Modal Concord Bridge — Register Approach #
@cite{rotter-liu-2025} @cite{van-de-pol-etal-2023} @cite{zeijlstra-2007}
Connects the empirical data from @cite{rotter-liu-2025} to the English modal fragment and modal typology infrastructure.
Section A: Semantic equivalence #
Must and have to share deontic necessity in the force-flavor space. This is the precondition for concord: two forms that are register variants of the same modal meaning.
Section B: Register variants #
Formalizes the register approach: must and have to are register variants
(same modal meaning, different register level). This is analogous to T/V
pronoun systems (Basque hi/zu, Japanese boku/watashi), where
forms sharing the same referential semantics differ in formality.
Register properties are derived from the fragment's AuxEntry.register
field and the Core.Register.Level type, not stipulated locally.
Section C: Competing predictions #
The register approach and the syntactic agreement approach make different predictions about the formality of stacked modals. The data confirms the register approach.
Section D: Connection to modal typology #
Section A: Semantic equivalence in the fragment #
Must expresses deontic necessity (from the English fragment).
Have to expresses deontic necessity (from the English fragment).
Have to has the same deontic-circumstantial meaning as must restricted to the non-epistemic flavors. Both express necessity over deontic and circumstantial domains.
Both must and have to satisfy IFF (Independence of Force and Flavor). Their meanings are Cartesian products of forces and flavors.
Both satisfy SAV (Single Axis of Variability): they vary on flavor only, with fixed necessity force.
Section B: Register variants #
Register properties are derived directly from the fragment's AuxEntry.register
field, which uses Core.Register.Level (formal/neutral/informal).
Must is marked formal in the fragment.
Have to is marked informal in the fragment.
Register opposition: must and have to are register variants — they differ in register level. Derived from the fragment entries.
Register ordering: have to < must on the formality scale (informal < formal).
Section C: Competing predictions #
Two theories of modal concord make different predictions about the formality of stacked modals:
Register approach:
- Must and have to are register variants of the same meaning
- Stacking creates a "split register" construction
- Prediction: intermediate formality (between must and have to)
Syntactic agreement:
- One modal carries interpretable [iNec], the other uninterpretable [uNec]
- The [uNec] modal is semantically vacuous (like negative concord)
- Prediction: formality of stacked form = formality of single form (the vacuous modal contributes nothing)
Register prediction confirmed: The empirical formality rating of must have to is strictly between must and have to. This is the register approach's central prediction (@cite{rotter-liu-2025} §4): mixing a formal variant with an informal variant yields intermediate formality.
Syntactic agreement prediction refuted (vs must): If have to were semantically vacuous [uNec], must have to should be as formal as bare must. It is not.
Syntactic agreement prediction refuted (vs have to): If must were semantically vacuous [uNec], must have to should be as formal as bare have to. It is not.
Concord preserves modal force: The meaning ratings for all three conditions are above midpoint and close to each other, confirming that must have to VP expresses single necessity (concord), not double necessity. If the stacked form expressed □□p, the meaning rating (paraphrase match with have to) should be much lower.
Section D: Connection to modal typology #
Modal concord only arises between forms with overlapping force-flavor meanings. The IFF universal predicts that natural-language modals have Cartesian-product meanings. Since Cartesian products with the same force axis share all force-flavor pairs, IFF-satisfying necessity modals are natural concord candidates.
The deontic necessity overlap between must and have to is non-accidental: both are IFF-satisfying necessity modals. Any two IFF modals with singleton force {necessity} and overlapping flavor sets share deontic necessity whenever both express it.