the overlap between causative and instrumental readings – a change that has been observed and proposed for other languages. While my intention is not to provide an elaborated theory of the diachronic origins of –ish here, I assume that, given the synchronic and diachronic form and functions of the morpheme, the more tenable explanation for the syncretism is that the causative morpheme spread to cover the instrumental applicative. Specifically, I assume the approach of Shibatani & Pardeshi (Reference Shibatani, Pardeshi and Shibatani2001), who argue that causatives often extend to include applicative readings; with instrumental meanings, reanalysis occurs via a ‘sociative causative’ meaning. Sociative causation is a causal relation in which the agent causes the patient to perform an action and performs the action alongside the patient. To cite their example, the Japanese lexical causative asoba-seru ‘to make someone play’ describes a situation in which the causer is playing with the causee, such as in the case of a caregiver and a child. Semantically, the use of an instrument is parallel for Shibatani & Pardeshi (Reference Shibatani, Pardeshi and Shibatani2001); an agent acting on a knife to cut bread is acting with the knife to bring about the change on the bread.

Although the sociative meaning is not obligatory for causative interpretations of –ish synchronically, this analysis accounts for the direction of change – namely, that the causative morpheme extended to cover the instrumental applicative. Many closely related Bantu languages have an applicative morpheme cognate to –ir which licenses several thematic object types, such as benefactive, locative, reason, and, crucially, instrumental (Wald Reference Wald, Maddieson and Hinnebusch1998:97; Bostoen & Mundeke Reference Bostoen and Mundeke2011). This general applicative, traceable to Proto-Bantu *–ɪd (Meeussen Reference Meeussen1967, Schadeberg Reference Schadeberg, Nurse and Philippson2003), is the default for all applied objects, including the instrumental. The morphological causative in these languages is cognate to –ish, traceable to Proto-Bantu *–ici (Bastin Reference Bastin1986, Schadeberg Reference Schadeberg, Nurse and Philippson2003). The most natural analysis of the synchronic uses of the morpheme is that the morphological causative extended to the instrumental applicative in Kinyarwanda. This historical account does not technically rule out the possibility that in the modern language, the instrumental and causative are different morphological operations. However, the simpler analysis is that the diachronic extension of the causative to the instrumental applicative remains as a single operation synchronically.

Thus, the use of the –ish as both the causative and an instrumental applicative in Kinyarwanda follows the proposed cline of grammaticalization proposed by Shibatani & Pardeshi (Reference Shibatani, Pardeshi and Shibatani2001). On an account that analyzes –ish as an instance of accidental homophony, there is no explanation for the historical extension of the causative to the instrumental applicative.

3.4 Further evidence

Another piece of evidence against the homophony view is that the doubling of –ish is prohibited, as in (24).Footnote ^[9]

A possible explanation of (24) is to propose that the doubling of all valency-adding morphology is blocked. On this view, the ungrammaticality in (24) is not due to the semantics of instruments and causees, but rather a syntactic blocking of two valency-increasing operations. This restriction is not found, however, when the applicative –ir (which licenses locative and benefactive applied objects) and the morpheme –ish are both used, as shown in (25) which has both –ish and the locative applicative use of –ir.

The unacceptability of the doubling of –ish in (24) does not follow from a general constraint against the use of multiple valency-changing morphemes, which suggests that the ungrammaticality of (24) comes from a dispreference to repeat two instances of the same morphological form. A homophony account cannot explain this restriction on doubling, which provides further evidence for analyzing –ish as as having a single operation from which the different readings are derived.

In fact, this kind of prohibition is also found in the related language Chicheŵa (Bantu; Malawi) where the causative –its and instrumental applicative –ir are formally distinct (Mchombo Reference Mchombo2004). Simango (Reference Simango1999) observes that the two forms cannot co-occur:

In both examples in (26), the simultaneous use of a causative and an instrumental morpheme is disallowed. The data in (27) show that there is also a restriction against the doubling of causatives in Chicheŵa, paralleling the restriction on doubling a causative and an instrumental in (26).Footnote ^[10]

Simango (Reference Simango1999) thus concludes that the causative and instrumental overlap in meaning, and this results in the inability to double the morphemes.

As with Kinyarwanda, the doubling of other valency-adding morphology is permitted in Chicheŵa; benefactive and locative applicatives may co-occur with causative morphology, as in (28).

The parallel ungrammaticality of causative–instrumental and causative–causative doubling in a language like Chicheŵa, where the causative and instrumental are formally distinct, is expected in the view that causatives and instrumental applicatives share an overlapping semantics.

4.1 Theoretical preliminaries

In this section, I propose an analysis of –ish in which a participant is introduced via an operation that adds a novel link and associated participant into the causal chain denoted by the verb. The key insight is that this new causal link can be interpreted as either initial in the overall causal structure – deriving a causative reading – or intermediary – deriving an instrumental reading. The idea that causatives introduce a new initial causal event is the standard analysis, and the idea that instruments are intermediary causees has been claimed in several previous works (Talmy Reference Talmy and Shibatani1976, Comrie Reference Comrie1989, Croft Reference Croft1991, Ichihashi-Nakayama Reference Ichihashi-Nakayama1996, Goldberg Reference Goldberg2002, Peterson Reference Peterson2007, Koenig, Mauner, Bienvenue & Conklin Reference Koenig, Mauner, Bienvenue and Conklin2008). For example, Van Valin & Wilkins (Reference Van Valin and Wilkins1996) argue that agent, force (cause), and instrument all derive from a broader effector role and differ only in both properties of the NP and their position in the causal sequence described by the verb. Similarly, Croft (Reference Croft1991: 190–191) shows that in Chechen-Ingush, instruments pattern with causees with respect to case assignment when they appear within specific classes of verb. Thus, I follow this work in treating causees and instruments as two outgrowths of the same semantic category.

With respect to –ish, the two different readings arise in turn from how the new causal subevent interacts with the existing events in the causal chain described by the verb, restricted by general constraints on possible event types – and the link between lexical semantics and argument realization – that ultimately conspire to rule out one reading or another in certain cases with certain verbs. Below, I provide two case studies of how two particular verb types constrain the possible readings that arise with –ish.

In the formal analysis I propose here, I assume a domain of discourse $U$ that consists of two major sorts: the subsets $U_{I}$ of individuals and $U_{E}$ of eventualities. Variables in the set $U_{I}$ are $x,y,$ and $z$ . I will utilize the variables $v$ , $r$ , $s$ , $e$ , and $e^{\prime }$ to represent all subevents.Footnote ^[11] The event variable $e$ is a complex event that is the summation of all subevents of the predicate, and each subevent is causally linked to the other subevents in $e$ , which I notate in the denotations of verbs with the subset operator (e.g. $v\subset e$ means that $v$ is a subevent in $e$ ). In cases where a derivational morpheme adds a new subevent to a verbal predicate (such as with a causative), the subevent added by the derivational morphology will also be a subevent of the larger event $e$ . Subevents within $e$ are causally ordered with respect to one another. It should be noted that causal precedence is not the same as temporal precedence, and even if one subevent causally precedes another, it is possible that the two subevents temporally overlap (even completely).

In most work, subevent structure is represented through hierarchical organization of what is often referred to as an event structure. Perspectives differ as to whether event structures are lexical (Dowty Reference Dowty1979, Jackendoff Reference Jackendoff1990, Levin & Rappaport Hovav Reference Levin and Rappaport Hovav1995, Wunderlich Reference Wunderlich1997), syntactic (Lakoff Reference Lakoff1965, Hale & Keyser Reference Hale, Keyser, Hale and Keyser1993, Harley Reference Harley, Pica and Rooryck2003, Ramchand Reference Ramchand2008), or constructional (Goldberg Reference Goldberg1995, Kay Reference Kay, Fried and Boas2005), but the hierarchical structure is useful for capturing things like sublexical scope (e.g. Dowty Reference Dowty1979) and correlating hierarchical relations in the syntax (e.g. Wunderlich Reference Wunderlich1997). However, the choice of notation does not bear on the generalizations I discuss here, and thus I instead take the common thread across all event structural approaches – the formalization of relations between subevents and their associated participants – and directly encode them as conditions on truth conditional content without utilizing a hierarchical representation. The benefit of the framework I implement is that it provides a way of stating that causal structure is underspecified in certain verb meanings – something more difficult to state using hierarchical event structures which rigidly restrict the position of arguments.

With this framework in mind, I propose that the argument introduced by –ish may be either the initial causer or an intermediary participant in the causal chain. Before discussing the details of this analysis, I first outline one key background assumption that will be important here, namely that arguments may be reordered. The insight for this approach comes from Zwicky (Reference Zwicky1986) and Dowty (Reference Dowty, Sijtsma and van Horck1991b), who challenge the dominant assumption in syntactic theory that constituent structure must be rigid in all languages. Dowty, for example, uses a categorial grammar with a compositional semantics in which syntactic operations are built up from words into a set of larger expressions. Crucially, the set of words is unordered, unless evidence for a specific ordering constraint is present in the language. In these cases, he adopts linear precedence principles which limit the relative ordering of specific expressions (Pollard Reference Pollard1984, Gazdar, Klein, Pullum & Sag Reference Gazdar, Klein, Pullum and Sag1985). Using this framework, he can capture several syntactic phenomena, such as the relatively free word order of Finnish and extraposition in English, without having to appeal to hierarchical syntactic structures.

As noted above in Section 3.2, Kinyarwanda is parallel to the Finnish data presented by Dowty in that Kinyarwanda allows scrambling in certain domains, specifically with the flexibility of ordering with multiple objects. However, rather than using a categorial grammar with linear precedence conditions, I adopt a typed lambda calculus for semantic representation and assume that arguments can be reordered lexically (subject to a few constraints which I discuss below), preserving the insight that arguments can in principle combine freely with the verb.Footnote ^[12] Instead of linear precedence conditions, I assume that there are general and lexical constraints on the order of causal subevents, and these constraints in turn rule out specific orderings of arguments.

One general constraint on the possible ordering of causal elements is that the last argument to be picked up by the verb will be mapped to subject as well as assigned the role of being the initial causer in the event structure of the verb. Wunderlich (Reference Wunderlich1997) proposes a similar method for subject selection in his Lexical Decomposition Grammar, where there is a level of semantic form in which arguments are related semantically to the verb. In his theory, argument structure relations are determined by the hierarchical position of the argument in the verb’s event structure, and the highest argument in the event structure is the subject (i.e. the last to be saturated). For him, the initial causer is always the highest argument semantically, thus deriving the link between subjecthood and initial causers with causative verbs through prominence preservation. Adopting the notion that argument realization is tied to order of composition in the semantics, I likewise assume for active verb forms that the final argument to be saturated (i.e. the subject) will be the initial causer of the event (i.e. the causer participant in a causal subevent that has no preceding causal subevent), as stated in (29).

One crucial difference, however, between Wunderlich’s approach and the one I propose here is that Wunderlich requires that causativization always adds a higher argument. However, in order to incorporate the instrumental uses of –ish (i.e. those where there is an intermediary causal link), I allow that the argument introduced by –ish is, in principle, unrestricted in its order of composition, although verb-specific constraints on the ordering of subevents will restrict its placement. In short, the final argument to be picked up will be the initial causer, regardless of whether that argument is linked to the causal event of the verb or the causal event introduced by –ish. This principle parallels the general assumption in the literature that causers are preferred to appear in subject position.

For clarity, in the denotations below I notate the argument (and associated subevent) that is assigned to initial causer with underlining, and any other arguments are mapped to objects. The argument mapped to subject will always be the highest (rightmost) $\unicode[STIX]{x1D706}$ -abstractor, while all other arguments (apart from the subject) are saturated post-verbally from the inside out. Thus, the lowest (leftmost) $\unicode[STIX]{x1D706}$ -abstractor corresponds to the object immediately adjacent to the verb. By means of example, consider the sentence in (30) with the ditransitive verb gu-ha ‘give’, and the denotation of the verb in (31).

The denotations of the nouns in (30) are defined in (32). The derivation in (33) shows step-by-step how each of the arguments in turn combines with the verb gu-ha ‘to give’. I assume that any event variables are existentially bound at a higher node in the derivation.

In (33), the first argument to be composed with the meaning of the verb is Habimana, then igitabo ‘book’, and finally Karemera. By virtue of being the final participant picked up by the verb, it is this latter argument that is mapped to subject. Crucially, the order of the $\unicode[STIX]{x1D706}$ -abstractors corresponds to the syntactic structure; with the denotation in (33), the order of arguments is that in (34a) and corresponds to the word order in (34b), where the subscripted variables notate which lambda abstracted element that argument corresponds to.

In the system I propose here, lambdas can be reordered, but constraints on verb meaning limit the possible orders of causal subevents (and thus the possible mappings between arguments and semantic representations). I discuss the different relevant constraints in the next subsection.

Before continuing, it is worth noting that there has been considerable discussion on the status of applied and causative objects in Bantu languages, especially Kinyarwanda (Gary & Keenan Reference Gary, Keenan, Cole and Sadock1977, Kimenyi Reference Kimenyi1980, Dryer Reference Dryer and Perlmutter1983, Jerro Reference Jerro, Kramer, Zsiga and Boyer2015). I largely set aside the question of syntax here and leave a formal analysis of the syntactic facts to future work. However, it should be recalled from Section 3.2 that both the instrumental and causative uses of the –ish morpheme behave like objects of monotransitives with respect to several objecthood diagnostics (such as the ability to be the subject of a passive and object-marked on the verb). I take these diagnostics as evidence that both of the post-verbal nouns are objects in sentences where –ish appears with a transitive verb. As a result, there is no difference in the grammatical status of any post-verbal nominals in the sentences under discussion here.

4.2 Caused change-of-state verbs

Specific verb classes may enforce additional restrictions on the possible orders of causal subevents. With caused change-of-state verbs such as write, which include a causing subevent and a caused change-of-state subevent, it is required that the causing event precede the caused change of state (Dowty Reference Dowty1979, Rappaport Hovav & Levin Reference Rappaport Hovav, Levin, Butt and Geuder1998, Beavers & Koontz-Garboden Reference Beavers and Koontz-Garboden2013). To capture this fact, I assume a lexical constraint which states that the caused change of state $s$ must be the final subevent in the causal chain. Formally, I represent this with the relation $fin^{\prime }(\unicode[STIX]{x1D6FC},\unicode[STIX]{x1D6FD})$ , which takes two event arguments $\unicode[STIX]{x1D6FC}$ and $\unicode[STIX]{x1D6FD}$ and says that $\unicode[STIX]{x1D6FC}$ is the final subevent in $\unicode[STIX]{x1D6FD}$ (more precisely, no subevent follows $\unicode[STIX]{x1D6FC}$ in $\unicode[STIX]{x1D6FD}$ ). Additionally, $\unicode[STIX]{x1D6FC}$ may be equivalent to $\unicode[STIX]{x1D6FD}$ in specific instances, as I discuss below for unaccusative verbs. Consider the denotation of the transitive verb kw-andika ‘to write’ in (35), where a writing event results in a state of some item becoming written.Footnote ^[13]

The meaning of kw-andika ‘write’ in (35) states that there is an event that contains two subevents: the causing event $v$ of writing and the caused change of state $s$ of being written. The writing event is linked to the agent participant, while the caused state is linked to the theme. The sentence in (36) provides an example of a typical use of the verb kw-andika ‘to write’.

The verb combines with the noun inkuru ‘story’ and the noun umwana ‘child’, which results in the following denotation (after existential closure over event variables):

The finality constraint on $s$ derives the fact that $v$ must causally precede $s$ . For the sentence with the verb kw-andika ‘to write’ in (36), this means that the writing event must precede the caused state of something being written. Given the lexical restriction that the caused change of state must be final in $e$ , the only available reading is one where there is a child who is the agent of a writing event and a story that becomes written as a result, consistent with the Initial Causer Realization Principle.

It should be recalled that this approach assumes that individual arguments can be picked up in any order. This allows, in principle, the ordering of arguments in (38), where the individual arguments apply in the opposite order to (36).

However, (38) is ruled out. With the ordering in (38), the theme is the final element to be picked up, which would map the theme to the initial causer (following the Initial Causer Realization Principle in (29) which makes the argument in subject position the initial causer). This is not possible due to the condition that the subject must be the participant of the initial causing event, which cannot be a theme because the theme is restricted lexically to be a participant of the final subevent of $e$ . Thus, the principle in (29) and the lexical semantics are in contradiction, making (38) an impossible denotation.

Turning to the analysis of –ish, I propose that the meaning of –ish is an operation that takes a verbal predicate and an individual as inputs and introduces a new argument and causal subevent $e^{\prime }$ .Footnote ^[14] The argument linked to the $e^{\prime }$ subevent introduced by –ish is assigned a general thematic role that subsumes agents, causees, and instruments (Schlesinger Reference Schlesinger1989, Croft Reference Croft1991, Dowty Reference Dowty1991a, Van Valin & Wilkins Reference Van Valin and Wilkins1996, Rissman Reference Rissman2011, Rissman & Rawlins Reference Rissman and Rawlinsto appear). Following this work, I adopt a generalized thematic role (notationally ag) as the label that subsumes agents, causers, and instruments. As noted in Rissman & Rawlins (Reference Rissman and Rawlinsto appear), there is no single necessary and sufficient condition for what constitutes an instrument. They argue that event participant categories are represented in terms of a cluster of properties. I assume the vague definition of an $agent$ introduced by –ish as capable of transferring the force of the causal chain. With these components in mind, I provide the definition of –ish in (39), developed from the definition of with in Rissman (Reference Rissman2011).

The morpheme –ish takes an argument y and a predicate P, which may have n participants and m subevents. It introduces a new subevent $e^{\prime }$ in $e$ existentially, and this subevent is linked to a participant that has the semantic role of agent. The novel subevent is underspecified in its position in the causal chain of the verb to which –ish attaches. The different readings follow from the possible positions in the causal chain into which the new link is inserted. Thus, instead of narrowly adding a causer or instrument to a particular argument position, –ish adds a new participant, and the reading(s) that arise derive from general and verb-specific constraints on the order of subevents.Footnote ^[15]

The denotation of –ish in (39) composes with the denotation of the verb kw-andika ‘to write’ in (35) via function application, as shown in (40), to give the denotation in (41), deriving (42) by further function application. Thus, there are two individual arguments and three event arguments.

The meaning in (42) is the combination of –ish with the predicate kw-andika ‘to write’. Here, there are three subevents: $v$ , $e^{\prime }$ , and $s$ . The subevent $s$ is the causally final subevent in $e$ by virtue of constraints imposed by the verb, but crucially $v$ and $e^{\prime }$ are unordered causally relative to one another. Thus, the actual ordering of the two can be resolved in one of two ways: $v$ before $e^{\prime }$ or $e^{\prime }$ before $v$ . However, constraints on argument realization – in particular the Initial Causer Realization Principle in (29), plus the possibility of reordering – ultimately determine which order arises in a given context, which I suggest captures the two readings. I discuss the instrumental reading first.

Consider the instrumental sentence in (43), where the teacher uses a pen to write a story.

The derivation of the sentence in (43) proceeds as in (45), with the meanings of the nouns defined in (44). The denotation in (42) first composes with ikaramu ‘pen’, which is the argument licensed by the –ish morpheme, shown in (45a). Next, the argument inkuru ‘story’ is composed in (45b), and finally umwarimu ‘teacher’ is the last argument to be picked up in (45c). The result is the denotation in (45e), where the events $s,v,$ and $e$ are existentially bound at a higher node.

The agent linked to the writing event $v$ is the last argument to be picked up and thus is the subject; therefore, by virtue of the Initial Causer Realization Principle, the event $v$ associated with that argument must be the first in the causal chain of $e$ . This ensures that the subevent $e^{\prime }$ licensed by the –ish morpheme (here, associated with the argument ikaramu ‘pen’) is causally intermediate. The reading, then, is that the teacher acts on the pen to bring about the writing event, i.e. an instrumental reading.

The flexibility of argument order permits an alternative reading, where the participant linked to the event introduced by –ish and the entity linked to the agent of the base verb are reordered.

In this case, the argument linked to $e^{\prime }$ is picked up last and is thus the initial causer. As a result, $e^{\prime }$ causally precedes $v$ , and both causally precede $s$ . This gives rise to a classic causative interpretation, like that in (47a), where the teacher is causing the student to write the story.

In (47b), the teacher is the initial causer, meaning that he or she is the agent of a subevent that precedes the event of the student writing the story. The finality constraint that the caused change of state $s$ is the final subevent is satisfied; there is no event that follows $s$ .

For clarity, let us compare the denotations in (42) and (47b). In (42), the agent of the writing event is the initial causer, meaning that the event added by the –ish morpheme is an intermediate event. In (47b), on the other hand, the initial causer is the argument linked to the event licensed by the –ish morpheme, and the agent of this event acts on the agent of the verbal causing event. The crucial difference between the two readings is whether the initial causer is the agent of the causing event denoted by the verb or the agent of the event introduced by –ish.

An additional prediction of this analysis is that due to the flexibility in the ordering of arguments, object word order should be free. Consider the order of the arguments in (48), which is nearly identical to the denotation in (46), except for the order of the $x$ and $z$ arguments.

This ordering has the same meaning as the causative sentence in (47a), but predicts that the two objects are picked up in the opposite order, resulting in a reversal in the linear order of the objects:

Thus, lambda reordering allows the flexibility of the order of the two objects in sentences with transitive verbs marked with –ish. It should be noted that due to the freedom of argument order assumed in the theory, it is technically possible for the sentence in (49) to have a derivation in which umwana ‘the child’ is the participant of the $s$ subevent and inkuru ‘the story’ is linked to the $e^{\prime }$ subvent. This would mean something akin to ‘The teacher wrote the child with a story’. I assume that for pragmatic reasons this is a highly implausible reading, although given the correct context it is technically a possible meaning of the sentence. In fact, in cases like these, speakers have joked at the risibly implausible nature of the alternative readings of sentences like (49).

There are two reorderings of participants that are always ruled out by the theory. The lexical specification $\text{fin}^{\prime }$ of the verb requires that the caused change of state $s$ must be the final event in $e$ , and thus it must be causally preceded by both $v$ and $e^{\prime }$ (although the causal order of $v$ and $e^{\prime }$ can vary). This rules out two possible orders: namely, those in which the thematic argument z is the innermost participant qua the subject, i.e the denotations in (50).

The final argument to be saturated is mapped to subject and initial causer, which means that this argument cannot be the participant linked to the caused change of state $s$ , which cannot be the initial causing event, as specified by the meaning of the verb. Any other ordering of arguments is in principle generated by the framework.

To summarize the different available orders with causative verbs, instances in which the agent participant of $e^{\prime }$ is the final argument to be picked up have $e^{\prime }$ as the initial causing event, meaning that $e^{\prime }$ causes $v$ which in turn causes $s$ , which must be final. This order corresponds to a causative reading. The alternative ordering is that $v$ is the initial causer and $e^{\prime }$ is intermediary. In this ordering, the agent of $e^{\prime }$ is an instrument acted upon by the argument linked to $v$ to bring about the caused change of state $s$ .

4.3 Intransitive verbs and –ish

I now turn to –ish with intransitive verbs. It should be recalled from Section 2 that unergative verbs allow both the causative and instrumental readings, while unaccusative verbs do not permit the instrumental reading. I show that this follows from the causal structure of the two types of intransitive verbs. Because intransitives only have a single subevent in their non-applied form, I assume that in the absence of other subevents (i.e. when there is no valency-adding morpheme to add additional subevents to the predicate), the pragmatic default is that the single subevent of the intransitive is equivalent to the entire event $e$ . This relation is notated formally with the symbol $\subseteq$ (i.e. $s\subseteq e$ means that $s$ is a subevent or equivalent to the event  $e$ ). In the presence of an additional subevent (such as when one is introduced via a valency-changing morpheme such as –ish), the subevent is not equal to  $e$ .

I assume that unaccusative verbs have a single change-of-state event $s$ and unergative verbs have a single action event $v$ . Furthermore, I argue that with unaccusative verbs there is a constraint that in the presence of other (derived) subevents, the change-of-state event $s$ must be final in the series of causal events as with causative verbs. With unergatives, on the other hand, there is no such restriction. These constraints I suggest conspire with the analysis of –ish above to produce the relevant readings. I discuss each verb class in turn, first discussing unergative verbs and then turning to unaccusatives.

Take, for example, the unergative verb gu-kora ‘to work’ in (51), in which the only subevent in its denotation in (52) is $v$ , which, by default, is equivalent to the main event $e$ in the absence of another subevent.

The meaning in (52) is that there is an event of working, which has an agent participant. There is no restriction on the ordering of any subevents that are present in addition to $v$ . Given that there is no restriction on the order of a causing event $v$ in relation to other subevents, it is predicted that there should be both causative and instrumental readings with unergative verbs.

Consider the combination of gu-kora ‘to work’ with –ish in (53).

With this ordering of arguments (the default), the participant of the causing event $v$ is the final argument to be picked up, which means that this subevent is interpreted as the initial causing event. This results in an instrumental reading, with $v$ causing $e^{\prime }$ . This is the reading of the sentence in (54), associated with the denotation in (55).

The instrumental reading arises because the agent of the working event $v$ causally precedes the agent of the event licensed by $e^{\prime }$ . In this situation, the two subevents temporally overlap as they move forward, although the event $v$ is what crucially causes $e^{\prime }$ . By implicature, the agent of the event licensed by $e^{\prime }$ is assumed to be involved in the action of the event $v$ (here, working). The reading for (54), then, is that the man acts on the hoe, and the hoe is used to do the work. It should be noted that temporally, $v$ and $e^{\prime }$ may overlap or even be (effectively) simultaneous, although the causality is still initiated by the agent of $v$ .

Consider now the alternative argument ordering in (56), where the $y$ participant linked to $e^{\prime }$ is the final argument to be picked up.

This order corresponds to a causative reading, since the participant of $e^{\prime }$ is the final argument to be picked up. Thus, the argument introduced by –ish is the causer subject. This is the interpretation that is found with a sentence like that in (57).

In (58), the subevent $e^{\prime }$ introduced by –ish causally precedes the subevent $v$ of the verb –kora, resulting in a causative reading in (57).

With unaccusative verbs, on the other hand, I assume that in the presence of other subevents (i.e. those added by morphology such as –ish), the change-of-state event $s$ must be the final event in the causal chain, which is formalized with the same finality condition used with caused change-of-state verbs above (i.e. $\text{fin}^{\prime }(s,e)$ ). In the absence of any other subevents, $s$ is the only subevent, and the finality constraint is satisfied by default. The intuition behind this constraint comes from restrictions on lexical verbs; it does appear to be the case that lexical verbs encode a chain of causal events where a change of state causes another event. I adopt this from Rappaport Hovav & Levin (Reference Rappaport Hovav, Levin, Butt and Geuder1998), who do not include changes of state causing actions in their inventory of possible event templates. In fact, it is difficult to imagine what kind of meaning a verb that describes such an ordering of events would have.

The constraint on the order of subevents predicts that the only available reading with verbs that denote a single change of state should be the causative reading. The instrumental reading is ruled out because the event $e^{\prime }$ licensed by –ish cannot be causally preceded by $s$ , since $s$ must be the final subevent in the causal chain. Consider, for example, the meaning of the verb ku-rumbura ‘to blossom’ in (59), which is the change of state of becoming bloomed. Here, as with gu-kora ‘to work’, $s$ is a subevent of $e$ unless there are no other subevents, in which case it is interpreted as equivalent to $e$ .

The composition of the denotation of ku-rumbura ‘to bloom’ (59) with the –ish morpheme gives the denotation in (60).

The denotation in (60) corresponds to the instrumental reading, where the participant of the subevent $s$ is the initial causer. However, this results in a violation of the finality constraint which states that $s$ cannot causally precede any other subevent, which rules out the instrumental reading in (61).

The alternative ordering is that in (63), where $y$ is instead the final argument to be saturated.

The denotation in (63) corresponds to the causative reading; because $y$ is the final argument picked up, it is the initial causer and thus $e^{\prime }$ precedes $s$ . This satisfies the finality constraint on $s$ since $s$ is the final subevent in the causal chain. It follows from the analysis that unaccusatives allow causative readings with –ish, as shown in (64), where an initial causer acts to cause the flowers to bloom.

In the analysis presented here, changes of state are final in the causal chain, which predicts that when unaccusative verbs combine with the –ish morpheme, the $e^{\prime }$ subevent must causally precede the event described by the verb. This is borne out, capturing the data in (61) and (64) where the instrumental reading is ruled out with unaccusative verbs.

4.4 Implicit arguments

So far, the cases of –ish have involved wholesale addition of a new participant into a verb’s argument structure both syntactically and semantically, where the interaction with verb meaning has served to rule in or out certain readings. However, it should be recalled from Section 2.1 that with verbs that entail the use of an instrument, the only reading available is one in which the argument introduced by –ish is an instrument. In this section, I implement the framework of the analysis of Jerro (Reference Jerro2016a) for the locative applicative with verbs of motion in order to capture the restriction of instrument verbs with –ish.

Verbs of directed motion in Kinyarwanda vary with respect to the semantic role (either source, route, or goal) that is assigned to the applied object of the locative applicative (Jerro Reference Jerro2016a, Reference Jerro, Payne, Pachiarotti and Bosireb). For example, the verbs kw-iruka ‘to run’, kw-injira ‘to enter’, and kw-ambuka ‘to cross’ in (66)–(68) are representative of different classes of translational motion verbs where the locative applied object is either a goal, route, or source, respectively.

Crucially, in each case the base verb describes motion, and thus there is a path – and with it also a source, goal, and route of the agent along that path; the applicative serves to give overt syntactic realization to one of these implicit participants. However, it is idiosyncratic to each verb which participant is the one realized by the applicative, and not entirely predictable solely from the meaning of the verb. In order to capture the idiosyncratic lexical variation in which semantic role is selected by different verbs, Jerro (Reference Jerro2016a) argues that the participant brought out by the applicative is already present in the meaning of the non-applied verb as a semantic argument of the verb. However, a single verb can only license one locative participant (a feature of Niger–Congo languages; Creissels Reference Creissels, Hickmann and Robert2006), and so this additional locative is bound off in the non-applied variant in order to resolve the mismatch between the number of semantic participants and the number of syntactic positions.

More specifically, consider as an example the denotation of the verb kw-ambuka ‘to cross’ in (69a). For clarity, the number of syntactic arguments is listed in what I will refer to as a ‘predicate argument structure’ (PAS), which enumerates the number of syntactic positions available; this is listed in (69b). This notation does not conform to any specific formalism, but is easily translated into notions such as the $\unicode[STIX]{x1D703}$ -grid of a standard Principles-and-Parameters type approach, the arg-st of HPSG, or the a-structure of LFG; the central point of the PAS is to track the number of overt syntactic arguments. In this notation, the underlining indicates the subject of the clause, and the order of non-subjects corresponds to their order in the clause. The subscripted thematic role labels are included for clarity and do not serve a theoretical function.

While there are three unsaturated semantic arguments in (69a), there are only two syntactic argument slots in the predicate argument structure of the verb, as notated in (69b).

For non-applied verbs in which there is such a mismatch, a lexical rule existentially binds off the supernumerary semantic argument prior to insertion into the syntax (and, crucially, prior to lambda reordering). This rule is formalized in (70a), where the input has a series of individual participants and a series of subevents as semantic arguments, and the output existentially binds off the first semantic argument. In (70b), it is indicated that there is no change in the number of syntactic arguments in the corresponding predicate argument structure.

With the verb kw-ambuka ‘to cross’, the source is bound off in the denotation via the rule in (70), which gives rise to two semantic and syntactic arguments.

After the existential binding of the argument $z$ , there are only two overtly realized syntactic arguments of the non-applied verb kw-ambuka ‘to cross’: the agent and the route, as in (72).

In the case of applied motion verbs, Jerro (Reference Jerro2016a) proposes a specific denotation for the locative applicative in which the applicative adds a syntactic argument and assigns it a locative role. This use of the applicative is couched in a larger typology of applicative morphology in which a particular applicative adds a syntactic argument and/or semantic participant depending on the class of verb that the applicative attaches to.

The denotation in (73) states that the first argument of the predicate (i.e. $x_{1}$ ) is associated with the $loc$ thematic role, which has a corresponding argument in the PAS. This argument, however, will also be associated with a participant that is linked to a source, route, or goal – depending on the verb. Since the verb already assigns a more specific type of locative role, the assigning of the locative does not alter the semantics. This has the effect of giving syntactic license to an unrealized semantic participant.

The meaning of the applicative in (73) combines with the meaning of the verb kw-ambuka ‘to cross’ to give the denotation in (74a) for the applied variant of kw-ambuka ‘to cross’, with the PAS in (74b).

The denotation in (74a) has three arguments: an agent, a route, and a source (as well as a redundant semantic participant $loc$ that is linked to the same argument as the $source$ participant). Correspondingly, there are three syntactic arguments in the PAS in (74b), which has an additional locative argument to that in the base predicate in (71a). Thus, the applied variant of the verb kw-ambuka ‘to cross’ brings out the source that could not be licensed with the non-applied variant.

Having laid out the details of this approach, I turn now to showing how the same analysis can be extended to the case of instrument verbs and –ish.

As briefly noted in Section 2.1, there is a specific class of verbs that entails the use of an instrument, such as the English verbs cut, amputate, dissect, guillotine, cleave, and sever (Koenig et al. Reference Koenig, Mauner, Bienvenue and Conklin2008). Consider the meaning of the verb cut in English, where a successful cutting event is entailed to be mediated by the use of some kind of instrument, such as a knife or scissors. These verbs are distinct from verbs like break or eat, where use of an instrument is possible but not required. With obligatory instrument verbs, the instrument is entailed to exist even if that participant is not realized as a syntactic dependent. For example, it is felicitous to say either sentence in (76), although the use of an instrument is assumed even when it is not overtly present in the clause, as in (76b).

For cases where –ish appears with an obligatory-instrument verb like cut, I propose that the participant of the intermediary subevent and the subevent introduced by –ish are the same, which has the effect of –ish licensing an implicit instrumental argument that is not licensed by the base verb. Take, for example, the denotation of the verb gu-kata ‘to cut’ in (77a), with the PAS in (77b). I assume that there is an additional subevent $r$ which is linked to the instrumental participant. As with other caused change-of-state verbs (such as kw-andika ‘to write’ above), the caused change of state $s$ must be final in the causal chain. Additionally, the verb gu-kata ‘to cut’ idiosyncratically requires that the causing event $v$ must precede the (instrumental) subevent $r$ , which in turn – given the finality constraint on caused changes of state – must precede $s$ . The intuition is that since these verbs are inherently instrumental, they must encode a more elaborated causal structure than verbs that take instruments and causees only due to –ish marking. This captures the fact that this verb implicates a causer acting on an instrument to bring about some change of state of the theme. I formally represent the causal precedence of $v$ before $r$ with the relation $\text{init}^{\prime }$ , which parallels the relation $\text{fin}^{\prime }$ above; namely, $\text{init}^{\prime }(\unicode[STIX]{x1D6FC},\unicode[STIX]{x1D6FD})$ states that $\unicode[STIX]{x1D6FC}$ is the initial subevent in $\unicode[STIX]{x1D6FD}$ (more specifically, $\unicode[STIX]{x1D6FC}$ is preceded by no other subevent in $\unicode[STIX]{x1D6FD}$ ).Footnote ^[16]

As with the motion verbs above, it should be noted that there are only two syntactic arguments in the PAS of the verb, indicating a mismatch between the number of syntactic argument positions and the number of semantic arguments. Following the analysis presented for locative applicatives, I propose that the outermost argument is existentially bound prior to insertion in the syntax in cases where there are more semantic arguments than syntactic argument positions.

Consider a sentence with the non-applied variant of the verb gu-kata ‘to cut’, such as that in (78), where the participant $z$ in (77a) is existentially bound in the non-applied variant.

In (79a), the intermediary participant is existentially bound in order to resolve the mismatch between the argument structure and the number of participants in the semantics. The variable $r$ is existentially bound in a higher node in the derivation, as I have assumed for all event variables.

I furthermore propose a related meaning of –ish for this particular class of verbs where there is no new participant added by the use of –ish equivalent to the locative applicative with motion verbs in (73). Instead, the argument linked to $e^{\prime }$ is the outermost participant of the base verb (formally represented as $x_{1}$ ).

In (80), a new subevent $e^{\prime }$ is introduced into the causal chain of the verb, but the participant linked to $e^{\prime }$ is the first argument of the verb to which –ish attaches instead of a new participant licensed by –ish. Crucially, I assume that the more general analysis of –ish in (39) is blocked by the lexicalized use of –ish with hit-type verbs. Thus, this is a subtype of the broader –ish morpheme and here presented in a compositional manner in order to clearly delineate the argument realization of the verb gu-kata ‘to cut’ when it appears with –ish.

When the meaning in (77a) composes with the meaning of –ish in (80), the result is the denotation in (81a), with the PAS in (81b), where there are three syntactic arguments that are mapped to four subevents: the causing event, the caused change of state, and the event $e^{\prime }$ introduced by –ish. The intermediary argument $z$ is linked to the subevent $r$ as well as $e^{\prime }$ .

In (81), the outermost argument $z$ is both the agent of the intermediary event $r$ as well as the participant linked to the subevent $e^{\prime }$ . I take the linking of the same participant to two separate subevents to indicate that the two subevents are treated as the same subevent in the causal chain. This has the effect of $e^{\prime }$ always being interpreted as the intermediary subevent $r$ with instrument verbs. Thus, it is predicted that with these verbs, –ish has an obligatorily instrumental reading, which is borne out in (82) with the verb gu-kata ‘to cut’.

In (82), the initial causer is the soldier, which is the last participant to be picked up. The restriction on $v$ to precede $r$ is satisfied, as the participant umuhoro ‘machete’ (linked to both $r$ and $e^{\prime }$ ) is not the initial causer, but rather it is intermediary in the causal chain.

Consider an alternative ordering of the arguments, where $z$ is the last argument to be picked up and is thus interpreted as the initial causer.

Such a denotation, however, is ruled out: given the constraint that $v$ causally precedes $r$ , it is not permissible for $z$ to be the initial causer; $z$ cannot simultaneously be the initial causer as well as the participant linked to an intermediary causal event. This predicts that the causative reading of –ish with the verb gu-kata ‘to cut’ should be ruled out, which is borne out in (85).

Given the restriction on the order of events specified by the verb gu-kata ‘cut’, the causative reading is ruled out for these verbs.

In this section, I have argued for an analysis of instrument verbs as a case in which a particular sense of –ish is used to bring out the implicit instrument entailed by the verb. This extends an analysis of the locative applicative in Kinyarwanda with verbs of translational motion in which a locative participant is brought out via the applicative. More broadly, I have made a case for how the lexical entailments of particular verbs determine the available readings of –ish.