Ying et al. (2025) — English-modal bridge to LaBToM threshold semantics #
Connects the English modal fragment (English.FunctionWords) to
the epistemic threshold semantics of [YZXW+25]
("Understanding Epistemic Language with a Language-Augmented Bayesian
Theory of Mind", TACL 13:613–637), formalized in
Semantics.Attitudes.EpistemicThreshold.
The Bridge #
Each English epistemic modal auxiliary maps to an EpistemicEntry with a
fitted credence threshold (LaBToM's grid-search best-fit values; see the
table in EpistemicThreshold.lean). The bridge proves:
- Form agreement: the Fragment's
formfield matches the Theory'sname - Force–threshold consistency: necessity-force modals have strictly higher thresholds than possibility-force modals on their epistemic reading
- Within-force scalar ordering: threshold ordering captures scalar differences (must > should, may > might) that binary force cannot express
Dependency Direction #
Fragments/English/FunctionWords.lean (AuxEntry, modalMeaning)
↓
Semantics/Attitudes/EpistemicThreshold.lean (EpistemicEntry, θ)
↓
Studies/YingEtAl2025.lean (this file)
Map an English modal auxiliary to its epistemic threshold entry.
Only epistemic modals have a threshold; non-epistemic uses (deontic,
circumstantial) are none.
The mapping derives from the Fragment's form field — no duplication
of lexical data.
Equations
- One or more equations did not get rendered due to their size.
Instances For
Extract the epistemic force of a modal auxiliary, if it has an
epistemic reading. Returns none for purely deontic/circumstantial
modals (e.g., shall).
Equations
- One or more equations did not get rendered due to their size.
Instances For
Per-entry verification: the Fragment's form maps to the Theory's
threshold value from [YZXW+25]
Table 1(b). These check the form→entry→threshold pipeline; they break
if either the Fragment's form field or the Theory's threshold changes.
Non-epistemic modals have no threshold entry.
The key empirical prediction: necessity-force epistemic modals have strictly higher thresholds than possibility-force epistemic modals.
□ modals: must (0.95) > should (0.80)
◇ modals: may (0.30) > might/could (0.20)
□ > ◇: should (0.80) > may (0.30)
This connects two independent characterizations of the same items:
Every necessity-force epistemic modal has a higher threshold than every possibility-force epistemic modal.
The epistemic force of must is necessity (derived from Fragment).
The epistemic force of might is possibility (derived from Fragment).
The epistemic force of should is weak necessity (derived from Fragment).
The epistemic force of may is possibility (derived from Fragment).
Thresholds decrease monotonically with force: must (□) > should (□w) >
may (◇) > might = could (◇). The □ > □w gap is captured by the 3-way
ModalForce distinction; the within-◇ gap remains a scalar difference.
□ > □w: must (strong necessity) > should (weak necessity).
Among possibility modals: may > might. Both are ◇ but may is stronger.
might = could in threshold (both 0.20).
[HF19] (Cognition 186) independently infers a credence
threshold for probably by Bayesian fitting against urn-production data,
reporting a posterior mean of 0.549 with 95% HDI [0.500, 0.594] (their Table 6).
LaBToM's grid-search threshold for likely (0.70) lies above the upper bound of
that HDI, so the two parameter-fitted accounts disagree at the 95%-credibility
level, not merely on the point estimate. Candidate explanations: lexical
(probably ≠ likely), task (urn production vs. Theory-of-Mind in a gridworld),
or posterior uncertainty (point values vs. intervals).
LaBToM's likely_.θ = 0.70 exceeds the upper bound (0.594) of the 95% HDI
that [HF19] report for the threshold of probably
(their Table 6). The two fitted theories disagree at the 95%-credibility
level.