Focus–cleft merger

This proposal, which may colloquially be termed the kü proposal, wishes to merge two features of the language:

• Focus markers, which attach to words or phrases and which express a relation of the marked material with respect to the rest of the clause – e.g., kú highlights information that the listener should consider as new and important, tó states it is only this choice of value that satisfies the clause, etc. For instance, Chuq jí kú máoja would translate as ‘I am eating the banana’ or ‘It is the banana that I’m eating’.
• Clefts, or nä phrases, which allow one to place a noun phrase or an adverbial at the front of a clause, and in the former case refer back to the noun phrase with hóa, primarily for convenience and not for focus. For instance, Máoja nä chuq jí hóa is another way of saying Chuq jí máoja but possibly more convenient (especially if instead of máoja we’re dealing with a looong phrase).
• Topic phrases, or bï phrases, which serve the opposite function to focus markers: they set the backdrop or context for the focused information. For instance, Báq maoja bï, bu cho jí hóa ‘As far as bananas go, I don’t like them’.

As a fun fact, the English construction found in ‘It is the banana that I’m eating’, which extracts ‘the banana’ to the front of the clause this way, is itself called a cleft (Wikipedia link)! You should see where we’re going with this.

The tofu of the proposal

We’ll be assuming Lynn’s Simple Focus proposal applies. (tl;dr, it makes all kú always bear , displacing the complex and incomplete rules found in the refgram, and also makes some additional statements about the scope prefixes operate on, which is also irregular officially.) It also frees for us, which will be useful right below:

The part where we let focus markers be clefts

Essentially, allow focus kü phrase, with exactly the same semantics as kú focus nä phrase. hóa is still bound in case of a noun phrase. Examples examples:

Máoja kü chuq jí hóa

[= Kú máoja nä chuq jí hóa]

[= Chuq jí kú máoja]

‘It is the banana I’m eating’

Báq kanı tö deq peo hóa ní chuao

[= Tó báq kanı nä deq peo hóa ní chuao]

[= Deq peo tó báq kanı ní chuao]

‘Only rabbits can slip through this hole’

Ní chuao tö deq peo báq kanı hóa

[= Tó ní chuao nä deq peo báq kanı hóa]

[= Deq peo báq kanı tó ní chuao]

‘It is just this hole that rabbits are allowed to pass’

He râo báq kıachaq bëı loı jí tú

[= He, ꝡä béı râo báq kıachaq nä loı jí tú]

‘It’s on Mondays (not on some other implied occasion / under some other implied condition) that I hate everything’

The win from this is that you get to combine focus and clefting, bringing the focused material to the front. This operation would remain optional, i.e., Chuq jí kú máoja would still remain in the language for you to use. The minor downside is that the signposting particle that announces focus – in this case, kü – now comes after the focused material.

The part where we let topic phrases be a focus marker

The idea is to take the generic pattern above, flip it, and apply it to bï:

TOPIC bï PHRASE → bí TOPIC nä PHRASE PHRASE … bí TOPIC …

For instance:

Báq maoja bï, he bu cho jí hóa ‘As for bananas, I don’t like them’

Bí báq maoja nä he bu cho jí hóa ‘ibid.’

He bu cho jí bí báq maoja ≈ ‘I don’t like bananas, if we’re speaking of bananas’

(Note that there is no semantic difference between these three forms – we’re just trying to demonstrate what this newborn bí means by reflecting it in the translation.)

The win here, in turn, is that we now get to topicalize any part of the sentence in afterthought, including at the far end of the sentence (as in the example – bí báq maoja came in at the veeery end). In addition, we may now topicalize any grammatical structure that kú can: he bı̣maı jí tó báq leuq ‘I love – as far as love/loving goes – queers and no others’.

Also note that this would extend bï’s range to adverbials. The official preference for AdverbialP in CompTopicP would be for it to mean something different than what nä does. In our proposal, we have to give bí/bï equal rights, so semantically we may assume that clause … bí phrase … actually compiles down to what would officially be phrased as

phrase bï, phrase nä clause.

In other words, the focused (or should I say topicked?) clause is reasserted (kept intact), but also raised/copied as the topic. So for Fa jí bí râo níchaq, instead of ‘As for [something being] today, I go’ (see reference), we should expect ‘As for [something being] today, I go today’.

A technical aside owing to bï’s semantics

tl;dr: Officially, bï should only take definite references. I posit that this means that bï’s topic must be reducible to something like λ𝑥′. 𝑥′ = 𝑥 for some predetermined 𝑥 : e. The section aims to expand this notion to all plausible topic phrase types if bí is to be expected to make any sense.

bï is restricted to definite references – cross-linguistically, topic phrases cannot include an indefinite referent (‘as for some crocheting’ only makes sense if we read ‘some’ as ké; as sá it is infelicitous). For this reason, we need to set down a definition of what it means for a noun phrase (and any other kind of phrase, given that bí would be allowed to attach to anything that kú can) to be “definite”. For this reason, we must stipulate that determiners which always denote a unique maximal reference, like ké, exophoric , or experimental cúaq – are definite, but then outer quantification may be flaky:

?Chı tú poq, ꝡä póq bï, mıe hóa ‘Every person thinks that as far as that person goes, they’re alive’

Should this be allowed? (You tell me.) After all, within the scope of the ꝡä, póq is a reified maximal reference. But then this would not stop us from saying things like

?Tú poq nä póq bï, mıe hóa ‘Every person, as far as that person goes, is alive’,

which, by rote function application (since that’s what nä’s denotation is for noun phrases), boils down to

*Tú poq bï, mıe hóa,

which is known to be illicit. (Remember that the English phrasing ‘As for every person, they’re alive’ is misleading here – it invokes túq semantics, not tú!) Also, this doesn’t shed light on non-NP usages like bí râo níchaq/râo níchaq bï. Conversely, we can’t just ban usages of anaphors or quantification seeing as the following examples are all validly definite:

Báq mala juku sâ kanı bï, uhuı hóa ‘Ones who have ever hunted a rabbit are evil’ (the predicate ‘who have ever hunted a rabbit’ is fully self-contained and can be báqed into a definite reference)

Hú poq nä, ké paı hôa bï, jaq zuoıde hóa ‘That person, as for their friend, they’re really elegant’ (beta-reducing the nä away we see that Ké paı hû poq bï, jaq zuoıde hóa is similarly self-contained and passes)

Let’s therefore carve out some theory by saying that a focus marker acts on an ordered pair of some fragment 𝑓 of type 𝘢 and some completion 𝑐′ of type 𝘢 → clause such that 𝑐′(𝑓) = 𝑐, the original clause. In other words, 𝑐′ could be understood as a “clause with a hole”, or a lambda expression with the bound variable appearing in place of the focused fragment. With that in place, we may treat focus markers as typed as 𝘢 → (𝘢 → clause) → clause. In the case of the ná/nä marker/cleft, for DPs specifically, its denotation is plain function specification: ⟦nä⟧ ≔ λ𝑓. λ𝑐′. 𝑐′(𝑓)), whereas other clefts do more convoluted semanticky things (such as attaching presuppositions) before putting the two cloven parts back together into a full clause. With this in hand we may posit a definition for definiteness which states that

a phrase is definite within the context of a root (!) clause 𝑐 if a fragment–completion pair (𝑓, 𝑐′) may be expressed where 𝑓 is not a function with codomain t.

The peculiar root clause restriction lets us escape the gotcha that this section was introduced with.

For instance, consider the following decomposition of a usage of ⟦bí⟧:

⟦Cho jí bí báq rua⟧ = ⟦bí⟧(⟦báq rua⟧)(λ𝑓. ⟦cho jí 𝑓⟧)

All fine and good, but ⟦báq rua⟧ is of type ⟨e, t⟩. For definiteness, which we may understand as “having one, unique, maximal reference”, we should not accept a function with domain e, but a value that’s itself of type e. So in our case, if we assume báq if we refactor our decomposition as

⟦bí⟧(⟦báq rua⟧)(λ𝑓. ⟦cho jí 𝑓⟧) = ⟦bí⟧(rua-kind)((λ𝑓. ⟦cho jí jéı 𝑓⟧) (Note: this is quite scuffed. I don’t exactly know how to expo this properly. If you know what’s going on then please edit as you please)

Notice how this overlaps with the determiner test, which states that a (c 1)-frame predicate 𝑃 is a determiner in disguise iff for all predicates 𝑄, sá 𝑃 𝑄 = tú 𝑃 𝑄 = báq 𝑃 𝑄 = etc., which another way to word is to say that 𝑃 : e → (e → t) → t is rephrasable as some 𝑃′ : (e → t) → e, which takes a unary predicate (e → t) and derives from it a unique reference (e). báq, ké, hú all have this property, which is to say that we may speak of a ⟦báq⟧′(⟦rua⟧) : e, which in the explication above was glossed over as “rua-kind”.