Non-Interrogative Questions in Yukatek Maya∗ Scott AnderBois, UC Santa Cruz [email protected] SULA V May 15-17, 2009

1

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

Non-interrogative Questions: (1)

a. b.

[Juan w´ aa Daniel] uk’ le sa’-o’ Juan Or Daniel drink.Agent.Focus the atole-Distal Question Reading: ‘Was it Juan who drank the atole or was it Daniel?’ Assertion Reading: ‘It was Juan or Daniel who drank the atole.’1

(2)

[Juan-w´ aah] uk’ le sa’-o’ Juan-Or drink.Agent.Focus the atole-Distal ‘Was 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(h) (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 interrogative morphology such as a Q-operator.

∗

Many thanks to all of the Yukatek Maya consultants on this project for their patience and cooperation. Thanks also to Pranav Anand, Adrian Brasoveanu, Donka Farkas, Bill Ladusaw, Jim McCloskey, Kyle Rawlins, audiences at SSILA 2009 and UCSC’s S-Circle for helpful feedback on portions of this work, and to all the participants in the Winter ’09 UCSC Research Seminar. Thanks also to Salvador Mascarenhas for LATEX help. All remaining errors are, of course, my own. 1 Impressionistically, intonation does not appear to regularly disambiguate the two readings. This would not be altogether surprising since non-disjunctive elements in the YM focus position are not intonationally prominent (Avelino (2008)). Furthermore, polar questions in English need not occur with a final rise (Bartels (1999)).

1

Non-interrogative questions in Yukatek Maya Road Map: • §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; • §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 with a brief look at inquisitive elements and focus cross-linguistically.

2

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) and Alonso-Ovalle (2006) 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. • Intuitively, though, conjunction could be thought of in these terms as well, differing only in how many alternatives are required to hold. • Inquisitive Semantics (Groenendijk (2007), Mascarenhas (2008), Groenendijk & Roelofsen (2009), inter alia) holds that disjunctions not only introduce a set of alternatives, but also raise the issue of which alternative holds. The key formal shift is that a sentence denotes a set of pairs of possible worlds, rather than a set of possible worlds. • These pairs are formalized in terms of a relation2 of indifference where the inclusion of a pair of worlds (w1 ,w2 ) in a denotation encodes two things: 2

More specifically, sentences in inquisitive semantics denote subsets of W × W which are reflexive and symmetric. Unlike previous work (e.g. Groenendijk (1999)) which treat question denotations as equivalence relations, Inquisitive Semantics relations need not be transitive. Indeed, it is this property which will be central to the account of ‘hybrid’ elements such as disjunction.

2

Non-interrogative questions in Yukatek Maya Informative component: Both w1 and w2 could (modulo intensionality) be the actual world (this is the classical denotation). Inquisitive component: the difference between w1 and w2 is not an issue in the discourse. • The omission of a pair (w1 ,w2 ) indicates that the difference between w1 and w2 is an issue (though both might still be live options). • Consider a model with only four worlds, two propositions, and two individuals as in (6): 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 no (identity pairs of) worlds have been eliminated. • (7) is indifferent because the relation in (7) is totally connected (i.e. there are arrows connecting each pair of worlds). Now, consider the denotation for P = drink-atole! (juan) as in the left figure in (8) (8)

Denotation for drink-atole! (juan):

Denotation for drink-atole! (daniel):

wjd

wd

wjd

wd

wj

w∅

wj

w∅

• drink-atole! (juan) (left) is informative because it eliminates worlds wd and w∅ from the context set (technically, it eliminates identity pairs of worlds). • Again, 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. 3

Non-interrogative questions in Yukatek Maya

2.2

(Unfocused) Disjunction in Inquisitive Semantics

Consider instead the update of an ordinary disjunction: [drink-atole! (juan) ∨ drink-atole! (daniel)] (9)

Denotation of 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). • (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.3 • 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.

3

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). • 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: ‘Was it Juan who drank the atole or was it Daniel?’ Assertion Reading: ‘It was Juan or Daniel who 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. 3 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]

4

Non-interrogative questions in Yukatek Maya

3.1

Semantics of the Focus/Cleft Position

The term Focus in the literature refers to what Kiss (1998) has argued are two distinct notions (Identificational focus vs. 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’

• A DP in the focus position, (11), differs from its non-focused counterpart at least in having the presupposition in (12) (assuming a classical interpretation of the existential): (12)

3.2

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

Deriving the Ambiguity of Focused Disjunctions

Consider again (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: ‘Was it Juan who drank the atole or was it Daniel?’ Assertion Reading: ‘It was Juan or Daniel who 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 at-issue update of (13), the input state is as in (14). (14)

Presupposition of the Yukatek Maya focus/cleft:

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 at-issue update of the disjunction is the same as ordinary disjunctions, repeated in (15): 4 We briefly undertake a more fine-grained comparison of the difference between YM focus clefts and English it-clefts in §6.

5

Non-interrogative questions in Yukatek Maya (15)

At-issue denotation 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 presupposed input state is to disconnect wj and wd (i.e. to remove the pairs (wj ,wd ) and (wd ,wj )). • The disjunction in (15) takes an input state with a single alternative and creates an output state with multiple alternatives, one per disjunct. • The update in (15) raises the issue of whether Juan drank the atole or Daniel did and contributes nothing else 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 like (13) can still be interpreted as an assertion provided that it is informative. • Assume a model where, in addition to the four worlds above, there is a world, wm , where Juan and Daniel did not drink the atole, but someone else (say, Maribel) did. • Given the existential presupposition, the input state will be as in (16). (16) wjd

Presupposition of the focus/cleft (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. • As indicated in (17), a sentence is interpreted as a question iff it is both inquisitive and uninformative (we can call this ‘the Inquisitive Principle’). (17)

4

Informative Uninformative

Inquisitive Assertion Question

Uninquisitive Assertion Assertion (Tautology)

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 (18) (repeated from (2) above), involve the focus/cleft construction and the disjunctive coordinator, w´ aa.5 (18)

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

• Unlike focused disjunctions, (18) is obligatorily interpreted as a question.

4.2

Polar Questions as Disjunctions with One Disjunct

• We analyze (18) as a single-disjunct version of a focused disjunction as schematized in (19). (19)

[Juan w´aa

] uk’ le sa’-o’

• The covert alternative question approach to (18) is supported by the fact that particle answers (e.g. ‘yes’, ‘no’, or ‘maybe’) are not licensed for such questions. 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): 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) 5 The coda [h] in (18) 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

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 (18), however, 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 (18) will only be interpretable as a question. Summary: Polar Questions like (18) 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.

5

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 (20) where the polarity is overt (i.e. when it is negative). (20)

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 position of the disjunctive coordinator, w´ aa, 6 is prosodically determined (it leans on the first prosodic word as in (21)). (21)

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 more detailed discussion of the position of w´ aa in such questions.

8

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, negation is the exhaustive set of elements disjoint from the positive polarity marker. The whole disjunction for (21) has the form in (22). (22)

5.3

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

(Obligatory) Interpretation as a Question

According to the inquisitive principle above, a sentence is interpreted as a question iff it is inquisitive and uninformative. • (22) 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.

6

Conclusion

Yukatek Maya has several constructions which function as questions despite the apparent lack of interrogative morphosyntax. • We have derived their use as questions from the interaction of two semantic elements which are quite widespread (inquisitive elements and focus). • We expect, then, that these elements in other languages will also be interpreted as questions. Polar Questions: While we mostly leave the exploration of the cross-linguistic predictions of our analysis for future work, the pattern does indeed appear more general. • One result of our account is that it makes sense of the peculiar fact that w´ aa in polar questions either occurs (i) after the first syntactic constituent a certain kind (a focused XP) or (ii) after the first prosodic constituent (the prosodic word). • This dual distribution for polar question particles is attested in unrelated languages, including Bulgarian li and Latin -ne (both of which are historically related to disjunctive coordinators). Wh-questions: The relationship between focus, indefinites and wh-questions in many languages (Yukatek Maya, Hungarian, etc.) can 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 existential presupposition. 9

Non-interrogative questions in Yukatek Maya • Indefinites, like disjunctions, have a capacity to latently raise issues; they are inquisitive. • Focused indefinites, then, would meet both requirements of the Inquisitive Principle and be interpreted as questions. • Note that the present theory differs from much previous work on focus and questions (Beck (2006), Eckhardt (2007), Tonhauser (2003) inter alia) which takes focus to be responsible for the issue-raising capacity of questions. One apparent counterexample are English it-clefts, (23), which are not interpreted as questions: (23)

a. b.

It was John or Daniel who drank the atole. #?It was someone who drank the atole.

• Note, however, that the examples in (23) are infelicitous in exactly the contexts where their Yukatek Maya counterparts are interpreted as questions. • For example, (23-a) is only felicitous in contexts where there is some other possible atoledrinker being ruled out (e.g. Maribel). • It seems that the English it-clefts in (23) presuppose not only that someone drank the atole, but also that who is at-issue. • The presupposition of the cleft in (23) is itself inquisitive. • The infelicity of (23-b), then, arises because its at-issue and presuppositional contributions are the same.

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. Bartels, Christine (1999) The intonation of English statements and questions. Garland Publishing. Beck, Sigrid (2006) Intervention Effects Follow from Focus Interpretation. Natural Language Semantics : 1–56. Echevarr´ıa Lope, Jorge (2004) X-La’ Boon Suumij. In Words of the True Peoples, 54–72. Eckhardt, Regine (2007) Inherent Focus on Wh-Phrases. In Proceedings of Sinn und Bedeutung 11. Groenendijk, Jeroen (1999) The logic of interrogation. In Proceedings of SALT IX. Groenendijk, Jeroen (2007) Inquisitive Semantics: Two Possibilities for Disjunction. In Tbilisi 2007: Seventh International Tbilisi Symposium on Language, Logic, and Communication. 10

Non-interrogative questions in Yukatek Maya Groenendijk, Jeroen & Floris Roelofsen (2009) Inquisitive Semantics and Pragmatics. In Proceedings of SPR 09. Kiss, Katalin (1998) Identificational Focus versus Information Focus. Language 74: 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. Tonhauser, Judith (2003) On the Syntax and Semantics of Content Questions in Yucatec Maya. In Proceedings of the 6th Workshop on American Indian Languages (WAIL). Zimmermann, Thomas Ede (2000) Free Choice Disjunction and Epistemic Possibility. Natural Language Semantics 8: 255–290.

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