Non-Interrogative Questions in Yukatek Maya∗ Scott AnderBois [email protected] LASC 2009 March 7, 2009

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Introduction • Yukatek Maya has sentences like (1)-(3) which have no interrogative morphosyntax, yet are interpreted as questions.

Interrogative Questions: (1)

a. b.

[Juan w´ aa Daniel] uk’ le sa’-o’ Juan Or Daniel drink.Agent.Focus the atole-Distal Question Reading: ‘Is it Juan who drank the atole or is it Daniel?’ Assertion Reading: ‘Juan or Daniel drank the atole.’

(2)

[Juan-w´ aah] uk’ le sa’-o’ Juan-Or drink.Agent.Focus the atole-Distal ‘Is it Juan who drank the atole?’

(3)

t´ aan-w´ aah u yuk’ik le sa’-o’ Juan Prog-Or Erg.3 drink Def atole-Distal Juan ‘Is Juan drinking the atole?’

Common morphosyntactic elements: 1. Disjunctive coordinator w´ aa (1, 2, and 3) 2. Focus cleft position (bracketed material in 1 and 2) Goal: An account deriving the uses of (1)-(3) from these two elements without positing covert morphology such as a Q-operator. Outline: • §2 reviews the Inquisitive Semantics approach to ordinary disjunctions; • §3 derives the interpretations of (1) from the interaction of disjunctions with the semantics of the focus/cleft construction; ∗ Many thanks to all of the Yukatek Maya consultants on this project for their patience and cooperation. Thanks also to Adrian Brasoveanu, Donka Farkas, Bill Ladusaw, Salvador Mascarenhas, Jim McCloskey, Kyle Rawlins, audiences at SSILA 2009 and UCSC’s S-Circle for helpful feedback on portions of this work, and all of my fellow participants in the Winter ’09 UCSC Research Seminar. Thanks also to Salvador Mascarenhas for LaTeX help. All remaining errors are, of course, my own.

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Non-interrogative questions in Yukatek Maya • §4 provides an account of (2) as a focused disjunction with only one disjunct; • §5 extends the analysis to examples with no focus fronted element such as (3); • §6 concludes and some welcome consequences of the analysis.

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Disjunctions and Inquisitive Semantics • Whereas focused/clefted disjunctions like (1) can be interpreted as questions, disjunctions in argument position and topic position, (4) and (5), can only be interpreted as assertions.

(4)

t-u yuk’ah le sa’o’ Juan w´aa Daniel Pfv-Erg.3 drink the atole-Distal Juan Or Daniel ‘Juan or Daniel drank the atole.’

(5)

Juan w´aa Daniel-e’ t-uy uk’ah le sa’-o’ Juan w´aa Daniel-Topic Pfv-Erg.3 drink Def atole-Distal ‘Juan or Daniel drank the atole.’

Goal for this section: Provide an Inquisitive Semantics account of ordinary disjunctions which will serve as the basis of the analysis of focused disjunctions.

2.1

Crash course in Inquisitive Semantics

• Simons (2005), Alonso-Ovalle (2006), and others have argued that natural language disjunction is best analyzed as collecting a set of alternatives rather than as the boolean connective corresponding to set union. • One way to formalize this idea is using Inquisitive Semantics (Groenendijk (2007), Mascarenhas (2008)). • The system will allow us to capture the intuition that disjunctions, unlike most sentences, raise issues. • That is, a disjunction introduces multiple possible alternatives, raising the issue of which alternative holds. The key formal shift in inquistive semantics is that a sentence denotes a set of pairs of possible worlds rather than a set of worlds. • These pairs are formalized in terms of a relation1 of indifference • The inclusion of a pair of worlds (w1 ,w2 ) in an update indicates that the difference between w1 and w2 is not an issue in the discourse • Conversely, the omission of a pair (w1 ,w2 ) indicates that the difference between w1 and w2 is an issue. • Consider a model with only four worlds, two propositions, and two individuals as in (6): 1

More specifically, sentences in inquisitive semantics denote subsets of W × W which are reflexive and symmetric. Note that these relations are not necessarily transitive, a property which will be central to the account of disjunction and questions.

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Non-interrogative questions in Yukatek Maya World wjd wj wd w∅

(6)

drink-atole! (juan) 1 1 0 0

drink-atole! (daniel) 1 0 1 0

We can represent the discourse-initial state pictorially in (7) where each arrow represents a pair (non-shaded worlds are those which do not appear in any pairs): (7)

Discourse-initial state (nothing is known, no issues are on the table):

wjd

wd

wj

w∅

• (7) is ignorant because pairs containing all worlds in the model are present (or rather their identity pairs are present). • (7) is indifferent because the relation represented in (7) is totally connected (i.e. there are arrows connecting each pair of worlds). Now, consider the update for P = drink-atole! (juan) as in the left figure in (8) (8)

Update for drink-atole! (juan):

Update for drink-atole! (daniel):

wjd

wd

wjd

wd

wj

w∅

wj

w∅

• σ[drink-atole! (juan)] is informative given the input state because it eliminates the worlds wd and w∅ from the context set (technically, it eliminates identity pairs of worlds). • The updates in (8) are not inquisitive since the relations are totally connected (all worlds which are included are linked with all other such worlds). • For the above sentences without disjunction, we do not see the effects of Inquisitive Semantics. • This is because the only issues raised is whether or not P holds of a given world. Summary: Inquisitive Semantics allows us to model the raising of issues within a discourse. 3

Non-interrogative questions in Yukatek Maya

2.2

(Unfocused) Disjunction in Inquisitive Semantics

Consider instead the update of an ordinary disjunction P = drink-atole! (juan) ∨ drink-atole! (daniel) (9)

Update for drink-atole! (juan) ∨ drink-atole! (daniel): wjd

wd

wj

w∅

• As in a classical semantics for disjunction, the update in (9) is the set union of the individual updates of the two disjuncts in (8). • The result of this is that (9) does not contain the pairs (wj ,wd ) or (wd ,wj ); the difference between these two worlds is an issue in this state. • Since (9) disconnects a pair of worlds, the update is inquisitive.2 • Importantly, an ordinary disjunction is also informative. It eliminates all pairs containing w∅ . Summary: Ordinary disjunctions such as (4) and (5) are always informative and inquisitive. They are interpreted as assertions.

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Focused Disjunctions • Unlike ordinary disjunctions, disjunctions in the focus/cleft construction – (10)– can be interpreted either as a question, (10-a), or as an assertion, (10-b).3 • It should be noted that (10) is the only (monoclausal) way to express (10-a). There is no separate alternative question structure.

(10)

a. b.

Juan w´aa Daniel uk’ le sa’-o’ Juan Or Daniel drink.Agent.Focus the atole-Distal Question Reading: ‘Is it Juan who drank the atole or is it Daniel?’ Assertion Reading: ‘Juan or Daniel drank the atole.’

Goal for this section: Derive the ambiguity in (10) from the interaction of the (latent) inquisitivity of all disjunctions and the semantics of the focus/cleft construction. 2

There is a crucial difference, then, between the disjunction ‘Juan or Daniel drank the atole’ (which is inquisitive) and ‘It’s not the case that neither Juan nor Daniel drank the atole’ (which is not). This is because, unlike in classic propositional logic, we no longer validate the equivalence in (i) since only the left side of the equivalence will disconnect wj from wd . (i)

P ∨ Q ↔ ¬[¬P ∧ ¬Q]

3 Intonation does not appear to play a role in disambiguating the two readings. This is not altogether surprising since non-disjunctive elements in the focus position are not intonationally prominent (Avelino (2008)).

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Non-interrogative questions in Yukatek Maya

3.1

Semantics of the Focus/Cleft Position

The term Focus is used in the literature to refer to two distinct concepts (Narrow/Contrastive/ Identificational focus vs. Wide/Presentational/Information focus). • The preverbal focus/cleft position in Yukatek Maya (illustated in (11)) is an instance of the former, more similar to the English it-cleft than to English focus.4 (11)

Juan uk’ le sa’-o’ Juan drink.Agent.Focus the atole-Distal ‘It was Juan who drank the atole’

• An example like (11) with a DP, Juan, in the focus position, differs from its non-focused counterpart primarily in having the presupposition in (12): (12)

3.2

Existential Presupposition of the Focus/Cleft for (11): ∃x:drink-atole! (x)

Deriving the Ambiguity of Focused Disjunctions

Consider (10), repeated as (13): (13)

a. b.

3.2.1

Juan w´aa Daniel uk’ le sa’-o’ Juan Or Daniel drink.Agent.Focus the atole-Distal Question Reading: ‘Is it Juan who drank the atole or is it Daniel?’ Assertion Reading: ‘Juan or Daniel drank the atole.’

Interpretation as a Question

• The above model with only four worlds (wjd , wj , wd , w∅ ) ensures that there are no worlds where anyone other than Juan and Daniel drank the atole. • The focus presupposition in (12) ensures that, prior to the update of the at-issue component of (13), the input state is as in (14). (14)

Update for the focus/cleft presupposition:

wjd

wd

wj

w∅

• The input state, then is indifferent since the relation in (14) is totally connected (in particular, wj and wd are connected). • The update of the disjunction (its at-issue component) is the same as ordinary disjunctions, repeated in (15): 4 An even closer parallel, perhaps, than the English it-cleft is the preverbal focus position in Hungarian (Kiss (1998) among many others).

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Non-interrogative questions in Yukatek Maya (15)

Update of drink-atole! (juan) ∨ drink-atole! (daniel) (repeated from (9)):

wjd

wd

wj

w∅

• Relative to the presupposed input state in (14), the update in (15) does not remove any worlds; it is uninformative. • The only effect of the update in (15) relative to the input state is to disconnect wj and wd (i.e. to remove the pairs (wj ,wd ) and (wd ,wj )). • The update in (15) raises the issue of whether Juan drank the atole or Daniel did. Summary: A focused disjunction like (13) is interpreted as a question if it is uninformative and inquisitive relative to the presupposed input state. 3.2.2

Interpretation as an assertion

A focused disjunction such as (13) can still be interpreted as an assertion provided that it is informative. • Assume that we have an input state which, in addition to the four worlds above, also contains worlds where Juan and Daniel did not drink the atole, but someone else did (say, Maribel). • For simplicity’s sake, assume that it contains only one such world: wm . • Given the existential presupposition, the input state will be as in (16). (16) wjd

Update for the focus/cleft presupposition (with wm ):

wd wm

wj

w∅

• In this scenario, (13) is informative since it removes wm from the input state. Summary: A focused disjunction like (13) is interpreted as an assertion if it is informative relative to a given input state. 6

Non-interrogative questions in Yukatek Maya 3.2.3

The Inquisitive Principle

There is an asymmetry, then, between the distribution of the assertive reading and the question reading. • Any sentence whose update is informative is interpreted as an assertion, regardless of whether it is also inquisitive or not (as in (17)); assertions are the default. (17)

Informative Uninformative

Inquisitive Assertion Question

Uninquisitive Assertion Assertion (Tautology)

• This distribution can be stated formally as in (18). (18)

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Inquisitive Principle: Given an input state c, a sentence S is interpreted as a question iff (i) σ[S] is uninformative w.r.t c and (ii) σ[S] is inquisitive w.r.t. to c.

Polar Questions with Focus • Having derived the ambiguity of focused disjunctions in §3, we turn now to a closely related construction, the polar question.

4.1

Data

• Like focused disjunctions, questions such as (19) (repeated from (2) above), involve the focus/cleft construction and the disjunctive coordinator, w´ aa.5 (19)

Juan-w´aah uk’ le sa’-o’ Juan-Or drink.Agent.Focus the atole-Distal ‘Is it Juan who drank the atole?’

• Unlike focused disjunctions, (19) is obligatorily interpreted as a question.

4.2

Polar Questions as Disjunctions with One Disjunct

• The basic approach we take is to analyze (19) as a single-disjunct version of a focused disjunction as schematized in (20). (20)

[Juan w´aa

] uk’ le sa’-o’

• The account of (19) as a covert alternative question is supported by the fact that particle answers (e.g. ‘yes’, ‘no’, or ‘maybe’) are not licensed for such questions. (see AnderBois (2009a) for further syntactic evidence for this approach) Semantically, the unpronounced disjunct is interpreted as ‘anyone else’. • This follows from three properties that hold of ordinary disjunctions (see Zimmermann (2000) for a recent discussion of these properties): 5 The coda [h] in (19) is part of a regular epenthesis process arising because w´ aa occurs phrase-finally, see AnderBois (2009b) for details.

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Non-interrogative questions in Yukatek Maya 1. Exhaustivity: provides the domain widening of any in ‘anyone else’ 2. Mutual exclusivity: contributes the ‘else’ in ‘anyone else’ 3. Like constituents: contributes the ‘one’ in ‘anyone else’ (for a disjunction of type e)

4.3

(Obligatory) Interpretation as a question

Recall that a focused disjunction was interpreted as a assertion only if it was informative relative to the input state. • For the focused disjunction, this only occurs if there are worlds in the input state where an individual other than Juan or Daniel drank the atole. • For the Polar Question in (19), this is not possible since the elided disjunct is interpreted as ‘anyone else’. • The existential presupposition of the focus/cleft still ensures that the input state will not include w∅ . Given this, both parts of the Inquisitive Principle must be fulfilled and (19) will only be interpretable as a question. Summary: Polar Questions like (19) are focused disjunctions with one disjunct in the narrow syntax. The absence of an assertive reading is predicted by the interpretation of the unpronounced disjunct according to ordinary properties of disjunctions.

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Polar Questions without Focus

While §4 made crucial use of the existential presupposition of the focus cleft, we also find polar questions which do not have an element in the focus position.

5.1

Data

In questions with no focused element, what is disjoined is the polarity of the sentence itself. • We see this clearly in (21) where the polarity is overt (i.e. when it is negative). (21)

ma’-w´ aah tuun xinbal-i’ k bin? Neg-Or then walk-Irreal Erg.1.Pl go ‘We will not be walking then?’

Echevarr´ıa Lope (2004) p. 59

• Since positive polarity is phonologically null, the disjunctive coordinator, w´ aa, leans on the 6 first prosodic word as in (22). (22)

t´ aan-w´ aah u yuk’ik le sa’-o’ Juan Prog-Or Erg.3 drink Def atole-Distal Juan ‘Is Juan drinking the atole?’

Summary: Polar Questions with no focused element involve disjunction of polarity, either positive or negative. 6

See AnderBois (2009a) for arguments that this is the case.

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Non-interrogative questions in Yukatek Maya

5.2

Interpreting the Unpronounced Disjunct

• Above, we saw that the unpronounced disjunct was interpreted as the exhaustive set of like elements which are mutually disjoint from the overt disjunct. • Since either a proposition is true or its negation is true, the negation of a proposition represents the exhaustive set of answers disjoint from the affirmative counterpart. The whole disjunction for (22) has the form in (23). (23)

5.3

drink-atole! (juan) ∨ ¬drink-atole! (juan)

(Obligatory) Interpretation as a Question

According to the inquisitive principle in (18), a sentence is interpreted as a question iff it is inquisitive and uninformative. • (23) is inquisitive for the same reason as all disjunctions. • It is also clearly uninformative since P ∨ ¬P is a tautology. • Due to the very nature of negation, disjunctions of polarity do not require the existential presupposition to be uninformative. Summary: Polar Questions with no focused element can only be interpreted as questions because they are always uninformative and, like all disjunctions, inquisitive.

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Conclusion

Yukatek Maya has several constructions which function as questions despite the apparent lack of question-specific morphology. • We have derived their use as questions from the interactions of the focus cleft with a particular semantics for disjunctions. • An approach positing a covert Q morpheme cannot easily explain why focused disjunctions exhibit such an alternation between questioning and assertive uses. Our account makes sense of the peculiar fact that w´ aa in Polar Question either occurs after the first syntactic constituent a certain kind (a focused XP) or the first prosodic constituent (the prosodic word). • This distribution for polar question particles is attested in unrelated languages, including Bulgarian li and Latin -ne (both of which are at least historically related to disjunctive coordinators). Future extension: The relationship between focus, indefinites and wh-questions in many languages (Yukatek Maya, Hungarian, etc.) can likely be given a treatment along the same lines as above. • When an indefinite occurs in the focus cleft position, the sentence is no longer informative given the presupposition of the focus cleft. 9

Non-interrogative questions in Yukatek Maya • Indefinites, like disjunctions, have a capacity to latently raise issues (evoke alternative in Hamblin-semantic terms); they are inquisitive. • Focused indefinites, then, would meet both requirements of the Inquisitive Principle and be interpreted as questions.

References Alonso-Ovalle, Luis (2006) Disjunction in Alternative Semantics. Ph.D. thesis, University of Massachusetts. AnderBois, Scott (2009a) Disjunction and Polar Questions in Yukatek Maya, handout from SSILA Annual Meeting. AnderBois, Scott (2009b) Strong Positions and Laryngeal Features. In Proceedings of NELS 39. Avelino, Heriberto (2008) Intonational patterns of Topic and Focus constructions in Yucatec Maya, presented at New Perspectives in Mayan Linguistics, SSILA Symposium. Echevarr´ıa Lope, Jorge (2004) X-La’ Boon Suumij. In Words of the True Peoples, 54–72. Groenendijk, Jeroen (2007) Inquisitive Semantics: Two Possibilities for Disjunction. In Tbilisi 2007: Seventh International Tbilisi Symposium on Language, Logic, and Communication. Kiss, Katalin (1998) Identificational Focus versus Information Focus. Language : 245–273. Mascarenhas, Salvador (2008) Inquisitive Semantics, an overview, unpublished manuscript. Amsterdam: ILLC. Simons, Mandy (2005) Dividing things up: the semantics of or and the modal/or interaction. Natural Language Semantics 13: 271–316. Zimmermann, Thomas Ede (2000) Free Choice Disjunction and Epistemic Possibility. Natural Language Semantics : 255–290.

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