A Correlative Typology Mixing Syntactic and Semantic Parameters

Abstract

The Dravidian correlative is formed with a wh-item containing sentence with -oo at the clause edge. The disjunction marker -oo in Dravidian languages participates in coordinating elements, forming indefinites, and questions. Given that the canonical semantics of correlatives, (Dayal 1991, 1995) analyses them as definite descriptions, which bind the pronoun variable via predicate abstraction, the question is what -oo is doing here, and how does the semantic composition work. This sketch towards a compositional derivation of the Dravidian correlative based on a question denotation proves that it is not only feasible but also quite advantageous—we keep a unified semantics of -oo, the disjunction marker that also participates in forming indefinites, and questions, and derive a number of properties of the Dravidian correlative from the semantics of questions and answers. In the literature, the typology of correlatives has been proposed to have two syntactic parameters—one, the kind of relative clause it originates from—EHRC, IHRC, FR; and two, the kind of left dislocation involved—HTLD, CLD, CLLD. We propose to add to this typology a third and semantic parameter, its denotation—property or propositional. We show that the Dravidian correlative is built out of the semantic choice of a proposition-based denotation. We locate this semantic parameter itself in the denotation of the wh-items of the language, its lexical semantic entry—as sets of alternatives or as property free variables.

A Case for Semantic Parameters

I would like to thank Pritha Chandra, the organizer of the Workshop on Approaches to Language Variation, IIT Delhi, and the audience for helpful discussion and comments.

One of the primary goals of current linguistic theory is to explain and locate cross-linguistic variation in human language. What is the locus of parametric variation? There have been various proposals in the development of linguistic theory in accounting for this:

• 1. UG = Universal pool of features + Universal principles of derivation/interpretation. This itself has seen three stages:

  • (a) Grammatical Parameters = Variation in principles + Variation in bundling of features into Lexical Items (LI)

  • (b) Functional Parameters = Invariant principles + Variation in functional LI bundling (Borer, 1984)

  • (c) Externalized Parameters = All parameters at PF (Chomsky, 2010, et seq.)

• 2. UG specified parameters versus UG underspecified parameters

  • (a) UG very rich: Parameter settings and values provided by UG

  • (b) Downsizing of UG: To explain sudden and recent emergence of particular properties of Human Language.

    • i. Parameters not provided by UG, but ‘emerge’ at points where UG is underspecified.

    • ii. (More) role for general cognitive processes: Third-factors (F3) of data processing, analysis and bootstrapping.

Most of these proposals have always focused on the PF or Syntactic side of things and have located variation there. In this paper, we focus on the question of whether there are semantic parameters. Semantic compositional and interpretational principles are considered invariant across languages (Higginbotham, 1986). But languages do vary in interpretation—tense/aspect, modification, comparison, complex predicates, etc. (Beck, 2018). There have been found to be remarkably few universals in semantics (Von Fintel & Matthewson, 2008). At the same time, few (if any) clear examples of parametric variation in semantics are identified. We all know of Comparative Syntax. Who has heard of Comparative Semantics? As Beck (2018, p. 3) says ‘the field has not yet developed a theory of semantic variation.’

But what could semantic parameters look like? One semantic parameter that has been proposed is the Nominal Mapping Parameter (Chierchia, 1998):

• 1. Nouns are predicative = Romance languages

• 2. Nouns are argumental = Chinese

Another semantic parameter that has been proposed has to do with Polarity Items (Chierchia, 2013), (1).

In this paper, we explore one semantic parameter, the denotation of wh-items. We do this by taking the case study of the Dravidian correlative and their role of the disjunctive particle -oo in the correlative, while at the same time looking to unify the semantics of this disjunctive particle-oo across its various appearances. In unifying the semantics of the -oo particle in Dravidian, we end up proposing a question semantics for the Dravidian correlative. We go on to propose a typology of correlatives based on a mix of syntactic parameters—headed-ness and kind of dislocation; and a semantic parameter—denotation of wh-items. This paper thus becomes part of a larger approach to the issue of cross-linguistic variation: Semantic parameters.

(1)	Exhaustifying operators	Formal features	Type of alternatives	Modus operandi	Operandum	Examples of targets
	${\text{E}}_{\sigma {\text{A}}}$	$[\sigma ]$	Degreealternatives, $\angle$ ordered Das	Single agree or Multiple agree	Assertive content	Give damn Koii bhii
	${\text{E}}_{\sigma {\text{A}}}^{\text{S}}$	$[\sigma ]$	$\sigma {\text{As}}$	Single agre or Multiple agree	Assertive content + presuppositions	Sleep a wink
	${\text{O}}_{\sigma {\text{A}}}$	$[\sigma ][{\text{n-}} \sigma ]$	$\sigma {\text{As}}$	Single agree or multiple agree	Assertive content	Ever, alcun, mai
	${\text{O}}_{{\text{C}}/\sigma {\text{A}}}$	$[\sigma ]$	${\text{C}}/\sigma {\text{As}}$ Contextually pruned $\sigma {\text{As}}$	Single agree or multiple agree	Assertive content	Some, and
	${\text{O}}_{{\text{DA}}}$	$[{\text{D}}][{\text{n-}}{\text{D}}]$	${\text{ DAs }}$	Multiple agree	Assertive content	Ever, alcun, mai
	${\text{O}}_{{\text{Exh-}} {\text{DA}}}$	$[{\text{D}}]$	Pre-exhaustified DAs	Multiple agree	Assertive content	Any, irgendein, some
	${\text{O}}_{{\text{ALT}}}^{\text{s}}$	$\begin{aligned} & \left[ {\left[ {\sigma ,{\text{D}}} \right]} \right] \\ & \left[ {\left[ {{\text{n - }}\sigma {\text{,D}}} \right]} \right] \\ \end{aligned}$	$\sigma {\text{A}} \cup {\text{DA}}$	Multiple agree	Assertive content + presupposition	In weeks Strong Nwords
	${\text{O}}_{\sigma {\text{A}}/{\text{DA}}}^{{\text{PS}}}$	$[{\text{PS-}}\sigma ,{\text{D}}]$	${\text{ PS - }}\sigma {\text{A}}/{\text{PS}} - {\text{DA}}$	Multiple agree or single agree	Assertive content	Qualsiasi Un N qualsiasi
	${\text{O}}_{\pi {\text{A}}}$	$[\pi ]$	$\pi {\text{As}}$ (presuppositional alternatives)	single agree	Assertive content	Because, Know

Semantics of the Dravidian Disjunctive Particle-oo

The disjunction marker-oo in Dravidian languages participates in coordinating elements, forming indefinites, forming questions, and even forming correlatives. These multiple roles for this marker are by no means special to Dravidian—Sinhala Slade (2011); Japanese Kuroda (1965); among others. These have been dubbed KA particles–Mitrovic (2014), Szabolcsi (2015). A cross-linguistic pattern of KA particles is shown in (2)

(2)
	TB	DR				IA			Jap	Slavic
Roles of -KA	Mei	Tel	Kan	Tam	Mal	Hin	Ban	Sin	Jap	Hun
Disjunction	-ra -la	-oo	-oo	-oo	-oo			-hari	-ka	vagy
Polar question particle embedded								-de
Polar question particle matrix		-aa	-aa	-aa				-hari
Constituent question particle	-no	-oo	-oo	-oo
Existential quantifier particle										vala
Correlative marker	-ke

XP-oo

The KA particle in Dravidian -oo attaches at the phrasal level, as a disjunctive marker, as shown in (3).

(3)	a.	john-*(oo)	bill-*(oo)	peter-*(o o)	MALAYALAM/KANNADA/TELUGU/TAMIL
		John-OO	Bill-OO	Peter-OO
		‘John, Bill or Peter’
	b.	john-oo	bill-oo varum		MALAYALAM
		John-oO Bill-OO come-will
		‘John or Bill will come.’

When the disjunct is a DP with an overt case-marker, the -oo comes outside the case-marker, as shown in (4).

(4)	a.	doDDa	bekki-g-oo	chikka naayi-g-oo
		big	Cat-DAT-oo small	dog-DAT-oo	KANNADA (Amritavalli, 2003)
		‘for/to a big cat or a small dog’
	b.	ada-ra	meel-oo ida-ra	keLag-oo
		that-GEN top-DISJ this-GEN under-DISJ
		‘on top of that or under this’
	c.	ada-ra	meel-inda-loo ida-ra	keLag-inda-loo
		that-GEN top-ABL-DISJ this-GEN under-ABL-DISJ
		‘from on top of that or from under this’

The -oo also acts as a QUANTIFIER PARTICLE when added to wh-words, and forms existential quantifiers –epistemic indefinites, as shown in (5).

(5)	a.	MALAYALAM (Jayaseelan, 2001)
		aar-oo who-OO	somebody
		ent-oo what-OO	something
		ewiDe-(y)oo where-OO	somewhere
		eppoozh-oo when-OO	sometime
		eNNine-(y)oo how-OO	somehow
	b.	naan	iruTT-il	aar-e-(y)oo	toTTu
		I	darkness-in who-ACC-OO touched
		‘I touched somebody in the dark.’

As Jayaseelan (2001, p. 132) notes: ‘The existential quantifiers are not polarity sensitive. They have a more restricted meaning, they can be used only when the identity of the person or thing being described is not known to the speaker.’ This is shown in (6).

(6)	a.	naan	iruTT-il	aar-e-(y)oo	toTTu
		I	darkness-in who-ACC-DISJ touched
		‘I touched somebody in the dark.’
	b.	#	naan innale	aar-e-(y)oo	paricayappeTTu
		I	yesterday who-ACC-DISJ met
		‘I met somebody yesterday.’

Sentence Final Particle -OO

This KA particle in Dravidian, -oo also occurs clause or sentence finally. When it occurs sentence finally, it forms POL/ALT questions. Malayalam Pol/Alt Qs are formed by adding -oo to each clause; Telugu/Tamil/Kannada embedded Pol/Alt Qs have a clause final -oo, as shown in (7).

(7)	a.	John wannu-(w)oo?		MALAYALAM
		John came-OO
		‘Did John come?’
	b.	John wannu-(w)oo illa-(y)oo?
		John came-OO	not-OO
		‘Did John come or not?’
	c.	John wacceeD-oo aDugu!		TELUGU
		John came-OO	ask
		‘Ask if John came!’
	d.	John wacceeD-oo leed-oo aDugu!
		John came-oo	not-oo	ask
		‘Ask if John came or not!’

Unlike in Malayalam (7a), the particle -oo cannot be used in a matrix clause to form Pol or Alt Qs, in Telugu, Kannada and Tamil, as shown in (8) from Telugu.

(8)	*anu	uma-ki	pustakam iccind-oo?
	Anu	Uma-DAT book	gave-OO
	‘Did Anu give the book to Uma?’

In Tamil, Kannada and Telugu, a question particle, that I’ll call the Polar Question Particle, Q, is required in Matrix Pol/Alt Qs, as shown in (9) from Telugu. There is no disjunction marker here.

(9)	a.	anu	uma-ki	pustakam iccind-aa?
		Anu Uma-DAT book gave-Qp
		‘Did Anu give the book to Uma?’
	b.	anu	uma-ki	pustakam iccind-aa leed-aa?	[Polar Alt Q]
		Anu Uma-DAT book gave-Qp not+FIN-Qp
		‘Did Anu give the book to Uma or not?’
	c.	anu	uma-ki	pustakam iccind-aa ivva-leed-aa?
		Anu Uma-DAT book gave-Qp gave-not+FIN-Qp
		‘Did Anu give the book to Uma or not give?’
	d.	anu	uma-ki	pustakam iccindaa pen iccind-aa?	[Alt Q]
		Anu Uma-DAT book gave-Qp pen gave-Qp
		‘Did Anu give Uma the book or the pen?’

This particle -oo also forms wh-QUESTIONS in Telugu, Tamil and Kannada. Embedded wh-questions (and Pol/Alt Qs) are formed by adding -oo to the clause, as shown in (10).

10	a.	Naaku evaru wacceer-oo telusu				TELUGU
		I-DAT	who	came-oo	know
		‘I know who came.’
	b.	anu	uma-ki	pustakam iccind-oo	leed-oo	naa-ku telusu
		Anu Uma-DAT book		gave–DISJ not–DISJ I-DAT		know
		‘I know if Anu gave the book to Uma’
	c.	anu	uma-ki	pustakam iccind-oo	pen iccind-oo naaku telusu?		[Alt Q]
		Anu Uma-DAT book		gave-DISJ pen gave-DISJ I-DAT		know
		‘I know if Anu give Uma the book or the pen.’

However, Malayalam wh-questions are not marked with -oo, as shown in (11).

11	a.	aar. wannu?
		who came
		‘who came?’
	b.	awan ewiDe pooyi
		he	where went
		‘Where did he go?’
	c.	[awan ewiDe pooyi enn] naan coodiccu
		he	where went C	I	asked
		‘I asked where he went.’

But contrary to this observational fact, Jayaseelan (2001) argues that wh-questions in Malayalam also have an underlying -oo.

In matrix clauses in Kannada, Tamil and Telugu, the question particle -oo with a wh-word, or in an Alt Q, gives the meaning of ‘wonder,’ as shown in (12).

12	a.	anu	uma-ki	eemi iccind-oo	TELUGU
		Anu Uma-DAT what gave-OO
		‘I wonder what Anu gave to Uma’
	b.	anu	uma-ki	pustakam iccind-oo leed-oo?	[Polar Alt Q]
		Anu Uma-DAT book		gave-OO not+FIN-OO
		‘I wonder if Anu gave the book to Uma or not’
	c.	anu	uma-ki	pustakam iccind-oo ivva-leed-oo?
		Anu Uma-DAT book		gave-OO gave-not+FIN-OO
		‘I wonder if Anu gave the book to Uma or not give.’
	d.	anu	uma-ki	pustakam iccind-oo pen iccind-oo?	[Alt Q]
		Anu Uma-DAT book	gave-OO	pen gave-OO
		‘I wonder if Anu gave Uma the book or the pen’

A summary of the distribution of -oo across the Dravidian languages in shown in (13)

13	Role of -KA	Malayalam	Telugu	Kannada	Tamil
	disjunction	-oo	-oo	-oo	-oo
	existential quantifier particle	-oo	-oo	-oo	-oo
	Pol/Atl-Q particle matrix	-oo	-aa	-aa	-aa
	Pol/Alt-Q particle embedded	-oo	-oo	-oo	-oo
	wh-Q particle matrix	–	–	–	–
	wh-Q particle embedded	–	-oo	-oo	-oo

Why Does KA Take on Multiple Roles?

On the one hand, the role of KA particles in multiple functions is taken to be homophony, and each role is treated in isolation (Cable, 2010). On the other, this is taken to signify an underlying property that justifies its many roles, and unification is attempted —Jayaseelan (2011); Szabolcsi (2015); Slade (2011), etc. The latest and perhaps most unificatory in this series is Uegaki et al. (2018).

Jayaseelan (2001, 2011, 2014) analyses coordination as being made up of the two operations: i. concatenation ii. serial substitution. The two operations are realized by two distinct functional heads in the syntax of coordination. Languages realize either one of these heads but not both. English and/or, are copies of the concatenation operator; the same appears to be true of Hindi aur/yaa. By contrast, Japanese/Malayalam coordination markers are copies of the substitution operator (choice function). Disjunction marker -oo which ‘marks off’ each disjunct is a copy of the substitution operator (choice function), and the concatenation operator has no lexical realization. A coordination operator is ‘silent’ (not phonologically realized) when its copies are present on the coordinands. The two parametrized structures are shown in (14).

(14)

But the -oo that appears in existential quantifiers, correlative clauses and questions is the realization of the choice-function operator itself. For him, a wh-word signifies a focused variable (Nishigauchi, 1990); and a disjunction choice-function operator applied to a variable interprets it as an ‘infinite disjunction’ (the meaning of an existential quantifier). The operator ‘applies to’ the question word by ‘association with focus’ (Rooth, 1985). The disjunction marker doubles as the question marker because a question clause has the disjunction operator in the head position of ForceP. All Malayalam questions have a clause final -oo, although this is overt only in Pol/Alt Qs. The quantifier exists in two parts. Universally, says Jayaseelan, questions contain a disjunction operator generated as the head of ForceP. From this position, it applies to question words by association with focus, yielding question interpretations.

Uegaki et al. (2018) treats each appearance of ka, the Japanese counterpart of -oo, as having only one semantic role, that of copying what is in the alternative semantic dimension into the ordinary semantic dimension, in a two-tier alternative semantics wh-in-situ (Beck, 2006; Kotek, 2014) model, as shown in (15).

15	$\left[ {\alpha {\text{ka}}} \right]^0 = \left[ \alpha \right]^{alt} \;\;{\text{and}}\;\;\left[ {\alpha {\text{ka}}} \right]^{alt} \left\{ {\left[ \alpha \right]^{alt} } \right\}$

When alternatives enter the ordinary dimension early in the sentence precipitated by a low attached ka, they cannot be handled by the semantic composition, and a repair strategy of folding the alternatives into a single (existential) element kicks in, as shown in (16).

(16)	a.	ka + wh-item = existential indefinite
	b.	ka + α … β = disjunction

But when ka attaches high, in the left periphery, the alternatives entering into the ordinary dimension can be handled by a question operator, as shown in (17).

(17)	a.	clause final ka + wh-item = wh-Q
	b.	clause final ka + α … β = Alt Q

This nice bifurcation in the readings, at two levels, speaks to this explanation, as shown in (18).

(18)	-oo is:	subclausal	Clause final
	α … β	declarative disjunction	Alt Q
	wh-	existential quantifier	wh-Q

Why Is There an -Oo in the Dravidian Correlative?

The Dravidian KA, the -oo, also appears in correlatives, as a correlative marker, as shown in (19). As Subbarao (2008, p. 64) notes ‘When the head of the relative clause is indefinite, non-specific, and hypothetical, the clause is labelled a free relative clause. In Dravidian languages and in some Tibeto-Burman languages, the main clause and the subordinate clause in such cases are linked by a marker called the “dubitative marker” (dub mkr) in traditional grammars.’

(19)	a.	[nii eng-enge pooriy-oo] angellam naanum varuveen	TAMIL
		you where-where go-OO there-all I-also will-come
		‘I too will come wherever you go.’
	b.	enn-e aar. nuLLi-(y)oo, awan duST-avan aaN	MALAYALAM
		I-ACC who pinched-OO he wicked-man is
		‘The person who pinched me is wicked.’

Interestingly, the morphosyntactic shape of the correlative is the same as the question, as shown in (20).

(20)	a.	wh-QUESTION
		eemi konnaaD-oo aDigeenu	TELUGU
		what bought-OO	asked
		‘(I) asked what (he) bought.’
	b.	CORRELATIVE
		eemi konnaaD-oo (adi) tinnaanu
		what bought-OO	that ate
		‘What (he) bought, that (I) ate.’

The [clause final +wh-] cell thus gets another occupant in Dravidian, as shown in (21).

(21)	-oo is:	subclausal	Clause final
	α … β	declarative disjunction	Alt Q
	wh-	existential quantifier	wh-Q/correlative

We can now update the cross-linguistic pattern of KA particles with the correlative role, as shown in (22), with the KA of Dravidian also playing a role in forming correlatives.

(22)	TB	DR				IA			Jap	Slavic
Roles of -KA	Mei	Tel	Kan	Tam	Mal	Hin	Ban	Sin	Jap	Hun
disjunction	-ra -la	-oo	-oo	-oo	-oo			-hari	-ka	vagy
polar question particle embedded								-de
polar question particle matrix		-aa	-aa	-aa
constituent question particle	-no
existential quantifier particle			-oo	-oo				-hari		vala
correlative marker	-ke	-oo

What semantic role does -oo have in correlatives? Correlative semantics is standardly given a denotation of properties not propositions (which is what questions are). The canonical semantics of correlatives (Dayal 1991, 1995) analyses them as definite descriptions, which bind the pronoun variable via predicate abstraction, as shown in (23).

(23)	a.	[jo laDakaa gaayaa hai]i voi mera bhai hai	HINDI
		REL-P boy Sang is he my brother is
		‘which boy sang, he is my brother.’
	b.	[[ι(λx.x sang and x is a boy)] [λ2 he2 is my brother]]

The question then is what -oo is doing here in the correlative, and if it has the Uegaki KA denotation, then how does the semantic composition work. The correlative, with its two word order locations illustrated in (24), is thus a problem.

(24)	a.	LEFT-ADJOINED CORRELATIVE
		[eemi tecceen-oo] ravi adi tinnaaDu	TELUGU
		what brought-OO Ravi that ate
		‘Ravi ate what (I) brought.’
	b.	DEM-ADJOINED CORRELATIVE
		ravi uma-ki[[eemi tecceen-oo] adi] icceeDu
		ravi uma-DAT what brought-OO that gave
		‘Ravi gave to Uma what (I) brought.’

Can we build the Dravidian correlative out of a question denotation? Our answer is: yes, as we show in the next section.

A Question Semantics for the Dravidian Correlative

Jayaseelan (2001) treats the appearance of -oo in questions and correlatives as the disjunction operator. This disjunction operator has the semantics of the logical boolean operator . For him, a correlative clause has the same structure as a question, but it is not interpreted as a request for information. Questions then, according to him, have an additional ‘request-for-information’ meaning, which could be accommodated if the head of ForceP contained, besides the disjunction operator, ‘another’ element. Also, the question’s illocutionary force may be signalled by intonation (or other means). There is thus no ‘question meaning’ in the correlative. Our analysis will however take the opposite position and integrate a question denotation into the correlative, as shown below.

Demirok (2017) already proposes that the Turkish correlative is built on wh-question semantics and an additional conditional semantics, reflected in the morphosyntax, as shown in (25).

(25)	[John kim-i davet-et-ti-yse]i oi gel-di	TURKISH
	John who-ACC invite-PST-SA DEM come-PST
	‘Whoever John invited, came.’

Each of the propositions in the Q-denotation pointwise restricts the modal conditional, thus delivering a free choice (FC) meaning. We get a generalized conjunction of conditional statements. The main clause DEM is given an E-type denotation. This works for Turkish because Turkish correlatives have a FC interpretation, but it won’t work for Dravidian because they have a definite interpretation.

Chierchia & Caponigro (2013) propose that all free relatives (FRs) are built on top of a question denotation in two steps, as shown in (26).

(26)	a.	a TP (‘Topical Property’) operator that extracts properties from questions: TP(what Mary cooked?) = λx. λw Mary cooked x in w
	b.	John ate[DP what [C P Mary cooked t]]
	c.	= John ate Drel (TP(what Mary cooked t?))
		= ∃x [x = ιx M cookedw x] ∧ J atew x

FRs are DPs with the same denotation as short answers to Qs. The subset relation of wh-items in free relatives to those of questions is due to the D_rel operator that is a partial function from question to free relative denotations.

But in Dravidian, all the wh-words that occur in questions also occur in correlatives. So we don’t need a partial mapping D_rel operator and instead can build directly on top of the answerhood operator, which occurs with all wh-questions. However what we need to use is the short answer to a question (of type e), and not the full answer, of type $\left\langle {s,t} \right\rangle$, since it has to bind the demonstrative in the main clause.

Liu (2017) develops a structured meaning for questions in an alternative semantics framework, to explain the Mandarin wh-conditional construction, out of which we can easily form a short answerhood operator, as he points out, and as shown in (27).

(27)

Dayal-answer: a possible answer of Q is a focus-background pair 〈F, B〉 belonging to Q; A Dayal-answer at w is the unique 〈F, B〉 that is the strongest true answer at w.

$\begin{aligned} & {\text{Ans}}({\text{Q}})({\text{w}}) = \iota \langle {\text{F}},{\text{B}}\rangle \in {\text{Q}}\left[ {({\text{B}})({\text{F}})({\text{w}}) = 1 \wedge \forall \left\langle {{\text{F}^{\prime}},{\text{B}^{\prime}}} \right\rangle \in {\text{Q}}\left[ {\left( {{\text{B}^{\prime}}} \right)\left( {{\text{F}^{\prime}}} \right)({\text{w}})} \right.} \right. \\ & \quad \quad \quad = \left. {\left. {1 \to B(F) \subseteq {\text{B}^{\prime}}\left( {{\text{F}^{\prime}}} \right)} \right]} \right] \\ \end{aligned}$

The denotation of the short answer of a question can be directly read off its Dayal-answer, which is just the F-part of the latter. We define the short answerhood operator, (28), using the Fox (2013) version of answerhood (that allows mention-some interpretations), and Liu’s 〈Focus Background〉 structure.

(28)	ANSs (Q)(w) = $\left \{F\left| {F \in \langle F,B\rangle \wedge w \in \langle F,B\rangle } \right. \in Q \wedge \forall \langle F^\prime,B^\prime\rangle \left[w \in \left\langle {F^\prime,B}^{\prime} \right\rangle \in Q \to \langle F^\prime,B^\prime\rangle \langle F,B\rangle\right]\right\}$
	({F| F is the focus denotation of $\langle F,B\rangle$F,B, a true proposition in Q, and $\langle F,B\rangle$ is not asymmetrically entailed by any true propositions in Q})

A Correlative Typology with a Semantic Parameter

Finally, moving to the larger picture, towards a correlative typology, we find that Cinque (2010, p. 210) posits two syntactic points of variation for correlatives: ‘Correlatives (at least those that do not contain multiple wh-phrases) are embedded in a DP which is left dislocated at the beginning of the matrix clause and is resumed by a correlative pro-form (or a full DP) inside the matrix clause.’ He considers Multiple correlatives as non-relative, free adjunct, CPs.

The left dislocation is of three possible types, as shown in (29).

(29)	a.	CLD (Contrastive Left Dislocation) = German, Bulgarian
	b.	CLLD (Clitic Left Dislocation) = Italian
	c.	HTLD (Hanging Topic Left Dislocation) = Hungarian

‘The left dislocated DP may contain, depending on the language, either an externally headed postnominal, or an externally headed prenominal, or an internally headed, or a headless (free), relative clause.’ Cinque (2010, p. 212). Thus, the kind of relative clause the correlative originates from is of the following types, as shown in (30).

(30)	a.	Externally headed postnominal = Slavic, Warlpiri
	b.	‘Headless’ /'free’ relative = Bulgarian, German, Italian
	c.	Externally headed prenominal = Sinhala
	d.	Internally headed = Wappo, Bambara, Georgian (Bhatt & Nash 2018)

To these two parameters of variation, both syntactic, that give rise to the variety of correlatives that are found cross-linguistically, we add a third and semantic point of variation, i.e. the denotation—property-based or propositional, as shown in (31). As we saw, Demirok (2017) builds propositions out of the wh-phrase containing antecedents, which pointwise restrict the modal associated with the conditional operator that is suffixed clause finally to the antecedent. We maintain, based on the occurrence of -oo suffixed clause finally to the antecedent, that in Dravidian also, the wh-item containing antecedent delivers propositional meaning.

(31)	a.	property-based = Georgian (Bhatt & Nash 2018), Hindi-Urdu (Dayal, 1995)
	b.	propositional = Turkish (Demirok, 2017), Dravidian

We locate this semantic parameter itself in the denotation of the wh-items of the language, its lexical semantic entry –as sets of alternatives or as property free variables. Thus, what we are proposing is a wh-word semantic parameter. The semantic entry typology for interrogative pronouns that we propose is shown in (32).

32	a.	wh-words as property free variables (Demirok, 2017, Šimık 2018):
		i. ${who}$ = $\lambda {\text{x}}.\lambda {\text{w}}.{\text{x}}$ in human in w Movement creates a semantic predicate:
		ii. ${{\text{ who }}\lambda_i {\text{ John hit }}t_i }$ = $\lambda {\text{x}}.\lambda {\text{w}}$ john hit x in w Combining with an iota operator turns the predicate into a definite description, that forms a wh-FR or correlative, etc.:
		iii. $\left[ {{\text{D}}\left[ {{\text{ who }}\lambda_i {\text{ John hit t}}_i } \right]} \right]$ = $\iota {\text{x}}.\lambda {\text{w}}.$ john hit x in w
	b	wh-words as sets of alternatives:
		i. ${{\text{who}}}^{\circ} = {\text{ undefined }}$ ${\text{ who }}^{dlt} = \left\{ {{\text{x}}\left| {{\text{x is }} \in {\text{ HUMAN}}} \right.} \right\}$ Composing with a predicate:
		ii. ${\text{ ran }}^{\circ} = \, \lambda {\text{x}},\lambda {\text{w}},{\text{ran}} ({\text{x}},{\text{w}})$ ${\text{ ran }} ^{alt} = = \{ \lambda x,\lambda w.{\text{ran}} ({\text{x}},{\text{w}})\}$ ${\text{Remember }} {\alpha {\text{KA}}} ^{\circ} = \alpha ^{alt} \;\;{\text{and}}\;\, {\alpha {\text{KA}}} ^{alt} = \left\{ { \alpha^{alt} } \right\}$
		iii. ${\text{ who -}} {\text{oo ran}} ^{\circ}$ = $= \exists {\text{x}}.\lambda {\text{w}} \cdot {\text{ran}} ({\text{x}},{\text{w}})\quad {\text{By }}\left[ \exists \right] \, ^{\circ} {\text{ repair }}$ ${ whoran} -{oo} ^{\circ}$ = $\{ \lambda x,\lambda w,{\text{ran}} (x,w),x{\text{ is human in }}w\}$

Combining with answerhood operators or pointwise restriction of conditional modals yields (definite) correlatives and Free-Choice correlatives, respectively.

Conclusions

This sketch towards a compositional derivation of the Dravidian correlative based on a question denotation leads us to conclude that it is not only feasible but also quite advantageous:

• 1. We keep a unified semantics of -oo, the Dravidian KA particle.

• 2. We derive a number of properties of the correlative from the semantics of questions and answers.