Factivity from pre-existence: Evidence from Barguzin Buryat

This paper examines a factivity alternation in Barguzin Buryat (Mongolic) with the verb hanaxa , whose meaning depends on its complement. When hanaxa combines with CPs, it behaves like a non-factive verb meaning ‘think’. However, when it takes nominalized clauses as its complement, it exhibits a factive inference and is naturally translated as ‘remember’. I assume the decompositional approach to the semantics of attitude reports (Kratzer 2016; Bogal- Allbritten 2017; Elliott 2017) and argue that the factivity alternation arises because CPs and nominalized expressions combine with the verb in different ways: while CPs modify the verb’s event argument and provide the content of thoughts, nominalized clauses saturate the internal argument, which for the verb meaning ‘think’ denotes the topic of thoughts — what the thinking is about. I propose that there is a pre-existence presupposition associated with this about -argument: an entity that is the topic of thoughts is presupposed to have started existing before the time of the thinking eventuality. I argue that this presupposition is what gives rise to the factive inference with nominalized expressions and what the ‘remember’ translation is trying to convey.


Introduction
Factivity alternation (Moulton 2009;Abrusán 2011;Özyıldız 2017a;Lee 2019) is a phenomenon in which verbs display both factive and non-factive uses depending on the type of the complement they combine with. This paper discusses a case of such alternation in the Barguzin dialect of Buryat (Mongolic). The data in this paper were gathered in the village Baraghan (Kurumkan district, Republic of Buryatia, Russia) through elicitation sessions with native speakers. Standard procedures for conducting semantics fieldwork (Matthewson 2004;Bochnak & Matthewson 2015; were followed, with felicity judgments of sentences which follow the verbal presentation of the discourse being the main method (for details, see Appendix A in the supplementary materials).
Barguzin Buryat has a verb hanaxa, which when combined with indicative CPs, is naturally translated as 'think'. 1 The sentence in (1a) does not have a factive inference, as illustrated in (1b).
When hanaxa combines with nominalized expressions (nmns), (2a), it is naturally translated as 'remember'. The sentence with the nmn in (2a) has a factive inference: it entails that a cat ate the fish in the actual world. This is illustrated by the infelicity of (2b): negating the proposition expressed by the nominalized complement leads to a contradiction.
(2) a. Dugar [ NMN mi:sgɘi-n zagaha ɘdj-ɘ:∫-i:jɘ-n'] han-a: Dugar.nom cat-gen fish eat-part-acc-3 think-pst 'Dugar remembered a cat's eating the fish.' b. Context: The fish was missing. Dugar is wrong about who ate it. #Dugar [mi:sgɘi-n zagaha ɘdj-ɘ:∫-i:jɘ-n'] han-a: xarin mi:sgɘi Dugar cat-gen fish eat-part-acc-3 think-pst but cat zagaha ɘdj-ɘ:-güi fish eat-pst-neg #'Dugar remembered a cat's eating the fish, but a cat didn't eat the fish.' I would like to argue that sentences like in (2) have a pre-existence presupposition: they presuppose that an event described by the nominalized clause has started before the thinking event. I propose that this presupposition gives rise to the factivity inference with nmns that we see in (2b): these nominalized clauses describe events in the world at which hanaxa is evaluated, and if these events start before the thinking event, then it means that they must already exist at the time at which hanaxa is evaluated. Thus, pre-existence is one of the sources of factivity. In this paper I explore the question of how this presupposition arises and why it is observed in sentences with nominalized expressions, but not with CPs.
The proposal advanced in this paper is different from the approaches that attribute factive inferences to definiteness (Kastner 2015;Hanink & Bochnak 2017a;b), nominal status or referentiality (Kiparsky & Kiparsky 1970;Kallulli 2010;De Cuba 2007;De Cuba & Urogdi 2010;Haegeman 2014). It is also different from approaches that build the inference into the denotation of the verb (Hintikka 1969;Percus 2006). My proposal shares with approaches developed by Özyıldız (2016; 2017a) and Djärv (2019) the idea that the argument structure of attitude verbs has important consequences for the presence of factive inferences. In particular, the idea that attitude verbs can have res arguments that describe the topic of the attitude (Özyıldız 2017a) will be crucial for my account of the factivity alternation with hanaxa.
In section 2 I argue that the inference that we observe when hanaxa takes a direct object is the pre-existence presupposition and that it cannot be coming from the nominalized complement itself. In section 3 I present my proposal. I argue that when hanaxa combines with the functional head θ Th , θ Th introduces an internal argument and establishes about theta-relation between it and the hanaxa's event argument. In other words, the internal argument is interpreted as specifying the topic of thoughts and functions somewhat like the res argument or about-argument discussed in the literature (Heim 1994;Moulton 2009;Deal 2018;Rawlins 2013;Özyıldız 2017a). 2 I propose that θ Th also introduces the pre-existence presupposition associated with this internal argument: the left boundary of an individual denoted by the internal argument is presupposed to be before the time at which hanaxa is evaluated. In section 3.1 I show how this proposal derives the fact that sentences in which hanaxa combines with a CP (1a) do not have a factive inference. Section 3.2 is devoted to deriving the meanings of sentences with nominalized expressions like the one in (2a). It also addresses the question of how the pre-existence presupposition projects. Section 4 explores two empirical predictions made by my proposal, and discusses a potential extension of it to attitude reports constructed from non-attitude verbs. Section 5 concludes the paper.

b. …(xarin) Sajana
[Badma tɘrgɘ ɘmdɘl-ɘ: gɘžɘ] han-a: (but) Sajana.nom Badma.nom cart break-pst comp think-pst '…(but) Sajana thought that Badma broke the cart.' In (3) the speaker explicitly says that they are ignorant about the truth of the complement, which makes the nmn complement infelicitous, in contrast to the CP. In this section I investigate the entailments that we get in sentences with hanaxa taking nominal complements in more detail.

The temporal component of the presupposition
Consider (4). If the speaker says (4a), they can follow it up with (4b), but not with (4c). In other words, Sajana remembering on Tuesday Badma's breaking the cart is compatible with Badma starting the breaking on Monday, but not on Wednesday (given that we are talking about the same week). 3 (4) a. Garag-ai xojor-to Sajana [Badm-i:n tɘrgɘ ɘmdɘl-ɘ:∫-i:jɘ-n'] day-gen two-dat Sajana.nom Badma-gen cart break-part-acc-3 han-a: think-pst 'On Tuesday Sajana remembered Badma's breaking the cart.' b. Badma tɘrgɘ garag-ai nɘgɘn-dɘ ɘmdɘlɘ-ʒɘ ɘxil-ɘ: Badma.nom cart day-gen one-dat break-cvb begin-pst 'Badma began to break the cart on Monday.' c. #Badma tɘrgɘ garag-ai gurban-da ɘmdɘlɘ-ʒɘ ɘxil-ɘ: Badma.nom cart day-gen three-dat break-cvb begin-pst 'Badma began to break the cart on Wednesday.' (4b) specifies the beginning time of the breaking event which is before the time of Sajana's thinking in (4a), while (4c) specifies the beginning time of the breaking event which is after (4a)'s matrix time. This example suggests that the nmn in (4a) describes an event that started prior to Sajana's mental state described by hanaxa.
I would like to argue that the temporal inference that we see in (4) is not about temporal precedence, but about pre-existence: an entity or event described by the nominal complement of hanaxa must have started existing in the world at which hanaxa is evaluated (henceforth matrix world) before the time at which hanaxa is evaluated (henceforth matrix time). This implies two things: (i) the left boundary of the entity or event described by the nominal is before the matrix time; (ii) the right boundary of the entity or event described by the nominal is not set and could in principle be after the matrix time. I will show that these are the characteristics of the temporal inference that we observe.
That the left boundary of the time interval corresponding to hanaxa's complement is before the matrix time can be illustrated with sentences in which hanaxa combines with non-derived noun phrases that denote entities. 4 I assume that a time interval corresponding to an entity is its life span, the left boundary of which corresponds to the start of its existence, while the right boundary corresponds to the end of its existence. In (5) we see hanaxa taking 'her future child' as its Theme argument: Context: Currently Seseg has a child. The speaker is talking about some time 7 years ago. Sɘsɘg gar-ga-x-a: bai-ga:n üxibü-jɘ: han-a: Seseg go.out-caus-pot-refl be-pfct child-acc.refl think-pst 'Seseg remembered her future child.' (lit. 'her child that will be caused to go out of her') a.  Context A: 7 years ago, Seseg was pregnant with a baby, she has seen her/him during an ultrasound.
b. # Context B: 7 years ago, Seseg was not pregnant. But she really wanted a baby and was planning to have one.
Seseg's child exists in the actual world at the utterance time, but this is not enough for (5) to be felicitous: the child needs to have existed before the matrix time, which in this case is some contextually salient time 7 years ago. This suggests that hanaxa's Theme has to pre-exist its event argument: Theme's left boundary must be before the matrix time.
Another piece of evidence for the pre-existence inference comes from sentences where hanaxa combines with fictional characters that are clearly taken to not be existing at the time of the attitude. Consider (6).

(6)
Context: Children at school are asked to imagine a magical animal that does not exist and draw it. a. #Badma naiman tarxi-tai mi:sgɘi-(ɘ) hana-na Badma eight head-com cat-(acc) think-prs # 'Badma is remembering an eight-headed cat.' b. Badm-ain tarxi so: naiman tarxi-tai mi:sgɘi or-o: Badma-gen head in eight head-com cat come-pst 'Badma thought of an eight-headed cat.' (lit. 'An eight-headed cat came into Badma's head.') In (6) the object which Badma's thoughts are about has to not exist before his thoughts. This leads to an infelicitous sentence when such a fictional individual is the internal argument of hanaxa. The desired meaning can be conveyed if a different construction, (6b), is used, where the mental attitude is expressed without a designated attitude verb.
The fact that noun phrases 'her future child' and 'an eight-headed cat' are internal arguments of hanaxa is crucial for the infelicity of (5b) and (6a). When such noun phrases combine via a postposition tuxai 'about', there is no pre-existence requirement. (7a) is fine in a context where Seseg is not pregnant, and (7b), although less preferred compared to (6b), is acceptable in a context where Badma imagines a non-existing animal. (7) a. Sɘsɘg gar-ga-x-a: bai-ga:n üxibü-n tuxai-ga: hana-na Seseg go.out-caus-pot-refl be-pfct child-nom about-acc.refl think-prs 'Seseg is thinking about her future child.'  Context: Seseg is not pregnant.
This suggests that being the topic/object of thoughts is not a sufficient requirement for being subject to the pre-existence inference; being the internal argument of the verb is a necessary condition.
When hanaxa combines with nominalized expressions, showing the pre-existence requirement is more complicated, because of the question of how it interacts with the temporal/aspectual properties of nominalized clauses (see sections 3.2.1 and 4.2 for discussion). Nevertheless, I take evidence from hanaxa combining with non-derived nouns to be suggestive of the requirement that the left boundary of the time interval corresponding to the object of hanaxa has to be before the matrix time. Now let us consider how the right boundary of hanaxa's Theme can be placed with respect to the matrix time. There are two facts suggesting that there is no restriction placed on it. First, when hanaxa combines with entities, e.g., with proper names, (8), the sentence does not presuppose that the individual denoted by the entity stopped existing: Badma does not need to be dead in order for (8) to be true.

(8)
Context: Badma is currently alive. Sajana Badm-i:jɘ han-a: Sajana.nom Badma-acc think-pst 'Sajana remembered Badma.' Provided that when the time function takes an entity, it returns its life span -the time interval corresponding to the entity's existence, (8) suggests that the temporal component does not require the right boundary of the Theme argument to precede the time of the thinking event.
Second, the placement of the right boundary of an event described by the nmn depends on the aspectual properties of the participle/form that it is based on. 5 There are nominalized forms such that the left boundary of a nmn-event is before the matrix time, but the right boundary can be after the matrix time. One such form is presented in (9), where an analytical verbal form consisting of the verb 'be' and a converb is nominalized. 6 If the pre-existence inference required the right boundary of an event described by the nominalized expression to be before the matrix time, we would have expected interpretations like in (9) to not be possible. Thus, I conclude that in sentences where hanaxa combines with a nominal phrase (noun or nominalized clause), there is a pre-existence inference, which places a requirement on the left boundary, but not the right boundary of hanaxa's object: (10) The pre-existence inference: (i) The Theme of the event described by hanaxa exists in the world at which hanaxa is evaluated (in the matrix world); (ii) The left boundary of the time interval that the time function τ returns when applied to the Theme of the event described by hanaxa is before the time at which hanaxa is evaluated (before the matrix time).
I propose that the factivity inference that we saw in (2b) and (3) is a consequence of (10): if the left boundary of an entity/event in the matrix world that one is thinking about is before the thinking, that entity/event has to exist at the time of thinking. Is this pre-existence presupposition responsible for turning 'thinking' into 'remembering'? I would like to argue that hanaxa in sentences with nominal arguments does not in fact get the meaning that verbs meaning 'remember' in other languages have, but that the pre-existence presupposition is responsible for hanaxa being translated as 'remember'. Buryat does not seem to have a designated verb whose meaning would describe memories of attitude holders, and hanaxa with nominal arguments does not have to describe memories either, as can be seen from examples like (11). In (11) hanaxa takes a nominalized clause as its complement, and is modified by an adverb türü:∫ɘnxijɘ: 'for the first time'. 8 5 I assume that nmn-forming participles introduce additional restrictions on the aspectual/temporal interpretation of events denoted by the nominalized expression (see section 3.2.1 for discussion), which are not present when hanaxa combines with individuals like 'Badma', (8), where the pre-existence presupposition is the only temporal relation established (see 3.2.3 for more details on how the composition procedes in each case). 6 When used as a finite form, the combination of 'be' and a converb usually results in progressive and habitual meanings. 7 The sentence in (9) is also compatible with a context where Sajana was singing and stopped singing before the time of thinking. 8 I am grateful to Kai von Fintel for raising the question of whether hanaxa can mean 'realize'. (11) Üsɘgɘldɘr Sɘlmɘg Badm-i:n hain xüdɘl-dɘg-i:jɘ türü:∫ɘnxijɘ: han-a: yesterday Selmeg Badma-gen well work-hab-acc for.the.first.time think-pst 'Yesterday Selmeg thought for the first time of Badma working well.'  Context A: We have all known for a long time that Badma works very well. Selmeg, however, didn't have any thoughts on whether Badma worked well until yesterday. Comment: 'Ojlgoxo 'understand, sense' is better fit for this context, but hanaxa is acceptable too.' 9 # Context B: We don't know if Badma works well. Selmeg didn't have any thoughts on whether Badma worked well until yesterday.
If hanaxa with a direct object described memories, then modification by türü:∫ɘnxijɘ: 'for the first time' should have been impossible: the attitude holder needs to have previous thoughts about an entity/event in order to remember them. The fact that such modification is possible suggests that hanaxa's meaning does not directly reference memories or previous mental states, and its pre-existence presupposition is about existence in the world at which hanaxa is evaluated. This conclusion is supported by the fact that (11) is infelicitous in the context B, where the discourse participants are ignorant about Badma's working skills in the actual world. 9 While hanaxa's meaning does not appeal to memories, its presupposition might be similar enough to presuppositions of verbs like remember to warrant the 'remember' translation in sentences with nominal complements. While hanaxa presupposes that its internal argument existed in the actual world before the matrix time, it could be that verbs like remember presuppose that their internal arguments existed in both the memory/mental state of the attitude holder and in the actual world before the matrix time. If that is so, then remembering an individual entails hanaxa-ing that individual. Thus, in the absence of a more specific verb like remember, hanaxa + NP can be used for describing remembering situations in a language like Buryat. I leave further comparison between hanaxa with nominal complements and verbs like remember for further research.
An anonymous reviewer raises an alternative hypothesis that hanaxa just requires that its object has been previously mentioned. I don't think hanaxa has such requirement. In (12) Badma's breaking a cart has not been previously mentioned in the discourse. Nevertheless, Dugar's utterance, which has the nominalized expression Badma's breaking the cart as the complement of hanaxa, is felicitous in this context.

(12)
Context: Dugar enters the room, sees Seseg, greets her and sits besides her to have a cup of tea. Seseg: Ju: honin? Ju: xɘ-x-ɘ: bai-na-∫? what news what do-pot-refl be-prs-2sg 'How are you? What are you planning to do?' Dugar: Badm-i:n tɘrgɘ ɘmdɘl-ɘ:∫-i:jɘ-n' han-a:-b. Tɘrgɘ Badma-gen cart break-part-acc-3 think-pst-1sg cart zaha-lsa-x-u: ali ügi:-g hur-a:d jɘrɘ-xɘ-m fix-soc-pot-q disj no-q ask-cvb2 go-pot-1sg 'I remembered that Badma broke a cart. I plan to go ask whether he needs any help to fix it.' In (13) Earth being flat is previously mentioned in the discourse. However, this is not sufficient for the nominalized clause Earth's being flat to be used felicitously as the object of hanaxa.

(13)
A: Urdanai grɘg-u:d gazar xabtagar gɘžɘ buru: hana-dag bai-ga: former Greek-pl Earth flat comp wrong think-hab be-pst 'Ancient Greeks mistakenly thought that the Earth is flat.' B: Gansa greg-u:d bɘ∫ɘ! # Dugar gazar-ai xabtagar bai-ga:∫-i:jɘ hana-dag only Greek-pl not Dugar Earth-gen flat be-part-acc think-hab Intended: 'Not only Greek people (had this opinion)! Dugar thinks that the Earth is flat.' Comment: 'The reply of the second person contradicts what the first one says.' Thus, being previously mentioned is neither necessary nor sufficient condition for using a nominal as hanaxa's object.

The presuppositional nature of the inference
The pre-existence inference behaves like a presupposition: it introduces backgrounded information which is common knowledge to the participants of the conversation, and it projects in questions and survives under negation, as illustrated in (14) and (15), respectively. This suggests that the inference at hand is a presupposition.

(16)
Projected inference: There is a nmn-event in the world at which hanaxa is evaluated that started before the time at which hanaxa is evaluated.
The inference that projects in (14)- (15) is that there is an event of Badma breaking the cart in the actual world that started before the matrix time. If this inference is part of the common ground, then the speaker cannot be ignorant about it (14) or directly contradict it (15). The analysis of how the pre-existence presupposition is encoded should ensure that the empirical generalization in (16) is derived.

The presupposition does not come from the complement
Factivity is one of the components of the presupposition under consideration. What part of the sentence contributes this inference? There are several hypotheses about the origin of factive presuppositions (see discussion in Özyıldız 2016); one prominent hypothesis is that factive presuppositions are contributed by the complement of the verb (Kiparsky & Kiparsky 1970;Kallulli 2010;De Cuba 2007;De Cuba & Urogdi 2010;Haegeman 2014;Kratzer 2006;Kastner 2015;Hanink & Bochnak 2017a). This hypothesis is attractive in light of cross-linguistic data, which suggests that there are correlations found between the syntactic category of the complement of attitude verbs and their factivity (Moulton 2009;Abrusán 2011;Özyıldız 2017). I will argue that this hypothesis cannot be maintained for Buryat. First, the factive inference does not always arise when otherwise non-factive verbs combine with nominalized expressions. For example, when verbs ɘtigɘxɘ 'believe' and naidaxa 'hope' take nmns as their complements, no factive inference arises, hence the felicity of (17)-(18). 10 (17) Sajana [Badm-i:n tɘrgɘ ɘmdɘl-ɘ:∫-tɘ-n'] ɘtig-ɘ:, xarin Badma tɘrgɘ Sajana Badma-gen cart break-part-dat-3 believe-pst but Badma cart ɘmdɘl-ɘ:-güi break-pst-neg 'Sajana believed that Badma broke the cart (lit. 'in Badma's breaking the cart'), but Badma didn't break the cart.' Sajana [Sɘsɘg-ɘi xada dɘ:rɘ gar-a:∫a-da] naida-na, xarin Sɘsɘg Sajana Seseg-gen mountain up go.to-part-dat hope-prs but Seseg xada dɘ:rɘ gar-a:-güi mountain up go.to-pst-neg 'Sajana hopes that Seseg went up the mountain (lit. 'in Seseg's going up the mountain'), but Seseg didn't go up the mountain.' This suggests that the nominal status of the argument does not suffice for the factive inference to come about. Note that the nominalized expressions in (17)-(18) are the same as the ones we have seen with hanaxa, except that they bear a different case. While hanaxa 'think' assigns accusative case to nominalized clauses, (2a), the verbs ɘtigɘxɘ 'believe' and naidaxa 'hope' assign a lexical case -dative. The argument structure of the attitude verb, reflected in case assignment, seems to play a role in whether the factive inference is present. Similiar observations have been made by Djärv (2019), who shows that verbs like believe and know have different argument structures (with different options for case assignment in German): believe, but not know, selects for individuals that describe source or vessel of the propositional content; know on the other hand combines with individuals without any relation to the propositional content. We can hypothesize that a distinction along similar lines is present in Barguzin Buryat, although a more thorough investigation of this issue is necessary.
Second, the nominalized expression under consideration can have indefinite uses, so the factive inference cannot be due to the definiteness of the complement (see Kastner 2015; 10 The same has been observed for other languages too, e.g. for Turkish in (Özyıldız 2017a). An anonymous reviewer points out that in English there are also cases where sentences with nominalized expressions do not have factive inferences, e.g., (i).
(i) I imagined her going to a restaurant with them. ⇏ She went to a restaurant with them.
Hanink & Bochnak 2017a for proposals of how definiteness can lead to factivity). Buryat does not have articles, but it can be still shown that the nmn can have indefinite uses. 11 Consider (19).
There were several performers at the concert, one of them was Sajana. She sang several songs about Buryatia and a few Russian folk songs. After a while I asked three women who were at the concert their impressions.
b.  Context B: They remembered the same singing. There were several performers at the concert, one of them was Sajana. She sang only one song about Buryatia and a few Russian folk songs. After a while I asked three women who were at the concert their impressions.
The fact that three women could have each remembered different singing of a song about Buryatia by Sajana suggests that the nmn does not have to be definite: definite descriptions have uniqueness presuppositions, and having a uniqueness presupposition would have made (19) infelicitous in the context A. Thus, given that nmns can denote indefinite descriptions and that the presence of the factive inference does not seem to depend on the context, I conclude that an account of the factivity alternation has to be able to derive the factive inference even for indefinite uses of nmns.
To sum up, the factive component cannot be attributed to the meaning of the nominalized clause: the fact that it is nominalized is not sufficient for the factive inference (nmn's θ-role seems to play a role), definiteness is not necessary for the factive inference (nmns can have indefinite readings). Therefore, while in (1a)-(2a) we saw that the type of the complement (CP versus NP) correlates with the presence of the presupposition, I conclude that the meaning of the nominalized expression itself does not supply the presupposition. I propose that the correlation is a result of CPs and NPs combining with attitude verbs in different ways. (20) a. Sue broke a vase. ⟹ There existed a vase before the time of the breaking event. b. Mary read a book ⟹ There existed a book before the time of the reading event. c. Alice wrote a poem. ⇏ There existed a poem before the time of the writing event.
What I would like to suggest is that attitude verbs can also place similar requirements on their arguments, and that these requirements can in certain cases lead to factive inferences. 13 If this intuition is correct, then analyzing the factivity alternation amounts to (i) making some assumptions about the semantics of attitude verbs and (ii) analyzing the argument structure of hanaxa. Following the decompositional approach to semantics of attitude verbs (Kratzer 2006;Moulton 2015;Elliott 2017), I assume that the complementizer of the embedded clause plays the main role in building the meaning of an attitude report by connecting the matrix verb eventuality to the embedded proposition via the Content relation.
As for the argument structure of hanaxa, here is my proposal. Hanaxa combines with a theta head θ Th , which introduces its internal (Theme) argument. This argument denotes the individual which is the topic of the attitude, which the attitude is "about" -also known as the res-argument (Heim 1994;Moulton 2009;Deal 2018;Rawlins 2013;Özyıldız 2017a). There is a pre-existence presupposition associated with this Theme argument: it is presupposed to have started existing before the time t at which the eventuality described by hanaxa occurs. Nominalized expressions (and other nouns) and CPs combine with the attitude verb through different paths: nominalized clauses saturate the Theme argument, and CPs are modifiers that serve to specify the content of the event described by the verb. The fact that NPs and CPs combine through two different paths explains the contrast in (1b)-(2b): NPs, which combine as the Theme argument, are subject to the pre-existence presupposition associated with it; CPs, which combine via the event argument, are not subject to the same presupposition.
My proposal that nominals and CPs combine via different routes makes a prediction about their distribution (first discussed by Özyıldız (2017b) for Turkish, which also allows examples like (21)): given that CPs and nmns don't compete for the same position, it should in principle be possible for the verb to combine with both a CP and a nmn at the same time. This is borne out: consider (21) with nmn and CP co-occuring with hanaxa. Badma-gen Kurumkan-abl come-cvb2 be-part-acc-3 [ CP gɘr-tɘ xulgai∫an or-o: gɘžɘ] han-a: house-dat burglar go.in-pst comp think-pst 'Sajana recalled the/an event of Badma returning from Kurumkan, (thinking) that a burglar entered the house.' 13 It might be difficult to completely unify the pre-existence presupposition of hanaxa and the inferences in (20a)-(20b) as a single phenomenon due to the difference in their projective behavior. While, as we saw in section 2.2, the presupposition of hanaxa projects out of questions and through negation, inferences in (20a) and (20b) do not seem to: (i) a. Sue didn't break a vase (because there were none). ⇏ There existed a vase before the verb's evaluation time. b. Mary didn't read a book (because there were none). ⇏ There existed a book before the verb's evaluation time.
In (21) the nmn describes an event (Badma returning from Kurumkan) which is the topic of Sajana's thoughts. The finite clause describes the thoughts of the attitude holder about that topic. There is an inference that this event has occured, and it happened before the time of Sajana's thinking. Examples like (21) are also important in another respect: they allow us to refute the hypothesis that hanaxa is simply ambiguous between a factive nominal-selecting hanaxa 1 'remember' and a non-factive CP-selecting hanaxa 2 'think'. The ambiguity hypothesis would not be able to account for sentences like (21), because the verb hanaxa that we see in (21) could neither be hanaxa 1 'remember' nor be hanaxa 2 'think'.
There are many ways to implement the proposal sketched out above. One question that arises is how the Theme argument of hanaxa is introduced into the sentence: is it an inherent argument of the verb, or is it introduced by a functional projection? Although either option would in principle work, in my implementation I will assume the second one. I will take logical representations to be strictly neo-Davidsonian in nature (Castañeda 1967;Parsons 1990) and will assume that this is reflected in syntactic representations: all arguments, including internal arguments of verbs, are introduced by separate functional heads. 14 (22) ⟦hanaxa⟧ w,t,g = λe e .think w,t (e) As we see from (22), the attitude verb denotes a function that takes an event e as its argument, and returns true iff e is a thinking event in world w at time t (abbreviated as think w,t (e)). Hanaxa is an attitude verb, and so its event argument has some content associated with it.

The meaning of the CP
According to the decompositional approach to attitude verbs, finite complement clauses denote functions that characterize sets of contentful events or entities. The details of proposals in this framework vary; here I will adopt the proposal in (Elliott 2017) for concreteness. Elliott (2017) argues that CPs denote predicates of events whose content is the proposition denoted by the embedded clause. Thus, the meaning for the CP in (23)  14 Adopting neo-Davidsonian representations allows me to avoid postulating pre-existence presuppositions in sentences with CPs, which we have no empirical evidence for. If the Theme argument was a true argument of the verb, then the pre-existence presupposition would always be part of the denotation of the verb, even in sentences with CPs. This would not lead to factivity, because CPs don't combine as Theme arguments. A very weak presupposition, which is difficult to test for, would be predicted: 'Something which the attitude is about pre-exists a thinking event with Content p.' 15 Note that under Elliott's proposal the result of Cont applying to an event stands in the equality relation to the embedded proposition (see Elliott 2017 for arguments in favor of this view). This is different from treating Cont(e) as a subset of the embedded proposition (Kratzer 2006;. While I will adopt Elliott's meaning for CPs, nothing in my analysis hinges on the choice between equality versus subset relation semantics for attitudes. The meaning for the CP in (23) in the system with the subset relation is in (i).

Combining CP with hanaxa
The LF for the sentence in (23)  The CP combines with hanaxa as a modifier of its eventuality argument by Predicate Modification, as shown in (27). (27) ⟦hanaxa that Badma broke the cart⟧ w,t,g = λe e . think w,t (e) ∧ Cont(e) = λw'.λt'. Badma broke the cart in w' at some time t" that precedes t' Then Voice introduces the external argument, with the resulting one-place predicate of events getting existentially closed, and this proposition is combined by Intensional Functional Application 17 with the contextually restricted (by the free variable t 1 ) past tense, which I assume to be an existential quantifier over times (Ogihara 1995). 18 Thus, we get the meaning in (29). 19 16 A question that might arise is whether the same event could have different Content in different worlds and at different times. I am neutral on this issue, but will assume for convenience that Content of events cannot vary with worlds and times. 17 The intension of the proposition needs to be a function that has not only a world argument, but a time argument as well, (i). So in our case the intension of the proposition is in (ii).
(28) ⟦past t 1 ⟧ w,t,g = λp sit . ∃t' < t ∧ t' ⊆ g(1) [p(w)(t') = 1], where ⊆ is a relation between two time intervals such that one falls within the other; a contextually supplied interval g (1) is the value of a free time variable t 1 (29) ⟦Sajana thought that Badma broke the cart⟧ w,t,g = 1 iff ∃t' < t ∧ t' ⊆ g (1) [∃e [think w,t' (e) ∧ Cont(e) = λw'.λt'. Badma broke the cart in w' at some time t" that precedes t' ∧ Exp(e) = Sajana]] This sentence is true relative to a world w, a time t and an assignment function g if there is a time within a salient time interval which is in the past relative to t at which there is an event of Sajana thinking whose Content is 'Badma broke the cart'. This analysis of sentences with CPs straightforwardly captures the absence of the preexistence presupposition in them: since the pre-existence presupposition is introduced by θ Th , and CPs do not combine via θ Th , no pre-existence presupposition is expected to occur in sentences with them. Hanaxa in sentences with CPs just means 'think'. The CP specifies the Content of the thinking event, but nothing forces this Content of thoughts to be true in the actual world. Thus, the absence of the factive inference is predicted.

Buryat CPs as predicates of (contentful) events
In this section I provide two arguments in favor of treating Buryat CPs with the complementizer gɘžɘ as predicates of events.
The first piece of evidence comes from the morphology of the complementizer. The complementizer gɘžɘ consists of two morphemes: the root of the verb gɘ 'say' and the suffix -žɘ, which is a converbial 20 suffix found with analytical verb forms and restructuring verbs, (30a), as well as in sentential adjuncts, (30b).
(30) a. Badma bɘ∫ɘg bɘ∫ɘ-žɘ ɘxil-ɘ: Badma letter write-cvb begin-pst 'Badma began to write a letter.' b. [Ojuna üxibü: türɘ-žɘ], Badma ɘsɘgɘ bolo-bo Ojuna.nom child give.birth.to-cvb Badma.nom father become-pst2 'As Ojuna gave birth to a child, Badma became a father.' Converbial clauses like those in (30a) or (30b) can be plausibly analyzed as event modifiers (specifying, e.g., the nature of the beginning event in (30a) and the cause of the father-becoming event in (30b)). If the morphology (the suffix -žɘ) reflects the denotations of these clauses, then the same morphology on the complementizer could indicate that finite CPs denote functions that characterize sets of events as well. 21 Additional evidence comes from proform substitution. Finite CPs can be substituted by the proform used for sentential adjuncts and restructuring clauses, (31a): ti:-žɘ (do.so-cvb), which is a converbial form of the proform-forming verb ti:xɘ 'do.so', (31b). CPs cannot be substitued for by a demonstrative pronoun tɘrɘ or an adjectival proform ti:-mɘ (do.so-adj), which are used for refering back to entities and predicates of entities respectivelly. 20 I use 'converb' as a descriptive notion: a non-finite verbal form that occurs in adverbial subordinate clauses (such as when/while-clauses, before/after-clauses, among others). 21 An anonymous reviewer raises the question of whether gɘžɘ could receive a compositional analysis. While diachronically gɘžɘ is indeed a non-finite form of the verb gɘxɘ 'say', it has undergone significant grammaticalization and now can be used in sentences where no speech act by the subject is entailed: e.g., gɘžɘ-clauses can be complements of verbs like du:laxa 'hear' or xaraxa 'see'. The only compositional analysis I can think of is that perhaps the root gɘ is what takes a proposition and returns a property of individuals x whose Content is p, while the suffix -žɘ contributes information that x is an eventuality. Whether such a sort-specifying role is something that morphemes can contribute to the meaning of constituents they combine with is a question that needs further inquiry.
(31) a. Üsɘgɘldɘr Badma bɘ∫ɘg bɘ∫ɘ-žɘ ɘxil-ɘ:, ba münödɘr (Badma) yesterday Badma letter write-cvb begin-pst and today (Badma) baha ti:-žɘ ɘxil-ɘ: also do.so-cvb begin-pst 'Yesterday Badma began to write a letter, and today he also began to do so [= write a letter].' b. Badma [Sajana bulj-a: gɘ-žɘ] han-a:, Ojuna baha Badma.nom Sajana.nom win-pst say-cvb think-pst Ojuna.nom also ti:-žɘ / *ti:-mɘ / *tɘrɘn-i:jɘ han-a: do.so-cvb do.so-adj that-acc think-pst 'Badma thought that Sajana won, Ojuna also thought so.' The second piece of evidence comes from the syntactic distribution of CPs: they pattern with adverbs with respect to the positions in the clause they can occupy. 22 Both adverbs and CPs can be positioned quite freely with respect to the arguments of the verb, (32). Under the assumption that syntactic distribution reflects the denotation of a constituent, we can conclude that finite clauses in Buryat, like adverbs, denote predicates of events.

The meaning of the nominalized clause
The nominalized expression under consideration, (35), is built from the following morphological pieces: the verbal root, the participle suffix -A:∫A, 23 and the nominal morphology -case and optional possessive marking. 24 (35) Sajana [Badm-i:n tɘrgɘ ɘmdɘl-ɘ:∫-i:jɘ-(n')] han-a: Sajana.nom Badma-gen cart break-part-acc-(3) think-pst 'Sajana remembered that Badma broke the cart.' In place of -A:∫A, a number of different participial suffixes can be used. Participles in Buryat are often used as relative clauses; some of them can also be used in constructing finite forms. Adding case morphology to participles transforms them into nominalized expressions that describe events.
Participial suffixes add aspectual and temporal specification to the eventuality descriptions they attach to, such as information about (im)perfectivity, habituality, or temporal orientation. These specifications remain to be investigated, and they will not inform the proposed analysis. I make the simplifying assumption that participial suffixes combine with predicates of events and return predicates of events which are supplemented by some aspectual or temporal specification.
The participle -A:∫A, which forms the nmn in (35) that I focus on in this paper, is pastoriented: 25 it is used when the time of the event denoted by the nmn (t N ) precedes the matrix time (t m ), as is illustrated by the felicity of (36) in context A and by its infelicity in contexts B and C.

# Context B (t N ≈ t m ):
Dugar is currently on his way here, returning from Baikal. # Context C (t N > t m ): Next week Dugar will return from Baikal.
While this, again, might be a considerable simplification of -A:∫A's meaning, I will assume that this participle suffix sets the right boundary of the time interval corresponding to the nmn event with respect to the matrix time (37): there is a time interval t N at which the event denoted by the nominalized expression is evaluated, and the right boundary (RB) of this time interval is before the matrix time.
(37) ⟦part.past⟧ w,t,g = λP siet .λe' e . ∃t N [RB(t N ) < t & P(w)(t N )(e') = 1] When -A:∫A combines with the verb phrase 'break the cart by Badma', (38), by Intensional Functional Application (with the intension of the VP as in (39)), it returns a predicate of events such that they are events of breaking the cart by Badma whose right boundary precedes the matrix time, (40). This is the meaning of the nominalized clause.
(38) ⟦break the cart by Badma VP ⟧ w,t,g = λe' e . break w,t (e') ∧ Theme(e') = the cart ∧ Agent(e') = Badma (39) ⟦break the cart by Badma VP ⟧ g ¢ = λw s .λt i .λe' e . break w,t (e') ∧ Theme(e') = the cart ∧ Agent(e') = Badma 25 This is true only of its uses in nominalized expressions. In relative clauses, it is commonly used for describing "a permanent property of an individual" (Sanzheev et al. 1962): (i) [Manai tai∫-a: tuxai du: garg-a:∫a] xün ɘnɘ-l da: 1sg.gen taishi-refl about song bring.out-part human this-ptcl emph.ptcl 'Here is that very person who composes songs about our taishi (a community leader in Mongolic culture).' (Sanzheev et al. 1962: 175) (40) ⟦Badma's breaking.part.past the cart⟧ w,t,g = λe' e . ∃t N [RB(t N ) < t ∧ break w,t N (e') ∧ Theme(e') = the cart ∧ Agent(e') = Badma] In order to simplify future derivations, I introduce the abbreviation in (41): (41) ⟦Badma's breaking.part.past the cart⟧ w,t,g = (40) = ABB λe' e . nmn w,t N < t (e') The denotation in (40) does not specify how such a nmn combines with the verb. This issue will be discussed in detail in section 3.2.3. For now, I would like to provide some arguments that this nominalized expression does not specify the propositional content of the thinking event (unlike CPs, see (24)). The denotation in (40) predicts that this nmn will not be able to describe beliefs of the attitude holder. While the beliefs of the attitude holder could be compatible with the existence of an event denoted by the nominalized clause, they do not have to be. I would like to argue that this prediction is borne out. Consider (42) In (42) we see two clauses with the verb hanaxa and the same attitude holder; in the first clause the verb combines with the nominalized expression, and in the second it combines with a CP with the lexical material identical to that of the nmn. If the nominalized clause described Badma's beliefs, then this sentence would have been contradictory due to the fact that the second use of hanaxa is under negation. However, (42) is felicitous. The description of an event denoted by the nmn 'Darima's driving too quickly' is the speaker's description, not Badma's: while Badma recalls something about an event of Darima's driving too quickly, his thoughts actually are that she didn't drive too quickly.
Another piece of evidence comes from the fact that nominalized clauses cannot report false memories. In the context in (43), while a CP can be used with hanaxa to describe Darima's false memory, the nmn cannot: (43) Context: Darima recalled a situation that happened recently. She heard some unexpected noise in the back yard while she was alone at home. She was afraid to look who it was. Now she is convinced that it was a thief entering the house, but I know for a fact that it was just her brother coming home earlier than expected from Kurumkan. a. Darima [gɘr-tɘ xulgai∫an or-o: gɘžɘ] hana-na, xarin tɘrɘ Darima.nom house-dat thief.nom enter-pst comp think-prs but that axa-n' Xurumxa:n-ha: jɘrɘ-hɘn bai-ga: brother-3.nom Kurumkan-abl come-pfct be-pst 'Darima thinks that a thief entered the house, but it was her brother coming back from Kurumkan.' b. #Darima [gɘr-tɘ xulgai∫an-ai or-o:∫-i:jɘ] hana-na, xarin Darima.nom house-dat thief-gen enter-part-acc think-prs but tɘrɘ axa-n' Xurumxa:n-ha: jɘrɘ-hɘn bai-ga: that brother-3.nom Kurumkan-abl come-pfct be-pst Intended: 'Darima thinks that a thief entered the house, but it was her brother coming back from Kurumkan.' The infelicity of (43b) supports the claim that the nominalized expression cannot describe the Content of the thinking event.
My proposal that the nmn denotes a function that characterizes a set of events is also supported by distributional facts. First, the nominalized clause can be referred to by the noun u∫ar 'event, situation ' and, unlike propositions, can 'happen outside', (44), suggesting that the nmn can denote a predicate of dynamic events without any Content. (44) a. Sajana [Badm-i:n tɘrgɘ ɘmdɘl-ɘ:∫-i:jɘ] han-a: Sajana.nom Badma-gen cart break-part-acc think-pst 'Sajana remembered Badma's breaking the cart.' b. … ɘnɘ u∫ar gaza: bol-o: this event outside become-pst '…This event happened outside.' Second, unlike CPs, nmns cannot be complements of 'stance' verbs (Cattell 1978)-verbs which require commitment of the attitude holder to some deictic stance on the truth of the complement. For example, a nominalized clause cannot be a complement of arsaldaxa 'argue', unlike a CP, even if the context supports a factive interpretation of the complement, (45). 26 (45) Context: There has been a debate about whether Seseg went up the mountain. After a while, Seseg herself came and settled the debate. Now everyone knows that Seseg indeed went up the mountain. a. Sajana aja:r xɘzɘ:-n-hɘ: xoi∫o [Sɘsɘg xada dɘ:rɘ gar-a: Sajana long.ago when-nom-abl back Seseg.nom mountain to go-pst gɘžɘ] arsald-a: comp argue-pst 'Sajana argued all along that Seseg went up the mountain.' b. *Sajana aja:r xɘzɘ:-n-hɘ: xoi∫o [Sɘsɘg-ɘi xada dɘ:rɘ Sajana long.ago when-nom-abl back Seseg-gen mountain to gar-a:∫-i:jɘ] arsald-a: go-part-acc argue-pst Intended: 'Sajana argued all along that Seseg went up the mountain.' I propose that the reason for the ungrammaticality of (45b) is that verbs like arsaldaxa 'argue' require an argument which specifies their propositional Content. If the nmn could provide Content, the sentence in (45b) would have been grammatical. However, since the nmn cannot specify Content of the attitude verb, it cannot satisfy this requirement, hence the ungrammaticality of (45b). 27 Thus, I conclude that analyzing the nominalized clause as a predicate of events which does not introduce a Content relation between an event and a proposition is supported by the data.

The pre-existence presupposition
I would like to propose that hanaxa combines with nominal arguments via the functional head θ Th , and that θ Th is the source of the pre-existence presupposition. The argument that θ Th introduces with hanaxa is interpreted as the topic of thoughts -an entity or event which the thinking event is about. The pre-existence presupposition places a restriction on this about-argument: the left boundary of the time interval corresponding to it is before the time at which hanaxa is evaluated. In (46) I show one possible entry for θ Th that captures this, which is simplified in that the second argument of θ Th is taken to be an individual rather than a predicate of individuals (which will be the final proposal). (47) demonstrates the LF of the VP. 28 (46) (to be modified later) ⟦θ Th ⟧ w,t,g = λP et .λx e .λe e : LB(τ(x)) < t. P(e) ∧ about(e) = x (where LB is 'left boundary'; τ is a function which takes an individual and returns its time span; 28 about is a function that takes an event with Content and returns its topic) The important contribution of θ Th is that in addition to introducing an argument and specifying its theta-role, it introduces a presupposition associated with this argument -LB(τ(x)) < t: the left boundary of an event or the starting point of an entity's life span has to be before the matrix time. This presupposition is not a consequence of aboutness: i.e., the theta-relation that is being established between an event and an individual (in this case, about-relation) is potentially independent of this presupposition that requires a certain temporal ordering between the left boundary of an argument and the matrix time. A reason for thinking this is that, as we have seen in section 2.1, phrases with a postposition tuxai 'about', which also denote the topic of thoughts when they combine with hanaxa, do not exhibit such a presupposition: Context: Seseg is not pregnant. But she really wants a baby and is planning to have one. a. #Sɘsɘg gar-ga-x-a: bai-ga:n üxibü-jɘ: hana-na Seseg go.out-caus-pot-refl be-pfct child-acc.refl think-prs 'Seseg remembers her future child.' (lit. 'her child that will be caused to go out of her') b. Sɘsɘg gar-ga-x-a: bai-ga:n üxibü-n tuxai-ga: hana-na Seseg go.out-caus-pot-refl be-pfct child-nom about-refl think-prs 'Seseg thinks about her future child.' (lit. 'her child that will be caused to go out of her') While NP 'her future child' in the object position of hanaxa is infelicitous in a context where it is common knowledge that Seseg does not have or bear a child yet, no infelicity arises when the same noun phrase combines via the postposition tuxai 'about'. This suggests that the presupposition comes from the functional projection that introduces the internal argument, and not just from the fact that the argument is interpreted as the topic of thoughts.
A question that arises about the denotation in (46) is whether some verbs besides hanaxa combine with their internal arguments via θ Th . To address this question, I need to make my assumptions about functional heads like θ Th explicit. I assume that both roots and functional heads can be subject to allosemy (Marantz 2013;Wood & Marantz 2017), i.e., interpretation of heads can be conditioned by the environment in which they appear similar to how exponents of heads are sometimes conditioned by their environment (allomorphy). Both processes obey locality restrictions. For the present purposes, it is enough to assume that the sister of a head can trigger allosemy.
I propose that θ Th is the functional head that introduces internal arguments of all verbs that take such arguments, but that its interpretation is subject to allosemy conditioned by the verb, which is the sister to θ Th (47). Thus, the denotation of θ Th has the following shape: (49) ⟦θ Th ⟧ w,t,g ⟺ λP et .λx e .λe e : LB(τ(x)) < t. P(e) ∧ about(e) = x /___ ⟺ λP et .λx e .λe e : ¬(LB(τ(x)) < t). P(e) ∧ r(e) = x /___ (where r is some theta-role relation) ⟺ … To the right of each double arrow is the denotation that θ Th will have provided that the context, which in this case is the verbal root that θ Th combines with, is met. In the context of hanaxa, θ Th 's denotation will be as in (46). In context of other verbs it could have different denotations. For example, perhaps verbs like write, create, invent, imagine create a context in which θ Th assigns a different theta-role to the internal argument and has an opposite presupposition, i.e., a presupposition that the left boundary of the internal argument is not before the matrix time. 29 Within Buryat, I think there are at least two other verbs which could be candidates for creating the same environment as hanaxa does for interpretation of θ Th . These are verbs du:laxa 'hear' and xɘlɘxɘ 'say', 30 which are non-factive when they combine with CPs. 29 I acknowledge that there are bigger questions that arise with respect to an analysis that makes use of allosemy: e.g., why do different roots condition θ Th 's meaning the way they do? Is this conditioning arbitrary or predictable from some properties of the eventualities denoted by the root? I have to leave these issues open for now. 30 For some consultants, this verb did not take nominalized expressions as complements at all. The judgments provided here are for those who did accept nominal complements with this verb.
When they combine with nominalized clauses, these nmns denote the topic of what has been heard or said, and the resulting sentences exhibit factive presuppositions: (50) a. Sajana Dugar-ha: Badm-i:n tɘrgɘ ɘmdɘl-ɘ:∫-i:jɘ du:l-a: Sajana Dugar-abl Badma-gen cart break-part-acc hear-pst 'Sajana heard from Dugar about Badma's breaking the cart.'  Context A: Badma broke the cart, and Dugar told Sajana about it. # Context B: Badma didn't break the cart. Dugar lied to Sajana that he did.
b. # … xarin Badma tɘrgɘ ɘmdɘl-ɘ:-güi but Badma cart break-pst-neg 'But Badma didn't break the cart.' b. #… xarin Sɘsɘg xada dɘ:rɘ gar-a:-güi but Seseg mountain to go-pst-neg 'But Seseg didn't go up the mountain.' Sentences (50a) and (51a) are incompatible with contexts in which an event described by the nmn does not exist in the actual world. This is corroborated by the impossibility of the continuations of (50b) and (51b) respectively. The question whether the temporal component of the presupposition is present with these verbs as well requires further investigation. 31 I expect that other languages could also have allosemes for θ Th similar to the one we see with hanaxa in Barguzin Buryat, leading to factive inferences with clausal complements (see section 4.3 for some potential candidates cross-linguistically). But more importantly, the proposal advanced in this paper gives rise to a more general expectation that presuppositions of attitude verbs could stem from presuppositions of argument-introducing heads, whatever those might be.

Existential quantifier from θ Th
In this section, I develop an implementation of my proposal and address the question of how the pre-existence presupposition projects. I focus on indefinite readings of nominalized expressions in order to guarantee that the pre-existence presupposition is derived with them as well. The general question of presupposition projection from quantificational sentences is an ongoing debate (Heim 1983;Beaver 2001;Chierchia 1995;Chemla 2009;Charlow 2009;Fox 2013). While contributing to this discussion is not a goal of this paper, I would nevertheless like to provide an account of how the pre-existence presupposition of hanaxa functions in sentences with indefinite complements in Barguzin Buryat. For 31 Another tentative hypothesis is that θ Th is the functional head that introduces accusative subjects that we see in sentences with CPs, which also seem to describe the topic of the attitude.

(52)
Context: The speaker wants to convey that Sajana's thoughts are consistent with reality. #[Badm-i:n tɘrgɘ ɘmdɘl-ɘ:∫-i:jɘ] Sajana han-a:-güi, Badma Badma-gen cart break-part-acc Sajana.nom think-pst-neg Badma.nom tɘrgɘ ɘmdɘl-ɘ:-güi cart break-pst-neg Intended: 'Sajana didn't think/remember that Badma broke the cart, (and) Badma didn't break the cart.' Nominalized clauses are bare noun phrases, and I will assume that they are predicates of events of type <e,t>. I propose that the existential quantifier corresponding to the indefinite does not combine with the nmn directly (see appendix B in the supplementary materials for some issues with such a view), but is introduced by θ Th when it combines with hanaxa. 32 Under this approach, the nominalized expression itself is not a quantificational phrase.
The LF for the sentence with a nmn, (53), is shown in (54). I assume the standard view that presuppositions are encoded as partial functions (Frege 1892), and therefore, the semantics that I am using is trivalent. More concretely, following Karttunen & Peters (1979), George (2008ba;), Fox (2013, I make use of Kleene logic to track how presuppositions project. 33 In the light of the foregoing, the final meaning of θ Th when it combines with hanaxa is in (55).
The nominalized clause, (40), which is a predicate of events, is able to directly combine with θ Th as its second argument. The fact that θ Th takes the extension of the nmn as its argument means that the nominalized expression will be interpreted in the same world in which hanaxa is evaluated. The existential quantifier in θ Th 's denotation binds the event argument of the nmn and also places a restriction that the left boundary of that event has to precede the matrix time. This is the pre-existence presupposition.
Note that the presuppositional component in this case is repeated in the assertion. This is just a way to write the truth-conditions that are more explicitly stated in (56). 34 As the denotation in (56) shows, I assume a theory with three truth-values: 1 (true), 0 (false) and # (undefined). The sentences are undefined just in case they are neither true nor false. Thus, the presupposition of a given expression is a disjunction of the condition which makes it true and the condition which makes it false. Trivalent logic (strong Kleene logic) provides a general recipe for transforming bivalent semantic values to trivalent ones. Imagine that we have a complex sentence which contains an expression α that receives the third value (#). The main idea of the strong Kleene approach is that the truth value of the complex sentence will be 1 iff all the ways of assigning bivalent truth values to α will make it true; it will be 0 iff all the ways of assigning bivalent truth values to α will make it false; and it will be # otherwise. In other words, # represents uncertainty about which value, 1 or 0, a certain expression has. This uncertainty projects only if it matters for the calculation of the bivalent truth values for the bigger structure.
(56) ensures that ∃x[Q(x) ∧ LB(τ(x)) < t] is the definedness condition by requiring it to be true both for the sentence to be true and for the sentence to be false. θ Th combines then with the verb (= the first argument P), with the nominalized clause (= the second argument Q), with the Voice head and the external argument, resulting in the denotation for VoiceP in (57).
# 34 Here and in the discussion to follow I will sometimes use single-bracket notation for better readability.
# Finally, the proposition in (59) is combined with the contextually restricted tense, (60), by Intensional Functional Application, resulting in (61). The sentence in (i) is true iff there is at least one student who smoked before and doesn't smoke now. This sentence is false iff all students smoked before and still smoke. The third value is an elsewhere case: the sentence in (i) will receive it when neither the truth nor the falsity conditions are met. In other words, this sentence is defined and does not result in presupposition failure if it is either true or false, (ic). As one can see, the presupposition we arrive at for quantificational sentences is a disjunctive presupposition. I will assume that all existential quantifiers have such disjunctive presuppositions. 36 The simplification step uses the equivalence ∀x[ψ ∧ φ(x)] ≡ ψ ∧ ∀x[φ(x)], which holds provided that ψ contains no free occurrences of x and that the domain D e is not empty, and the equivalence ∀x[¬ψ( cart and e is an event of Sajana thinking about e', and the left boundary of e' is before t'. This is the right meaning. (61) also gives the correct falsity condition: in order for it to be met there needs to exist an event denoted by the nmn such that its left boundary is before all times within the contextually given past time interval. This means that if the pre-existence requirement is not met, the sentence will receive the third value (#), and thus be a presupposition failure. 37 To sum up, we have seen that treating the nominalized expression as a predicate of events and having the existential quantifier introduced by θ Th predicts the attested projection behavior of the pre-existence presupposition, (16), repeated here as (62).

(62)
Projected inference: There is a nmn-event in the world at which hanaxa is evaluated that started before the time at which hanaxa is evaluated.
However, this implementation raises the question of how θ Th , when it combines with hanaxa, takes individuals like proper names (see 'Badma' in (8)) as its arguments, which I assume to denote entities and not functions that characterize sets of entities. I propose that DPs like 'Badma' are shifted to predicates by an operator like ident (Partee 1986) in order to combine with θ Th in the context of hanaxa. After that, the composition proceeds in the same way as with the nmn: the result of combining θ Th with hanaxa takes the property of individuals λx [x = Badma] as its argument and states that there exists an individual of this kind whose left boundary (= beginning of the life span) is before the matrix time. This analysis of the factivity alternation shares some similarity to the proposal in (Özyıldız 2017a) for a factivity alternation in Turkish, for which the res/about argument of the attitude verb and semantic composition play an important role in generating the factive inference as well. Beyond that however, these two approaches are quite different. Özyıldız (2017a) analyzes Turkish nominalized expressions as denoting propositions, something that is implausible for Buryat, given the evidence that participle-based nmns cannot describe beliefs of attitude holders in this language (see section 3.2.1). Özyıldız (2017a) derives the factive reading by hypothesizing that nominalized clauses undergo movement, and the binder created in this movement binds not only the trace of the nmn, but also a situation-denoting pronoun that is part of the covert definite description that is the res-argument of the attitude verb. Thus, as he himself points out, his proposal is in line with approaches which derive factivity from definiteness, with the difference that nominalized clauses do not directly compose with the ι-operator. Given that Buryat nmns allow indefinite readings (see (19) in section 2.3), it is difficult to see how Özyıldız's proposal could be extended to the Buryat factivity alternation. 37 "Unwrapping" the meaning of nmn results in (i) (c = the cart, B = Badma, S = Sajana). As one can see, this does not affect presupposition projection.
Thus I make a prediction that when a nmn like (63) is an object of hanaxa, there should be no factive inference that an event of the kind described by the clause under g-ɘ:∫ɘ (Badma's reading a book yesterday) exists in the actual world. This is so because an event of the embedded proposition is not itself an object of hanaxa. This prediction is borne out: (65) Context: The cat didn't eat the fish, but someone made a false claim that it did. Dugar [mi:sgɘi-n zagaha ɘdj-ɘ: g-ɘ:∫-i:jɘ] han-a:, xarin mi:sgɘi Dugar cat-gen fish eat-pst say-part-acc think-pst but cat zagaha ɘdj-ɘ:-güi fish eat-pst-neg 'Dugar remembered (the claim) that the cat ate the fish, but the cat didn't eat the fish.' The absence of a factive inference here is not surprising under my proposal. I assume that (64), just like other noun phrases, combines as the second argument of θ Th . The preexistence presupposition introduced by θ Th is still present in (65), but since θ Th 's argument is a predicate of individuals with Content 'The cat ate the fish', it presupposes that an individual with this propositional Content pre-exists the matrix time rather than that an event of the cat eating fish pre-exists the matrix time.
This presupposition about the existence of an argument with Content is illustrated in (66): in a context where Dugar was the first person to think that the cat ate the fish, (66) is infelicitous.
(66) #Mi:sgɘi zagaha ɘdj-ɘ: gɘ-žɘ xɘn-∫jɘ xɘzɘ:-∫jɘ han-a:-güi, (xarin) cat fish eat-pst say-cvb who-ptcl when-ptcl think-pst-neg (but) dugar [mi:sgɘi-n zagaha ɘdj-ɘ: g-ɘ:∫-i:jɘ] han-a: Dugar cat-gen fish eat-pst say-part-acc think-pst # 'Noone has ever thought that the cat ate the fish, (but) Dugar remembered (the claim) that the cat ate the fish.' To sum up, the pre-existence presupposition is observed with all nominalized clauses, which combine with hanaxa via the θ Th projection. The pre-existence presupposition will lead to a factive inference only if the nominalized expression denotes a predicate of events of the kind described by the embedded predicate, but not if it denotes a predicate of individuals whose Content is the embedded proposition.

nmns with a future/modal morpheme -xa
Another prediction that the current proposal makes is that combining hanaxa with a nominalized clause based on a participle that sets the left boundary of the nmn-event after the matrix time should result in presupposition failure. This is so because the presupposition introduced by θ Th in (55), repeated in (67), explicitly states that the left boundary of the nmn-event should precede the matrix time.
Testing this prediction turns out to be quite complicated. The main issue is that we need to find a morpheme that indeed sets the left boundary of an eventuality after the matrix time, and it is not obvious that a morpheme with exactly such meaning exists in Barguzin Buryat. The best candidate is the morpheme -xA (pot), which can describe future eventualities when it occurs in finite forms: (68) Bi jɘxɘ bolo-xo-d-o:, tomo gɘr aba-xa-b 1sg.nom big become-pot-dat-refl huge house buy-pot-1sg 'When I will grow up, I will buy a huge house.' In addition to future reference, xa seems to express modal meanings, as can be seen in the following sentence from (Skribnik & Darzhaeva 2016): (69) Tɘ:d-∫jɘ, ∫i ü∫ö: baga-∫, bu: ürgɘl-xɘ-∫ni ü∫ö: üdi: but-ptcl you still little-2sg, gun lift-pot-2sg still neg 'Moreover, you are still little, you still can't lift a gun.' (Skribnik & Darzhaeva 2016: 201) When -xA (pot) occurs in embedded contexts, its interpretation is often not identical to its finite uses, and seems to depend on a number of factors, among which are the meaning of the matrix verb, the type of the embedded clause, aspectual class of the embedded eventuality. A thorough investigation of -xA (pot) in embedded contexts would be necessary to properly understand the combination of xA-nmns with hanaxa, which is beyond the scope of this paper. Here I only present some initial observations related to this issue.
Consider the sentence in (70), in which hanaxa combines with a nominalized clause based on the -xA participle.
(70) Badm-ain gurban buti:lka hü aba-x-i:jɘ hana-n-u:-∫? Badma-gen three bottle milk buy-pot-acc think-prs-q-2sg 'Do you remember Badma's buying three bottles of milk?'  Context A: Some time ago Badma bought three bottles of milk.  Context B: Someone is making a list of things to buy, and I see them write "3 bottles of milk" on that list. They might not realize that Badma already has planned to buy 3 bottles of milk himself.
The interpretation corresponding to context A seems to be the most prominent one, which is surprising given how xA-forms are interpreted in finite sentences, (68)-(69). One could hypothesize that the pre-existence presupposition introduced by hanaxa somehow is able to override the semantic contribution of xA, but what kind of mechanism would be responsible for that is unclear. 39 The second interpretation requires more support from the context, but seems to be generally available. When (70) is uttered in context B, the eventuality of buying three bottles of milk is in the future with respect to the matrix time, and what is being remembered, it seems, is the plan to buy three bottles of milk. As two anonymous reviewers point out, this pattern is similar to English remember, which when taking a future-oriented complement, also requires that there is a plan in place already at the time of the remembering. 40 (71) Pam remembered she would go to Boston in the morning. ⟹ there is a plan for Pam to go to Boston in the morning.
Does the existence of such an interpretation for the xA-nmn with hanaxa pose a problem for my proposal about the pre-existence presupposition? It seems impossible to answer this question without an understanding of how (and why) the "planned eventuality" reading comes about. Given that the idea that a plan for an event can constitute an early stage of the event has been entertained the literature (Dowty 1979;Cipria & Roberts 2000), it could be that the shift observed in the meaning of the nominalized clause is happening in order to satisfy hanaxa's pre-existence presupposition. While the question of why a plan could count as an early stage of an event is beyond the scope of this paper (see Copley 2008; 2014 for discussion of this issue in light of futurates), I would like to provide some evidence that it is indeed the plan, and not the event itself, that xA-nmns denote when they combine with hanaxa. Consider (72).

(72)
Context: The speaker knows that Badma was planning to buy meat at the store. Then they realize that the store he was thinking of going to is closed for the day.
Oi. Badm-i:n mjaxa aba-x-i:jɘ-n' haja hana-ba-b. Ba:rhan Badma, oh Badma-gen meat buy-pot-acc-3 just.now think-pst2-1sg poor Badma mjaxa aba-xa-güi. meat buy-pot-neg 'Oh. I just remembered (about) Badma's buying meat. Poor Badma, he will not buy meat.' In this example the speaker doesn't think that Badma will buy meat at a future time, but the use of a xA-nmn with hanaxa is still acceptable, and what the speaker recalls is Badma's plan to buy meat. 39 Some other matrix verbs, e.g. mɘdɘxɘ 'know', seem to not allow such past-oriented readings of xA: (i) Context: Dugar returned from Baikal yesterday.
#Bi Dugar-ai Baigal-ha: jɘrɘ-x-i:jɘ mɘdɘ-nɘ-b 1sg.nom Dugar-gen Baikal-abl come-pot-acc know-prs-1sg Intended: 'I know about Dugar's returning from Baikal.' 40 A reviewer also points out that non-attitude verbs like buy, which normally involve a Theme argument that already exists, can also sometimes be used in cases where the Theme has not yet come into being but when its existence is planned for: (i) John bought three bottles of wine before the grapes were even harvested.
This is an intriguing parallel. It would be interesting to see if the analysis of (i), whatever it might be, could be also extended to attitude verbs like in (70).

Conclusion
In this paper I examined a case of factivity alternation in Barguzin Buryat: this language has an attitude verb hanaxa which is non-factive in sentences with CPs, but exibits factive inferences when it combines with nominal complements. I have argued that this is not a case of ambiguity, but rather a consequence of CPs and nominals combining with the verb in different ways: CPs combine by modifying the event argument of hanaxa and specifying the Content of thoughts, while nominal arguments combine via a functional head θ Th which introduces internal arguments.
In the context of hanaxa, the internal argument is interpreted as the topic of thoughts (what the thinking is about), and θ Th places a pre-existence presupposition on this argument: the about-argument is presupposed to have started existing before the time of thinking. I have argued that this presupposition (i) is responsible for the factive inference; (ii) is what the 'remember' translation in sentences with nominal complements is trying to convey. Since CPs do not combine as Theme arguments, no pre-existence presupposition is present in sentences with them.
The proposal advanced in this paper suggests that one source of factive inferences is presuppositions of verbs about their internal arguments, and one source of factivity alternations is the availability of several paths for combining with the verb.