Steinert-Threlkeld, Imel and Guo (2023): A semantic universal for modality #
This file formalizes the Independence of Force and Flavor universal of
[STIG23], the substrate's Modality.ForceFlavorIndependent,
against the Single Axis of Variability universal of [Nau08] it replaces. The Washo verb
-eʔ, which [Boc15b] finds specified for neither force nor flavor, varies on both axes
yet is a product, the hypothetical mighst is neither, and the singleton meanings of Paciran
Javanese ([VK13a]) satisfy the universal trivially. The paper's equivalence of
independence with convexity for the grid betweenness of [CBD19] is the
substrate's forceFlavorIndependent_iff_pair_product_subset.
Section 4.1 notes gaps in the uses of -eʔ that Bochnak elicits: bouletic necessity and weak
necessity but no bouletic possibility, and weak necessity with no other flavor
(washoAttested_gaps), so the attested uses are not a product. The paper still takes the
universal to hold of -eʔ, since nothing rules the missing pairs out and the analyses of
[Boc15b] and [Boc15c] leave force and flavor free (washo_attested).
The paper offers path-connectedness as a weaker fallback universal, defined by replacing the
"and" of independence with an "or" and glossed in a footnote as any two points being joined by a
path. The two readings come apart. Read as a path through the rook's graph on the force-flavor
grid, whose edges change one coordinate, the property follows from the "or" formulation
(PathConnected.connected), but the second modal of Table 1, given as satisfying
path-connectedness without independence, is connected in the grid and fails the "or"
formulation: its weak teleological and strong epistemic points share no corner
(table1b_connected_not_pathConnected).
The Koryak attitude verb ivək is the paper's other counterexample to Nauze's universal, with
the doxastic and assertive flavors of [MA19] on the flavor axis. Section 4.1
reads them as reporting all four combinations of the two forces and the two flavors, which is
what their lexical entry predicts (ivek_forceFlavorIndependent). Their footnote 10, however,
could not confirm an existential 'say', and without it the attested uses are not a product;
they satisfy only path-connectedness (ivek_attested).
Implementation notes #
The paper's space has two forces, weak and strong, and the flavors epistemic, deontic and
teleological; the library folds teleological into circumstantial. The doxastic and assertive
flavors of ivək lie outside that space, and the universal is stated for any types of forces
and flavors. So do the metaphysical and generic uses of -eʔ, which washoAttested leaves
out; the weak necessity of [Boc15b] is the library's ModalForce.weakNecessity.
References #
Washo -eʔ, which leaves force and flavor to context, varies on both axes, against Nauze's universal, and is a product.
forceTable maps the force label of a row of [Boc15b] to its force.
Equations
- SteinertThrelkeldImelGuo2023.forceTable = [("possibility", Modality.ModalForce.possibility), ("weak necessity", Modality.ModalForce.weakNecessity), ("necessity", Modality.ModalForce.necessity)]
Instances For
flavorTable maps the flavor label of a row of [Boc15b] to its flavor, when the
flavor lies in the space.
Equations
- One or more equations did not get rendered due to their size.
Instances For
washoAttested collects the pairs of the uses of -eʔ that [Boc15b] elicits, in §3
and, with the prejacent negated, in §5.
Equations
- One or more equations did not get rendered due to their size.
Instances For
As Section 4.1 notes, the uses [Boc15b] reports include both forces with the epistemic and the deontic flavor, bouletic necessity and weak necessity but no bouletic possibility, and weak necessity with no other flavor.
The attested uses of -eʔ vary on both axes but fail the universal, which holds of the entry predicting the unreported pairs.
Koryak ivək, on the lexical entry of [MA19], expresses all four pairs of two forces and its doxastic and assertive flavors, so it varies on both axes and satisfies the universal.
The pairs [MA19] attest for ivək, without the existential 'say' their footnote 10 could not confirm, fail the universal and satisfy path-connectedness.
Paciran Javanese mesthi, oleh and iso express one pair each.
The hypothetical mighst expresses epistemic possibility and deontic necessity only, which the universal rules out; it is the third modal of Table 1.
Equations
Instances For
Table 1 and the two readings of path-connectedness #
The first modal of Table 1 expresses both forces with the epistemic and teleological flavors.
Equations
- One or more equations did not get rendered due to their size.
Instances For
The second modal of Table 1 expresses weak deontic and teleological and strong epistemic and deontic.
Equations
- One or more equations did not get rendered due to their size.
Instances For
rookGraph is the rook's graph on the force-flavor grid, in which pairs differing in exactly
one coordinate are adjacent.
Equations
Instances For
Two pairs of a meaning sharing a coordinate are joined in the rook's graph.
A path-connected meaning induces a connected subgraph of the rook's graph, any two pairs being joined through a corner, so the "or" formulation implies the footnote's.
The second modal of Table 1 fails independence and the "or" formulation of path-connectedness, yet is connected in the rook's graph.
mighst, the third modal, is disconnected on either reading.