Latent homomorphism and content satisfaction : The double life of Turkic auxiliary – ( İ ) p bol –

This paper argues that the Turkic auxiliary construction –(İ)p bol–, at least in Uyghur and Uzbek, is actually a pair of auxiliaries with distinct meanings. The first auxiliary is described as expressing “full completion” of the event, but its use is highly restricted, to events with incremental or universally quantified themes. Using targeted context-based elicitation, we find that the expression of completion is indirect. Instead, the auxiliary asserts that the event description is homomorphic, in that all of its events are both event-mapped and theme-mapped. Homomorphism requires every part of the theme to undergo a part of the event, and this derives the reported sense of completion. The second auxiliary is not attested in the literature. It applies to all kinds of events, and expresses what we call “content satisfaction,” the conventional implicature that the event as described satisfies some salient propositional content by rendering it true. For instance, it makes part of a plan come to fruition. This plan is presupposed, and the content is accessible through a content-generating function. We apply the methodologies of formal semantic fieldwork to tease these auxiliaries apart, including scope tests that apply differently to the two auxiliaries. Having distinguished them, we suggest new ways to typologically distinguish Turkic auxiliaries and auxiliaries cross-linguistically.


Introduction
Most research focusing on auxiliaries as a grammatical phenomenon is typological and diachronic in nature, focusing on their path to grammaticalization (Heine 1993;Kuteva 2001;Anderson 2006).These studies rely on descriptive research to provide a clear and precise synchronic understanding of what auxiliaries mean and how they function, inasmuch as we can treat them as a single class of objects.However, recent developments in formal semantics have shown for a number of phenomena that these descriptions are vague.While still invaluable, they would benefit from a deeper exploration (Matthewson 2017).These developments also show that once such exploration is made, new discoveries and new facets of semantic typology emerge (Matthewson 2004;Rullmann et al. 2008).
In this paper, we offer a new analysis of a Turkic Auxiliary Verb Construction that clarifies vague descriptions in the literature, and offers a new route to understanding the process by which auxiliaries become auxiliaries.
We also open up a line of formal semantic research on auxiliaries.To date, such research has almost exclusively covered modal auxiliaries, abstracting from their status Glossa general linguistics a journal of McKenzie, Andrew, et al. 2018.Latent homomorphism and content satisfaction: The double life of Turkic auxiliary -(İ)p bol-.Glossa: a journal of general linguistics 3(1): 47. 1-34, DOI: https://doi.org/10.5334/gjgl.422 as auxiliaries to focus on their modality.What little discussion that has occurred has been fairly superficial in nature.Anderson (2006) finds that auxiliaries can be semantically classified into one of several functional types: Tense-Aspect-Modality, polarity and negation, voice, direction and orientation, and also adverbial functions like degree.These functional types correspond roughly to semantic types.

Turkic Auxiliary Verb Constructions
The Auxiliary Verb Construction in Turkic (AVC) is a major feature of most of the languages in the group.An AVC is built by impressing a lexical verb to serve as an auxiliary to a verb phrase marked by a participial or converbial form. 1 Ibrahim (1995: 40) claims that speakers employ simple forms to assert the mere existence of an event, while AVCs are used to add specific information as they see fit, noting that "Compound verbs [AVCs] are more frequently used than non-compound verbs, especially in the spoken language."Descriptively, an AVC is preceded by a verb phrase and followed by TAM marking as shown in (1).Example (2) exemplifies this pattern for Uyghur with the AVC 'try to', which is built from the impressed verb baqmaq 'to look'. (1) Surface pattern: [Verb phrase]-[non-finite marker] Auxiliary-TAM (2) Uyghur (ISO Code: uig) [Kitab-ni oqu]-p baq-tim.book-acc read-cvb try.aux-pst:1s 'I tried to read the book.' The AVC often resembles a conjunctive converbial but its meaning is distinct (3).The lexical verb's meaning is bleached and the AVC itself is idiomatic.For instance, the Uyghur AVC with the converb -(İ)p2 and the verb tashlamaq 'to throw, drop' combines to give a sense that the event took place suddenly and involuntarily (4).When we list an AVC in citation form, we will provide the lexical meaning of the impressed auxiliary verb in square brackets.
(3) Men kül-üp ket-tim.I laugh-cvb go-pst:1s converbial: 'I laughed and then I went.' AVC: 'I suddenly laughed hard.' (4) -(İ)p tashla-[throw, drop] 'event is sudden and involuntary' Men kül-üp tashli-dim.I laugh-cvb throw-pst:1s 'I laughed involuntarily.' AVCs remind one of phrasal verbs in English or particle verbs in German in the following way: A verb combines with a lexical item of a distinct category whose meaning is generally bleached to form an apparent lexical unit.For instance, the Kazakh (ISO: kaz) AVC -(İ)p al-[take] means 'do for one's benefit', while - A al-[take] means 'be able to'.One difference between phrasal verbs and AVCs is that with the latter, the main verb is not part of the construction; any semantically compatible verb can be used.
Descriptive material on Turkic languages, increasingly written by native-speaker linguists, lists dozens of AVCs and examines them in varying levels of detail.AVCs are attested as far back as the earliest Turkic texts, the 8th century Orkhon inscriptions.Some of them have kept their form and meaning from early times unto the present, as the example from the Mongol-era Maitrimisit demonstrates (5).Every Turkic language still employs AVCs routinely, although they are not as numerous in the Oghuz group, which includes Turkish and Azeri.
(5) -(İ)p ber-[give] 'the event benefits someone besides the subject' Old Turkic, ISO: otk (Erdal 2004: 261) bašla-p ber-iŋ start-cvb give.aux-impr.2s'Do us a favor and start.' Reflecting the importance of AVCs in Turkic languages, a description of their meanings features in every Turkic reference grammar.However, the descriptions remain fairly vague, in two ways.First, the terminology in the descriptions is not always clear and uniform, so it is difficult to determine the extent to which AVCs correspond across languages.Second, the descriptions discuss what these forms "express," but none specify the semantic or pragmatic nature of that expression.Can it be broken down into parts?Are those parts asserted, presupposed, or implicated?What is the compositional structure, which helps determine what the arguments are?Does the AVC entail anything?These questions are crucial, as we can see with the case of Uyghur -(İ)p baq-.This AVC is translated as 'try to'.However, with many predicates, it entails success (6), while English try to never does.Hahn (1991: 613) suggests that this AVC expresses an action undertaken with uncertainty about the outcome.Perhaps, then, a better English translation is 'give VP a try'.
B.-dat go-cvb look.aux-pst:1s'I gave going to Boston a try.' entails that I arrived in Boston

The focus of this paper
In this paper, we will not cover a broad array of AVCs or languages; that would require one or several books.In fact, we will focus on a precise target: The single AVC -(İ)p bol-in Uyghur and Uzbek (where it is -(i)b bo'l-), with an emphasis on Uyghur.
A. teacher become-pst:3s 'Ali became a teacher.' Together, these parts combine to form a new meaning, and they cannot be divided syntactically.It is not clear that the meaning is composed semantically, but both the converb and the auxiliary make a semantic contribution, notwithstanding idiomaticity.The auxiliary bol can be used with a number of converbs, and the converb -İp can be used with a number of different auxiliaries.In this paper, though, we will treat the AVC -(İ)p bol-as a single form in the semantics and leave its ultimate semantic (and syntactic) composition for future research.
A glance at Table 1 shows a clear consensus on this AVC's meaning: It indicates that the described event was fully completed.
Given this consensus, one might feel there is little about -(İ)p bol-for us to add.However, several facts cloud this clear picture and warrant a thorough exploration.First, it is not clear what "full completion" means, given that any sentence with -(İ)p bol-could have been truthfully expressed without -(İ)p bol-(8).At the very least, we will need to employ a formal perspective to understand precisely what the completion reading is expressing.

Kazakh
Somfai Kara (2002: 49) expresses the completion of the event Second, some sources indicate that -(İ)p bol-can express modal possibility (9).However, this is limited to cases where the auxiliary is marked with the aorist/present, at least in Uyghur.These will be discussed in more detail in section 2.5. 49) Uyghur Men bu hékayi-ni oqu-p bol-mas=men.I this story-acc read-cvb become.aux-aor.neg=cop.1s'I cannot read this story' Third, and most importantly, full completion does not always matter for -(İ)p bol-.In many cases, its availability depends on the context.For instance, a sudden cough does not license -(İ)p bol-even if it is completed, but a cough conducted as part of a routine (men's) medical physical exam does. (10) Uyghur/Uzbek Yötil-ip bol-dum.Yo'tal-ip bo'l-dim.cough-cvb become.aux-pst:1s'I coughed.' (discussing my physical) In the rest of this paper, we will restore clarity to -(İ)p bol-by dividing its meaning into two readings.The first is the "full completion" reading seen in the literature, and the next section will lay out the exact semantics that brings about that reading.The second reading is what we call "content satisfaction."This previously unattested reading expresses that the event as described satisfies some contextually salient propositional content, like the steps of a physical exam.Section three will discuss this reading in detail, especially the differences between readings that require us to consider them as being provided by distinct but identical morphemes.Section four will formalize this reading's meaning and situate the AVC in the phrase structure.

The methodology for this project
The findings of this paper rely on targeted context-based elicitation.With this method (Matthewson 2004;Bochnak & Matthewson 2015), the investigator provides a specific scenario to a native speaker to use as a context for judgment or translation, rather than asking for translations or general statements of meaning, like "Can you say this?" or "Does this mean the same thing as that?"This method relies on the observation that the meaning of a linguistic expression depends largely on the real-world conditions that make it a true description.As a corollary of this observation, semantic judgments are most informative when the investigator knows which truth-conditions the speaker is using.Since we cannot read minds, we provide the speaker with those conditions.
(i) Uzbek (Bodrogligeti 2003: 725) Hozirgi zamon-da har kim-ga ishon-ib bo'l-adi=mi?present time-loc every person-dat believe-cvb become.aux-prs.3s=q'In our times is it possible to believe anyone?' Providing a context is especially crucial for a study like this, where context matters.If you simply ask a speaker how to say 'I coughed', they will give you a sentence without -(İ)p bol-, like Yöteldim in Uyghur.If you then ask if it's possible to say that with -(İ)p bol-(Yötelip boldum), they will reject it, and we linguists would mark it as ungrammatical.As it turns out, the phrase is perfectly grammatical, but relies on a specific sort of context to be true.
Context: Imagine you had a physical exam and had to cough for it.Later, you tell me.
In this case, we can ask for a translation of 'I coughed' given this context, or to judge the targeted expression for truth, not grammaticality.We can also offer targeted expressions we expect to be false, and thus gain negative evidence if our expectations are correct.
For this study, we consulted with two native speakers of Uzbek who studied at our campus.For the Uyghur data, we mainly relied on a native speaker investigator, but also consulted with a native speaker now in Kazakhstan.We also consulted two Turkish speakers to confirm that no equivalent of -(İ)p bol-is found in that language.Some of the examples were gathered in Uyghur after we lost access to the Uzbek speakers, so they are only confirmed for Uyghur.

Full completion derives from homomorphism
This section argues that the full completion reading of -(İ)p bol-, whose discussion is widespread in the literature, is derived from an actual meaning of homomorphism.Our argument begins with a question: When we say "full completion," what is actually being completed?We can begin to answer this when we explore a crucial limit on this reading: It only applies when the event's theme has distinguishable parts across which the event is distributed.

Limited to incremental and universal themes
Tömür mentions the use of -(İ)p bol-to express an event "related to all relevant objects", as his example in (11) shows.He is a native speaker of Uyghur, so his judgment seems like an intuitive clarification of what "full completion" means. (11) Uyghur (Tömür 2003) Kél-idighan-lar-ning hemmi-si kél-ip bol-di, come-ipfv-pl-gen everyone-3s.posscome-cvb become.aux-pst:3majlis-ni bashla-yli meeting-acc begin-opt.1p'All who are coming have arrived, so let's begin the meeting.'Building off his observation, if we look through the literature we do see a pattern: Every attested instance of -(İ)p bol-involves a verb phrase where the theme is incremental or universally quantified.In the relevant literature on -(İ)p bol-, examples with universal quantifiers tend to have theme subjects (11), but it is easy to elicit cases with a theme object.Incremental themes are themes with distinguishable parts such that the event fully applies to each of those parts (Dowty 1979;Krifka 1992).For instance, the predicate eat the bread has an incremental theme, because to eat the entire piece of bread, you must eat each part of it.As we expect, -(İ)p bol-works well with this predicate.

Context
( I treasure find-cvb become.aux-pst:3s'I found the treasure.'c. #Oyog'-im-ni sin-dir-ib bo'l-dim.leg-1s-acc break-caus-cvb become.aux-pst:1s'I broke my leg.' Crucially, it does not suffice for the event itself to be incremental.Incremental events like traveling along a path do not license -(İ)p bol-.To account for these restrictions, we propose that -(İ)p bol-denotes an event description that is sensitive to the thematic relations and event structure of the event that it describes.We will first discuss the meaning semi-formally, with a fully formal discussion following.

Sensitivity to event structure
The exact nature of -(İ)p bol-'s sensitivity to event structure is fairly subtle.The use of -(İ)p bol-does not say that the event is completed or merely incremental, as we saw in ( 16).Instead it says that the event description is homomorphic (Krifka 1992).Homomorphism is a property of verbs that have a theme argument and an event argument, viz.that the theme's parts and event's parts map to one another.Homomorphism can be broken down into two basic properties.
• Mapping to the theme.Every part of the entire event affects a distinct part of the theme in the same way the entire event affects the entire theme.5 • Mapping to the event.Every part of the theme undergoes a distinct part of the event in the same way that the entire theme undergoes the entire event.
We can think of -(İ)p bol-as expressing that the VP predicate is homomorphic.Incremental theme predicates are homomorphic.If you have a complete event of 'eating the bread', every part of that event involves eating a part of the bread, and every part of the bread undergoes an eating event that is part of the eating of the whole.If you have an event of reading an entire book, every part of that event involves reading a part of the book, and every part of the book undergoes a part of the reading event. 6n contrast, breaking your leg is not homomorphic despite being an accomplishment, since it is not necessarily true for a complete event that every part of your leg undergoes a breaking.Looking at the ocean for five minutes is not homomorphic, since it is not automatically true that in such an event, every part of the ocean undergoes a look.Going to Korla is not homomorphic because its parts do not involve a part of the subject going all the way to Korla separately from the other parts, followed by the next part and so on.The increments of this event are laid out along the path of travel until the goal is reached.
Many predicates are ambiguous between an activity reading and an accomplishment reading, like read "War and Peace."A completed event like this can either culminate at its intrinsic end, or simply come to a stop ((17a), (18a)).Using -(İ)p bol-removes this ambiguity, for the event must have culminated at its intrinsic end ((17b) We can see that the AVC -(İ)p bol-provides a sense of full completion that disambiguates these cases, but we argue that it only provides it indirectly.We cannot simply claim that -(İ)p bol-signals culmination, for some cases, like go to Korla in ( 16), culminate without allowing -(İ)p bol-.Instead, the verb phrase with -(İ)p bol-must be homomorphic, and will entail the culmination of any process it describes.A predicate of reading the book with -(İ)p bol-is only true for an event-book pair if every part of that event was a book-reading, and if every part of the book was read during the event.Thus, every event involves reading the entire book.Without -(İ)p bol-, the predicate of reading the book is not necessarily homomorphic; some of the events in its extension are complete readings, but others are not.
In more formal terms, the set of events that are part of -(İ)p bol-event-theme pairs is a proper subset of all the events that culminate.A predicate like 'read the book' is not homomorphic by Krifka's definition, since homomorphism only applies if all the eventtheme pairs map to each other's parts.There is only one possible mechanism for converting a non-homomorphic predicate into a homomorphic one: A subset relation.We have to divide predicates that can be homomorphic into those that are fully homomorphic and those that are partially homomorphic.A fully homomorphic predicate is one like Krifka describes.A partially homomorphic predicate is one where only some of the event-theme pairs map to each other's parts.The partially homomorphic predicate has a subset that is fully homomorphic.The predicate without -(İ)p bol-is partially homomorphic, and -(İ)p bol-restricts the proposition to the largest homomorphic subset.
Let's consider a ship-sinking event to show what we mean.Figure 1 shows a number of ways that a ship can sink, from not at all (1) to all the way to the sea floor (5, 6).The predicate without -(İ)p bol-, Kéme chökti 'the ship sank', is true whether the ship sank partway (pictures 2, 4, 5) or all the way (3, 6).It's false in 1, since the boat has not sunk at all.The proposition with -(İ)p bol-, Kéme chöküp boldi, is only true if every part of the ship sank (pictures 3, 6).Notably, -(İ)p bol-is not made true by the ship sinking all the way to the seabed where it can sink no further (5).It only applies when every part of the ship has sunk.Table 2 summarizes these truth-values.
What these judgments show us is that 'the ship sank' in Uyghur is partially homomorphic.Theme-event pairs like 2, 4, 5 are not, but theme-event pairs like 3 and 6 are.The use of -(İ)p bol-says 'this is homomorphic', and rules out the non-homomorphic pairs.The only pairs left are those where the entire ship sank (3, 6).The meaning of -(İ)p bolthus entails full completion but does not directly express it.
This ambiguity lets us rule out predicates like 'draw a circle' or 'build a house'.The use of -(İ)p bol-is allowed with predicates that are partially homomorphic, but barred from predicates that are fully homomorphic.This is an odd restriction, but it is what we observe.We propose that -(İ)p bol-'s domain is restricted: It takes the VP/vP predicate as its argument, but only if it isn't fully homomorphic, and asserts that it has a part that is homomorphic.The assertion rules out predicates that cannot be homomorphic at all.The following section analyzes the formal nature of this meaning.
Expressing -(İ)p bol-'s meaning in terms of homomorphism not only derives the full completion reading, it also explains why it works with universally quantified themes.These too are partially homomorphic.In an event where 'everyone arrived', the universal quantifier is defined such that everyone in the salient group undertook an arrival event.If we consider their arrivals to be parts of the described event (which aspect links to tense), then the expression is effectively theme-mapped.
It is not necessarily event-mapped, however.The meaning of the universal quantifier only asserts that every part of the theme is mapped to a part of the event, but asserts nothing about the nature of the event, because the event parts are outside the quantifier's domain.Some of the theme-event pairs in which everyone arrived are homomorphic, some are not.This makes universally quantified expressions partially homomorphic, and they thus allow -(İ)p bol-.If -(İ)p bol-is used, then the event is theme-mapped: Every part of the event of 'everyone arrived' is mapped to a part of the theme.This rules out extraneous parts, and also seems to enforce distributivity.

A formal denotation for -(İ)p bol-
In this subsection we lay out a formal analysis of -(İ)p bol-'s meaning which results in the intuitive meaning we detailed in the last subsection, and which derives the relation between homomorphism and the full completion reading.We begin by providing a syntactic position for -(İ)p bol-to feed the semantic composition.However, we do not decide whether it is composed of one syntactic head or two.Determining the underlying syntax of -(İ)p bol-is only possible through comparing it to other AVCs, and that is well beyond the scope of this paper.Since no constituents are observed splitting -(İ)p and bol-, and since -(İ)p bol-behaves as a single element in the semantics, we will treat -(İ)p bol-as a single element in the syntax, but we do not claim or imply here that it actually reflects a single syntactic head or lexical item.We place -(İ)p bol-between the argument structure and the higher inflectional structure.
Although −( İ)p bol− is situated above the vP, it cannot take more than one vP in its scope.While the clauses in chains of converbial clauses all share tense/aspect and mood information, they do not share the information provided by the AVC −( İ)p bol−.In ( 23), which exemplifies this fact, the conjunctive converbial form of −( İ)p is highlighted.
Although -(İ)p bol-is situated above the vP, it cannot take more than one vP in its scope.While the clauses in chains of converbial clauses all share tense/aspect and mood infor- We saw that -(İ)p bol-applies when the VP/vP is partially homomorphic, and ensures that the event itself is in the homomorphic subset of the VP/vP's denotation.For Krifka, homomorphism is defined on relations, but due to -(İ)p bol-'s syntactic position, we must also consider it to apply to event properties.This shift is not consequential for the semantics, because we observe that for any relation R that is fully homomorphic, and any of its possible themes x, we can describe the event property R(x) as fully homomorphic as well.c.Let M Ɛ be the set of event-mapping event properties R(x), Partially homomorphic relations and event properties are those that contain a proper subset that is fully homomorphic, and a non-empty subset that is not homomorphic.
( The value condition of this denotation rules out any predicate that has no homomorphic event members at all, like states (which are not events), activities (which cannot be event-mapped), or achievements.It also rules out accomplishments that are not homomorphic, like breaking one's leg, because those are not theme-mapped.These verbs will never return a value of 'true' on this reading unless their themes are universally quantified.Event properties with universally-quantified themes are compatible with -(İ)p bol-, even if the verb phrase describes an event that -(İ)p bol-cannot usually be used with, like arriving (11), or breaking a bone (12).The partial homomorphism comes from the effective theme-mapping imposed by universal quantifiers.Accessing this part structure requires lightly adjusting the meaning of universal quantifiers.Instead of the classic definition of 'everyone arrived' (30a), we get one that involves parts of a larger event. 8 The main event here, e, is necessarily theme-mapped, but not necessarily event-mapped, since its domain is not a set of events.In the case where everyone arrived, there may be parts of the main event e that do not involve the individuals picked out by the domain.Thus, the predicate itself is only partially homomorphic.Using -(İ)p bol-restricts us to the largest fully homomorphic subset of this predicate.In this subset, every person has an arrival, and every part of the main event is one of these arrivals.Within this event nothing else happened.Again, a sense of full event completion is entailed, but not directly asserted.We note that it seems unlikely that the use of -(İ)p bol-in these cases is very informative, since the partially homomorphic use of the universal quantifier strongly implicates the fully homomorphic reading.This might explain why this use is not as common as the simple incremental use.

Interactions between -(İ)p bol-and negation
It is crucial to test any proposed denotation with sentential negation, since the result is predictable.The use of -(İ)p bol-indicates that the largest homomorphic subset of the predicate, MaxHS(⟦vP⟧), holds of the event.Negation thus indicates that the event is not in this subset.As we see in Figure 2, if an event is not in MaxHS(⟦vP⟧), it must either be in the rest of ⟦vP⟧ or outside it altogether.That is to say, if -(İ)p bol-is negated, there is either a non-homomorphic event or no event at all.Earlier we derived the full completion reading from homomorphism.Negating that homomorphism negates the full completion reading.An event in the non-homomorphic part of a partially homomorphic ⟦vP⟧ is necessarily incomplete.For instance, in the bookreading case, negation expresses that there was no homomorphic event (in the topic time) where I read the book (31).This statement is true in two kinds of conditions: Either there was no book-reading event at all, or there was a non-homomorphic event of book-reading.Book-readings are necessarily theme-mapped; every part of the event is the reading of a part of the book.Therefore, if a book-reading is not homomorphic it is not event-mapped, and some of the book is left unread.
As we saw with the positive readings, the effect of completion or incompletion is indirect, due to the homomorphism of the predicate.

The aorist and ability readings
The use of −( İ)p bol− is compatible with all tenses and moods.With most of these, nothing remarkable occurs.However, with aorist marking, the AVC can undergo an apparent change in interpretation, to express possibility or impossiblity (9).The availability of this reading with the aorist is discussed incidentally in a few sources, like Tömür (2003)  As we saw with the positive readings, the effect of completion or incompletion is indirect, due to the homomorphism of the predicate.

The aorist and ability readings
The use of -(İ)p bol-is compatible with all tenses and moods.With most of these, nothing remarkable occurs.However, with aorist marking, the AVC can undergo an apparent change in interpretation, to express possibility or impossiblity (9).The availability of this reading with the aorist is discussed incidentally in a few sources, like Tömür (2003) for Uyghur -Ar, or Bodrogligeti (2003) for Uzbek -adi. 9We find that in Uyghur, the modality is provided by the aorist, not -(İ)p bol-, based on two observations.First, we note that the aorist can be used literally, in that it adds aorist/generic meaning to an -(İ)p bol-phrase, and no possibility modal results.This suggests that the ability reading is a conversational implicature.
(  We conclude that the reading has to do with the modal nature of genericity as expressed by the aorist.In essence, if an event generally happens, it certainly can happen.If it does not generally happen, it is easy to draw the implicature that it cannot happen.It may be the case that -(İ)p bol-marked aorist verbs are especially prone to this implicature, although we do not venture a reason.It is clear, however, that -(İ)p bol-is not a source of modality.

The full completion reading
This section required some intricate formal discussion, but intuitively the result is quite straightforward.The use and meaning of -(İ)p bol-to indicate full completion is derived through homomorphism.Speakers only apply -(İ)p bol-to predicates with incremental or universally quantified themes, which are partially homomorphic, in order to turn them into fully homomorphic predicates.The fact that homomorphism derives from theme-mapping and event-mapping is the source of speakers' sense of full completion: Every part of the theme is affected by the event, and every part of the event affects the theme.
We have accounted for the full completion reading in Uyghur and Uzbek.It is probable that our account works with other Turkic languages as well, and it demonstrates the value of carefully distinguishing a reading from the semantic truth-conditions that derive it.We leave the question of decomposing the AVC for future research, and in the rest of this paper we dedicate our efforts to a very distinct reading of -(İ)p bol-.

Content satisfaction
The use of -(İ)p bol-to signal full completion is noted in nearly every descriptive source on Uyghur and Uzbek.However, direct elicitation finds a second meaning for -(İ)p bol-, which must be kept distinct from the full completion auxiliary, for three crucial reasons.First, its use is wholly dependent on the context.Second, it can be used with any predicate except states.Third, it is immune to negation and other scope-bearing items.We will propose in this section that this auxiliary does not assert homomorphism, but rather conventionally implicates that the event would satisfy some at-issue content.

Contextual effects and event types
We saw that -(İ)p bol-cannot be used with several types of eventualities.However, given the right context, it becomes perfectly felicitous with them.Coughing events are classic semelfactives, and do not allow the full completion -(İ)p bol-, since not every part of the subject coughed.However, if the cough is made to satisfy the demand of a doctor during a physical exam, -(İ)p bol-is felicitous.

(35)
Uyghur/Uzbek Yötil-ip bol-dum.Yo'tal-ib bo'l-dim.cough-cvb become.aux-pst:1s'I coughed' Breaking one's leg is another semelfactive, and doesn't allow -(İ)p bol-, unless the context allows.In (36), breaking your leg as part of a plan is such a context.Context: You are due to fulfill army service, but don't want to do it.You hatched a plan to get out of military service by breaking your leg, and now you're telling your friend you've gone through with it. (36) Uyghur/Uzbek Put-um-ni sun-dur-up bol-dum.Oyog'-im-ni sin-dir-ib bo'l-dim.leg-1s-acc break-caus-cvb become.aux-pst:1s'I broke my leg.' Outside of such contexts, these sentences are rejected outright.Indeed, (36) tended to make speakers laugh when given out of the blue.
Accomplishments are also acceptable with -(İ)p bol-.Merely going to a place does not license -(İ)p bol-, but if it is part of a pre-established itinerary, it does.
Context: You and your son are traveling on a trip along the following itinerary: Along the way, you get a call from your spouse, who is at home, where you started.They ask how it's going, and you reply: Activities also license -(İ)p bol-in the right contexts.In (20) we saw that temporal adverbial NPs unmarked for case can be used to modify the duration of activities.Meanwhile the full completion use of -(İ)p bol-adds an accomplishment that requires locative case marking.In a context where an activity is prescribed, however, -(İ)p bol-is allowed even when the predicate remains an activity.
Context: Your doctor prescribed for you to walk along the sea every day, and look at it for five minutes.You did so today.

The two meanings cannot be combined
We can generalize over these contexts: They all involve some salient at-issue content, and express that the described event makes some of this content true.We say that it satisfies this content, so we call this reading content satisfaction.In section 4 we will discuss the details of this reading.Here we will show that the full completion and content satisfaction readings cannot be derived from a single vague morpheme, which means that the string -(İ)p bol-is ambiguous between two lexical items.
We have already seen that the content satisfaction reading is compatible with many event types that the full completion reading is not.More importantly, the proposition of content satisfaction is not part of the assertion.This can be ascertained with negation and other high scope-bearing expressions.
With the full completion reading, negation indicates that the event is not in the homomorphic subset of the ⟦vP⟧.In that case, the event is either true but not for the entire theme, or it is not true at all.We can schematize this relation as a ∧ b: a is the assertion that the event happened at all, and b is the proposition that the event-theme pair is homomorphic.For the case of a ship sinking, that's 'it sank some' and 'it sank all the way'.Taking scope over a conjoined condition, negation should be able to negate either or both of these, and it does.We can schematize the possible meanings as a ∧ not(b), or not(a) ∧ not(b).The former can be true and felicitous.The latter can be true, but is infelicitous, for if the event does not happen at all, the negated form without -(İ)p bol-is preferred.For logical completeness we can include not(a) ∧ b, but this form is always false, since b is a subset of a.These results are summarized in Table 3.
With the content satisfaction reading, negation with -(İ)p bol-signals that the VP-event did not occur, but that it would have satisfied the content at issue (Table 4).For instance,    it works if you plan to break your leg to get out of army service, but never manage to, or have not yet done so.This negation can be schematized with not(a) ∧ b, the meaning that was impossible with the full completion reading.Also, negation with the content satisfaction reading cannot mean that you did break your leg but it does not satsify the content; the content condition is immune to negation.
(41) content satisfaction: NEG [ I broke my leg -(İ)p bol-] = it is not the case that I broke my leg, but breaking my leg satisfies my plan ≠ it is the case that I broke my leg, but breaking my leg does not satisfy my plan Similar results emerge with epistemic modals like belki 'maybe'.With the full completion reading (42), the modality can take scope over both the verb description and -(İ)p bol-, just -(İ)p bol-, but never just the verb description (Table 5).In contrast, with the content satisfaction reading (43), the modality can only take scope over the verb description (Table 6).
( = it may be the case that Ali read this book, and reading this book satisfies the plan ≠ it is the case that Ali read this book, and reading this book may satisfy the plan Going further up the tree, evidential marking affects the full completion reading of -(İ)p bol-, but not the content satisfaction reading.In (44), the evidential applies to the homo-    morphism, or the homomorphism and the event description, but not to the event description by itself (Table 7).
Context: You see Ali reading a book, but don't see him finishing it.Later, you hear from a friend that he read the whole thing.Later, you are talking to Ali's sister, and say: (44) Uyghur Ali kitab-ni oqu-p bol-uptu.A. book-acc read-cvb become.aux-past.evid:3s'Ali read the book, and I heard he read it all./Ihear he read the whole book.'By repeating this task with other contexts, we arrive at a complete Table 7.
On the other hand, in (45) the evidential ignores the content satisfaction reading (Table 8).The report that triggers the evidential marker does not involve the plan, but the proposition the report delivers satisfies the plan, and that licenses the speaker to use -(İ)p bol-in reporting that information to someone who knows about the plan.
Context: You and your friend Samia know that Ali is trying to get out of army service by getting injured.Your other friend Ibrahim does not know this.But he saw Ali in a cast and knows that he broke his leg.Ibrahim told you Ali putuni sundurdi 'Ali broke his leg' without -(İ)p bol-.You tell Samia: (45) Uyghur Ali put-i-ni sun-dur-up bol-uptu.A. leg-3s-acc break-caus-cnv become.aux-past.evid:3s'Ali broke his leg.' (I heard) Incidentally, examples like this show that evidentials in Uyghur are modal in nature rather than illocutionary.Going even further up in the structure, we find that embedding under attitudes affects the full completion reading ( 46)-( 47), but not the content satisfaction reading ( 48)-( 49).This finding, summarized in Table 9, fits with the finding that the satisfied content of -(İ)p bol-is immune to scope.It also demonstrates clearly that the difference between the two readings is not due to scope alone, since the attitude predicate is in a superordinate clause.( 46 Several scope and distribution facts demonstrate that the full completion reading and the content satisfaction reading occur in very distinct environments.Therefore, they must be delivered by distinct, surface-identical morphemes.This requirement even holds with predicates that allow both readings, like 'eat the cookies', whose judgments are summarized in Table 10.bo'l-ma-dim.cookie-pl-acc eat-cvb become.aux-neg-pst:1s'I didn't eat the cookies.'

-(İ)p bol-as a conventional implicature
The previous discussion shows that when -(İ)p bol-expresses the proposition that the described event satisfies at-issue content, it is immune to scope.Immunity to scope is a hallmark of two types of expressions: Presuppositions and conventional implicatures.These are secondary propositions, not necessarily asserted by the uttered expression but intrinsically tied to it.Several diagnostics distinguish these meanings, but we will rely on a simple one, which involves a context that ensures that the secondary proposition is false.
If the secondary preposition is a presupposition (PR), its falsehood prevents the central proposition from being true or false. (51) The King of France is bald.PR: There is a king of France There is no King of France, so it cannot be true that he is bald.It can also not be true that he is not bald.
Meanwhile, a conventional implicature (CI)'s falsehood does not affect the truth or falsehood of the central proposition.
(52) Bob Dylan, who is from Canada, won a Nobel Prize.CI: Bob Dylan is from Canada.Dylan is not from Canada, yet it is still true that he won a Nobel Prize.
With the content satisfaction reading of -(İ)p bol-, we saw that -(İ)p bol-is infelicitious even if the described event happened but does not satisfy the content at-issue.This is the case in the detour example (38), where the sentence with -(İ)p bol-is rejected, but it is still true that you went to Qashgar/Qarshi.Given that -(İ)p bol-is immune to scope-bearing objects above it, and that its falsehood does not affect the truth-value of the rest of the expression, we conclude that it adds a conventional implicature to the primary asserted proposition.

(53)
Uyghur/Uzbek = (38) Qeshqer-ge bér-ip bol-duq.Qarshi-ga bar-ip bo'l-dik.Assertion: We went to Qashgar/Qarshi (true) CI : Going there was part of our itinerary (false) We can confirm this conclusion by verifying another property of conventional implicatures.Potts (2005) highlights their non-challengeability.In a discourse, assertions can be rejected by interlocutors, most clearly with a simple "no."Conventional implicatures, however, cannot be targeted this way.Rejecting them requires stopping the conversation altogether for a detour.Given this, we predict that the content satisfaction reading of -(İ)p bol-cannot be challenged, and indeed it cannot.
"No" here can only mean, "No, you did not go to Qashgar."By contrast, the asserted full completion reading is challengeable, as we expect.(55) shows this for Uyghur, but similar results are observed for Uzbek.

How this proposal may work with other Turkic AVCs
This section has shown the importance of determining the nature of the propositional content expressed by the AVC -(İ)p bol-.In doing so, it reveals the necessity of determining for any Turkic auxiliary verb construction whether it expresses asserted, presupposed, or implicated content.We can begin to apply this method to these other AVCs.For instance, Uyghur -iwal-(>-ip al-[take]) indicates that the described event benefits the subject (56a), or at least fulfills the subject's desire.What is the nature of this indicated content?Negated, it is ambiguous.On one reading, the event did not happen, but it still would have fulfilled the subjects' desire (56b).On the other reading, it did happen, but not to fulfill the subject's desire.For instance, it was a commissioned professional shoot.
(56) Uyghur -(İ)wala.Men u-ning resim-i-ni tart-iwal-dim.I her-gen picture-3s-acc pull-cvb.take-pst:1s'I took her picture.'(because I wanted one) b.Men u-ning resim-i-ni tart-iwal-mi-dim.I her-gen picture-3s-acc pull-cvb.take-neg-pst:1s'I did not take her picture.'(though I would have liked one) 'I took her picture, but not for my benefit.' This ambiguity tells us that -(İ)wal-in Uyghur expresses a self-benefit condition that is subject to negation, which makes it part of the assertion.
The nature of the propositional content of the AVCs, and of auxiliaries generally, is an under-researched area.However, we suspect that a typology along these lines might prove very fruitful and even crucial for synchronic and diachronic studies of auxiliary constructions in general.Nonetheless, this paper focuses on -(İ)p bol-, so we will now move on to formalizing the details of its content satisfaction reading.

Details of content satisfaction
The content satisfaction reading is provided by a distinct morpheme from that which provides the full completion reading.Now that we have shown this, we must provide the exact formal meaning of the content satisfaction morpheme.Basically, -(İ)p bol-in this reading expresses the conventional implicature that the described event renders true some salient propositional content.More precisely, it indicates that given a content-bearing object a, if the event has the VP description, some proposition in the content of a is true.To capture this meaning, we will need four formal elements: A set of propositions forming the content, an anaphoric object bearing these propositions as content, a function generating the former from the latter, and a modal condition using this generated set outside the domain restriction.We will take these parts in order.

The propositional content being satisfied
We have observed content satisfaction readings in Uyghur and Uzbek in a number of scenarios: • A plan with several steps • The parts of a physical exam • The steps of an itinerary • A doctor's orders In each of these cases, there is a set of propositions involved.For instance, Ali's plan to get out of the army (a 2 ) might consist of the following set of propositions: (57) Ali's plan = a 2 = { λw.Ali signs up in w, λw.Ali gets injured in w, λw.Ali gets doctor's note in w, λw.Ali gets released in w } In such a case, -(İ)p bol-would be felicitous if his leg-break makes at least one of these propositions true.In our example, it does, as Ali gets injured.
The propositions are often ordered, at least partially, but they do not have to be ordered.For instance, if you are describing the steps of a recipe, you can use -(İ)p bol-for those steps.For many of these recipes, the order does not always matter.
The propositions can be rendered true directly or by entailment.This allows for serendipitous accidents to satisfy content (58).
Context: You have a plan to get out of army service.You told your friend two days ago that you'd break your leg in a week.But yesterday, a car hit you.

(58)
Uyghur/Uzbek Put-um-ni sun-dur-up bol-dum.Oyo'g-im-ni sin-dir-ib bo'l-dim.leg-1s-acc break-caus-cvb become.aux-pst:1s'I broke my leg.'In (59), the event has no involvement at all from the plan holder.In fact, the passive marker signals the lack of an agent, which shows that the use of -(İ)p bol-does not depend on the presence of a local agent.Instead, only the plan itself matters in this case.So long as the key part of the plan is the result, rather than the means, then a serendipitous accident can satisfy the content.
Context: You have a plan to wreck your car to get a new one with the insurance money.You told your friend two days ago that you'd do it in a week.But yesterday, someone hit your car.
(59) Uyghur Mashina-m soq-ul-up bol-di.car-1s smash-pass-cvb become.aux-pst:3s'I got in a wreck.' (lit.'my car got smashed') Essentially, the vaguer the content propositions are, the more kinds of events can satisfy them, and the more readily they license -(İ)p bol-.In (60), the propositions allow for any bad thing, so any bad thing happening makes one of these true.
Context: A soothsayer tells you and your friend that three bad things will happen tomorrow.You both laugh it off, but the next day, you trip and break your leg.You tell the friend: (60) Uyghur/Uzbek Put-um-ni sun-dur-up bol-dum.Oyo'g-im-ni sin-dir-ib bo'l-dim.leg-1s-acc break-caus-cvb become.aux-pst:1s'I broke my leg.' The more specific the propositions are, the fewer kinds of events can satisfy them, and the less readily they license -(İ)p bol-.If the content propositions require intent, that intent must be present in the described event, or -(İ)p bol-will fail.For instance, if a travel itinerary is tied to a purpose, like tourism, reaching a point on the itinerary for another reason does not result in content satisfaction (61a).The same observation applies in Uzbek with the locations switched out (61b).
Context: You are on a trip with your son from Hoten to Urumchi to see the sights of Xinjiang.Near Korla on the way to Urumchi, your son gets sick.You cancel the rest of your trip.You drive him to the hospital in Korla.You call home, your spouse asks "Are you in Urumchi?"You reply: Whether the propositions are so precise is an area of context-sensitive vagueness, to be determined on a case-by-case basis.

Presupposition of the content-bearing object
So far we have discussed a salient set of propositions, but as we've seen that set can be quite vague.As it turns out, the conversation's participants do not have to know exactly which propositions form the content.Instead, they have to be aware of a particular salient content object.For instance, if Ali has a plan to get out of army service, describing his leg-break with -(İ)p bol-is only felicitous if everyone in the conversation knows that he has a plan.They do not need to know how he plans to get out of army service, but they must know about his plan.That is to say, the plan itself is subject to an existence presup-position.Like any presupposition, its failure renders a clause infelicitous, and it cannot felicitously be used with speakers unaware of it, as (63) demonstrates.

(63)
Uyghur #Ali putini sundurup boldi./Uzbek#Ali oyog'ini sindirib bo'ldi./'Alibroke his leg' a.No plan context: Ali is a healthy guy on an ordinary day, and not even subject to military service.He trips and falls, lands hard, and breaks his leg.b.Unaware context: You know that Ali wants to get an injury to avoid army service, but his parents don't.They do know he wants to avoid army service, but not that he actually has a plan to do so.He broke his leg this morning and he's in the hospital, so you are the one who must break the news to them.
If presuppositions fail, the proposition whose meaning they contribute to is non-sense: neither true nor false (51 C. with kiss-recp-cvb become.aux-pst:3s'Harry and Cho kissed.'Similar observations can be made for the other kinds of scenarios.In each case, there is an anaphoric object-a plan, a prophecy, an itinerary, and so on-whose existence is presupposed, whose identity is known, and whose content is satisfied by the described event.The salient content is not directly accessed, but is instead accessed through this anaphoric object.The next subsection will describe that process.

Generating content from content-bearing objects
For the meaning of -(İ)p bol-, we propose a content-generating function, Cont, which takes a content-bearing object and returns its propositional content.(66) Eliza said that the mayor was an alien.
(67) the rumor that the mayor was an alien Moulton proposes that content is accessed by a Content-generating function (f c ) provided by the complementizer.This function returns the set of possible worlds where all the con-tent is true.The complementizer equates that set with the set denoted by the embedded proposition.
(68) Combining events and entities Let D e ⋃ D s be the union of the set of individuals and the set of events.
(69) a. ⟦ that C° ⟧ = λp.λa∈ D e ⋃ D s .f c (a) = p read: The set of worlds where the content of a is true is the set of worlds where p is true b. ⟦ say that the mayor was an alien ⟧ = λe.e is a saying event, and the set of worlds where the content of e is true is the set of worlds where the mayor was an alien c. ⟦ rumor that the mayor was an alien ⟧ = λx.x is a rumor, and the set of worlds where the content of x is true is the set of worlds where the mayor was an alien Moulton's function takes an individual and gives you the set of worlds (the proposition) that equals the content of that individual.This is useful for individuals whose content is one proposition, like a rumor.However, the content we are discussing, like a plan, usually has more than one proposition.We must therefore adjust the content function to give a set of propositions rather than a set of worlds (a single proposition).This set of content propositions is akin to a modal base, but we will see that -(İ)p bol-does not employ it as the basis of a modal.

The nature of content satisfaction
Put in more compositional terms, Moulton's content function combines the modal force (in all the worlds) with the modal base (the content at issue).However, the content satisfaction reading requires us to split these components, because of how a modal base works.
A modal base is a set of propositions used as the basis for modal reasoning.In a phrase like You have to leave, the modal base expresses what requires you to leave.A modal base is generated from a modal anchor, which can be an event (Hacquard 2006;2010), an individual (Moulton 2009), a situation (Arregui 2009), or a possible world.Circumstantial modals can be thought of as relating certain relevant facts concerning the Davidsonian event argument which is in the evaluation world (Abusch 2012).We lay this out in (70).The event argument will be bound by aspect in the case of circumstantial modals, and by higher operators in the case of epistemic modals.Crucially, a modal base has two properties.First, the speaker assumes that every proposition in it is true (in all worlds where these facts hold…).Second, the modal evaluation is made in light of that assumption (if those facts hold, the proposition holds).The content generated by our function Cont has neither of these properties.The content in question comes from the application of Cont to an object (event or individual) with content, like a plan, or even the formulation of that plan.The result, in the same semantics, so we will employ the simpler structure that can be decomposed in future research. (74) In the structure that feeds the semantic interpretation, the content-bearing object needs to be represented.We assume it to be the first argument of −( İ)p bol− .The vP will be the second argument.In the semantics, the input to aspect is an intensional property of events (type ⟨e, wt⟩), so the AuxP will need to denote something of that type.11In essence, it will denote the property of events of Ali breaking his leg, which satisfies the content of a 2 .We thus propose this denotation for the content satisfaction reading of −( İ)p bol−.

(76)
Denotation of content satisfaction −( İ)p bol− Let D s,wt be the set of intensional properties of events, and W be the set of all possible worlds.
11 In section 2.3, we used a semantics that set aside possible worlds, which are of type w.We did so out of convenience, since possible worlds do not affect the full completion reading.The analysis in that section works just as well if we include them.
In the structure that feeds the semantic interpretation, the content-bearing object needs to be represented.We assume it to be the first argument of -(İ)p bol-.The vP will be the second argument.
(75) Ali putini sundurup boldi.'Ali broke his leg.' (satisfying content) a.Let a 2 be the content-bearing object in this sentence.We get the following structure: b.

Latent homomorphism & content satisfaction 39
(74) AuxP In the structure that feeds the semantic interpretation, the content-bearing object needs to be represented.We assume it to be the first argument of −( İ)p bol− .The vP will be the second argument.In the semantics, the input to aspect is an intensional property of events (type ⟨e, wt⟩), so the AuxP will need to denote something of that type. 11In essence, it will denote the property of events of Ali breaking his leg, which satisfies the content of a 2 .We thus propose this denotation for the content satisfaction reading of −( İ)p bol−.

(76)
Denotation of content satisfaction −( İ)p bol− Let D s,wt be the set of intensional properties of events, and W be the set of all possible worlds.
11 In section 2.3, we used a semantics that set aside possible worlds, which are of type w.We did so out of convenience, since possible worlds do not affect the full completion reading.The analysis in that section works just as well if we include them.
In the semantics, the input to aspect is an intensional property of events (type ⟨e,wt⟩), so the AuxP will need to denote something of that type. 11In essence, it will denote the property of events of Ali breaking his leg, which satisfies the content of a 2 .We thus propose this denotation for the content satisfaction reading of -(İ)p bol-.
( This denotation asserts that the vP property (P) holds of e in world w, with the conventional implicature that any world where P holds is one where some proposition in the content of a holds.We follow Potts's (2005) convention of marking the CI as truth-conditionally independent of the main assertion, but do so with a |-marker.Thus, the formal expression p|q represents the assertion of p with the conventional implicature of q.
If we apply the denotation in (72) to the structure in (75b), we get the following composition.
(77) implicature that P(e) satisfies the content of a content-bearing object a.
This denotation asserts that the vP property (P) holds of e in world w, with the conventional implicature that any world where P holds is one where some proposition in the content of a holds.We follow Potts (2005)'s convention of marking the CI as truth-conditionally independent of the main assertion, but do so with a | marker.Thus, the formal expression p | q represents the assertion of p with the conventional implicature of q.
If we apply the denotation in (72) to the structure in (75b), we get the following composition.
(77) λeλw.break(leg)(e)(w This denotation captures the observed meaning of the content satisfaction reading.Once aspect is added, we assert that there is an actual event of Ali breaking his leg, and conventionally implicate that in any world where such an event exists, some of the content of his plan is true.Since the actual world is one of these worlds, this condition entails that some of the content is actually true. If we negate the structure in (77), we assert that there is no actual event of Ali breaking his leg, but still conventionally implicate that in any world where Ali breaks his leg, some of the content of his plan is true.That is, the event would satisfy the content of the plan.Other scope-bearing elements will similarly avoid the content satisfaction condition.
Immunity to scope also predicts that the presupposed content object is not subject to quantificational variability, and this is the case.For instance, if we take our itinerary from Hoten to Korla every week, and every week we pass through Qashgar to do so, we cannot use −( İ)p bol− for this general trait.This is expected if the This denotation captures the observed meaning of the content satisfaction reading.Once aspect is added, we assert that there is an actual event of Ali breaking his leg, and conventionally implicate that in any world where such an event exists, some of the content of his plan is true.Since the actual world is one of these worlds, this condition entails that some of the content is actually true.
If we negate the structure in (77), we assert that there is no actual event of Ali breaking his leg, but still conventionally implicate that in any world where Ali breaks his leg, some of the content of his plan is true.That is, the event would satisfy the content of the plan.Other scope-bearing elements will similarly avoid the content satisfaction condition.
Immunity to scope also predicts that the presupposed content object is not subject to quantificational variability, and this is the case.For instance, if we take our itinerary from Hoten to Korla every week, and every week we pass through Qashgar to do so, we cannot use -(İ)p bol-for this general trait.This is expected if the content-object refers to a specific itinerary.Each trip has its own content-bearing object (its own itinerary), even if each object bears the same set of propositions as content.In contrast, the full completion reading is part of the assertion, and it can apply to each quantified-over event.

Summarizing content satisfaction
This section has explored the nature of content satisfaction, and proposed a formal denotation that captures its properties.Essentially, event properties satisfy the content of an object when their truth entails some of that content.Since the satisfaction is expressed with a conventional implicature, it is immune to further scope operations.This exploration also demonstrates that the components that contribute to the meaning of modals can be found in other kinds of uses.

Conclusion
We have argued that the Turkic AVC -(İ)p bol-is actually two AVCs, at least in Uyghur and Uzbek.The first AVC expresses the full completion reading found in the literature, but does so by asserting the event description's homomorphism.From this homomorphism, a sense of completion or culmination can be derived.This assertion is subject to scope-taking operators like negation or modals.Since many event descriptions cannot be homomorphic, the use of this AVC is limited.
The second AVC expresses the conventional implicature that the event satisfies the content of some anaphoric content-bearing object.This content satisfaction reading is highly dependent on the context, but does not restrict the type of event it can occur with.Also, its contribution lies outside the scope of negation and other operators.This paper is the first to attest morphemes that denote content satisfaction in the Turkic literature, or anywhere else.We should not think it to be rare, however.As this linguistic phenomenon exists in one language, it possibly exists in most if not all of them.Given how often humans think of events in terms of the content they satisfy, it seems that many if not most languages should exhibit grammaticized ways of expressing it one way or another.This paper offers methods of finding these expressions, thereby showing promise toward a new line of descriptive and theoretical inquiry.
This study also has several important consequences for linguistic theory and the study of auxiliaries.First, with the full completion reading, it demonstrates the role played by homomorphism.More broadly, it informs us about the formal structure of events by deriving descriptive notions of what full completion is, and demonstrates the value that formal attention brings to fine-tuning grammatical description.
Second, with the content satisfaction reading, this study demonstrates a new role for propositional content that adds to our understanding of content management in the semantics.With content satisfaction we propose a novel phenomenon through which the grammar depends on the context, and we show that pieces of modality can be used outside their use in modals.This point matters because it provides new support for the Kratzerian model of modality.As widely accepted as it is, it is composed of a number of parts that are never seen anywhere else in the semantics.We show here that the functions that take conversational backgrounds to create modal bases can in fact be used elsewhere to create sets of propositions with other functions.This demonstrates that some pieces of modality do in fact have independent existence.
Third, this study offers new light on the function, structure, and meaning of Turkic AVCs.-(İ)p bol-is but one of dozens of AVCs in Uyghur and Uzbek alone, and these are but two of the dozens of Turkic languages.By focusing on the interaction of the auxiliary's meaning with the rest of the proposition, we suggest a new way of typologically categorizing these constructions.Moreover, AVCs are often thought to be like light verbs or serial verbs (Butt 2010), which occur across a number of languages worldwide.This study may thus lead to new hypotheses about possible universal organizations of verbal meaning.
A final consequence is methodological.This study amply demonstrates the value of formally-informed targeted semantic elicitation.A corpus-based approach, as valuable as it is, did not lead any previous researchers to even find the content satisfaction reading.We ourselves only stumbled upon it during the course of trying to confirm the full completion reading.Nevertheless, even untrained speakers swiftly and robustly accept it.Without testing for negative evidence with elicitation, we could not possibly have untangled such fine strands of meaning.In addition, a corpus could not easily tell us whether an expression's meaning is asserted, implicated, etc., since speakers are not in the habit of making such metalinguistic commentary while they speak.On the other hand, working with native speakers to judge expressions in specific contexts, rather than asking general questions of acceptability, has led us to discover exactly what these morphemes mean.Framing these discoveries in terms of a formal semantics, including the composition, led us to discover that we dealt with two distinct morphemes.This framework clarified our questions and allowed us to formulate hypotheses precise enough to test properly.In writing this paper, we hope to set a replicable example for the study of AVCs and auxiliaries in general.

Figure 1 :
Figure 1: Some of the ways a ship can sink.
e = the set of individuals (type e) D s = the set of events (type s) D i = the set of time intervals (type i) D t = the set of truth-values (type t) b.For any types σ, τ, D σ,τ = the set of functions from D σ to D τ (type ⟨σ,τ⟩) (26) Homomorphism in event properties a.Let H R be the set of fully homomorphic relations of type ⟨e,⟨s,t⟩⟩ Let H P be the set of fully homomorphic event properties of type ⟨s,t⟩.b.Define ⊑ as a part-of relation.
not sink all the way not (a) ∧ not(b) I (nfelicitous) it did not sink some, and it did not sink all the way break my leg, but breaking my leg would satisfy the plan a ∧ not (b) # I did break my leg, but breaking my leg would not satisfy the plan not (a) ∧ not(b) # I did not break my leg, and breaking my leg would not satisfy the plan read some of the book, but he did read the whole thing a ∧ may (b)  Ali did read some of the book, and he may have read the whole book may (a) ∧ may (b) I Ali may have read some of the book, and he may have read the whole book this book, and reading this book would satisfy the plan a ∧ may (b) # Ali did read this book, and reading this book might satisfy the plan may (a) ∧ may (b) # Maybe Ali read this book, and reading this book might satisfy the plan read the book, and I know firsthand that he read it all a ∧ evid (b)  I know firsthand that Ali read the book, and I heard that he read it all evid (a) ∧ evid (b) I I heard that Ali read the book, and I heard that he read it iall firsthand that it satisfies his plan a ∧ evid (b) # I know firsthand that Ali broke his leg, and I heard that it satisfies his plan evid (a) ∧ evid (b) # I heard that Ali broke his leg, and I heard that it satisfies his plan Two readings of -(İ)p bolwith negation (50).meaningfull completion content satisfaction not (a) ∧ b #  a ∧ not (b)  # not (a) ∧ not (b)  # (50) Uyghur/Uzbek Pirenik-ler-ni ye-p bol-mu-dum.Shirinlik-lar-ni yi-b (61) Uyghur (a)/Uzbek (b) a. #Yaq, Korli-gha bér-ip bol-duq.No, Korla-dat go-cvb become.aux-pst:1p'No, we went to Korla.' b. #Yo'q, Samarqand-ga bar-ib bo'l-dik.No, Samarqand-dat come-cvb become.aux-pst:1p'No, we went to Samarqand.'On the other hand, if circumstances change, and new content becomes at-issue, the factors licensing -(İ)p bol-change, and it is allowed.Context: You are near Korla (Navoiy for Uzbek) on the way to Urumchi (Tashkent) and your kid gets sick.You call home, tell your spouse, who says "Take him to the hospital in Korla (Navoiy)."So you do, and the next day you update your spouse: (62) Uyghur (a)/Uzbek (b) Korli-gha kél-ip bol-duq.Navoiy-ga kel-ib bol-dik.(city)-dat come-cvb become.aux-pst:1p'We have come to Korla/Navoiy.' a that bears content, Cont(a) = the set of propositions comprising that content A content-bearing object is an individual or event that contains or bears propositional content.Content-bearing events are described by verba dicendi and attitude verbs(think, say,  feel, claim).Content-bearing individuals are described by nouns like claim, rumor, or fact.Either kind of expression routinely combines with complement clauses(Moulton 2009).
/circumstantial modal base For any event e, let fact(e) be the set of worlds where all the selected relevant facts concerning e are true (71) ⟦ You have to leave ⟧ = λeλw.∀w′[ w′ ∈ fact(e) → you leave in w′ ] read: In all worlds where the selected relevant facts concerning e are true, you leave (75)   Ali putini sundurup boldi.'Ali broke his leg.' (satisfying content) a.Let a 2 be the content-bearing object in this sentence.We get the fol- boldi.'Ali broke his leg.' (satisfying content) a.Let a 2 be the content-bearing object in this sentence.We get the fol- ) Denotation of content satisfaction -(İ)p bol-Let D s,wt be the set of intensional properties of events, and W be the set of all possible worlds.⟦ -(İ)p bol-CS ⟧ = λa ∈ D e ⋃ D s .λP∈ D s,wt .λe∈ D s .λw∈ W. P(e)(w)|∀w′[ ∃e′[ P(e′)(w′) = 1 ] → w′ ∈ ⋃Cont(a) ] read:The assertion that property P holds of event e, with the conventional implicature that P(e) satisfies the content of a content-bearing object a.

bo'l-dim. sea-dat five minute look at-cvb bol-pst:1s 'I looked at the ocean for five minutes.' b. #Men xazina top-ib bo'l-dim.
Besh sa'et kitab-ni oqu-p bol-dum.five hour book-acc read-cvb become.aux-pst:1s'I read the book for five hours.' five hour book-acc read-pst:1s 'I read the book for five hours.' (21) Uyghur a. Besh sa'et-te kitab-ni oqu-p bol-dum.five hour-loc book-acc read-cvb become.aux-pst:1s'I read the book in five hours.' b. #
For consistency in our denotations, let us define two functions.MaxHS maps a set of events to its maximal homomorphic subset, and Hom allows us to use MaxHS in a composition.
27) Partial homomorphism a.A relation R is partially homomorphic if and only if: R ∉ H R ∧ ∃Q ⊂ R; Q ∈ H R b.A property of events P is partially homomorphic if and only if: P ∉ H P ∧ ∃Q ⊂ P; Q ∈ H P f: D s,t → D s,t ∀P ∈ D s,t , if MaxHS(P) ⊂ P, f(P) = g : D s → D t ∀e ∈ D s , g(e) = 1 iff e ∈ MaxHS(P) Given these definitions, we can define -(İ)p bol-quite simply.(29) The denotation of -(İ)p bol-with the full completion reading ⟦ -(İ)p bolfull completion ⟧ = λP ∈ D st .λe∈ D e .Hom(P)(e) read: Given a property P and event e, e is in the largest homomorphic subset of P.
You saw Ali finish his homework, and you believe he did it.b.Content satisfaction accepted: You know that Ali is trying to get out of army service, and you heard he broke his leg.The report is reliable but you aren't quite sure.
).The presupposition of the plan is part of the added content of -(İ)p bol-, which is a conventional implicature.The CI fails, but as a CI, its failure does not affect the truth of the rest of the expression.As a result, the use of -(İ)p bol-is infelicitous if Ali broke his leg with no plan at all, but he still broke his leg.Another context where shared knowledge matters involves story adaptations.For instance, if you and a friend have read the Harry Potter books, and you are watching the movie adaptation, you can tell your friend what you're seeing using -(İ)p bol-.This only works, though, if they know the story that was adapted.