Docs / Semantics / Questions / Polar

Polar questions

import Linglib.Semantics.Questions.Polar · namespace Question

Source

The polar question polar p is the join ofSet p ⊔ ofSet pᶜ of the declaratives of p and of its complement, Hamblin's yes/no question as an inquisitive content and Punčochář's ?α := α ⩒ ¬α. It is the non-informative projection of the declarative (query_ofSet), and a nontrivial polar question has the alternatives p and pᶜ (alt_polar_of_nontrivial).

References

Polar question via inquisitive disjunction

The polar interrogative content of a proposition p, defined via Punčochář 2019's ?α := α ⩒ ¬α. Alternatives are p and pᶜ; non-informative (info = univ); inquisitive iff p is non-trivial.

def polarL29–34
{W : Type u_1} (p : Set W) :
Question W

Used by polar_compl, polar_eq_sup, polar_eq_generate_orbit, polar_smul, query_ofSet, mem_polar, isNormal_polar, info_polar, not_isInformative_polar, isInquisitive_polar_iff, coe_polar, alt_polar_of_nontrivial, alt_polar_eq_orbit, polar_empty, polar_univ, alt_polar_iff, mem_alt_polar_of_nontrivial, mem_polar_inf_polar_iff

Used in Discourse/Commitment/Table, Pragmatics/NeoGricean/Basic, Semantics/Conditionals/Reading, Semantics/Mood/State, Semantics/Questions/Entailment and 23 more

L52–53
L58–60

alt-characterization of polar

L75–77
L86–88

Polar degenerate-case identities

alt-characterization of polar (full)

L100–113
L115–118

Inf of two polar questions classified by a partition

When two polar questions polar p ⊓ polar q are answered together, the joint resolution carves the world space into the four "corners" p ∩ q, p ∩ qᶜ, pᶜ ∩ q, pᶜ ∩ qᶜ. Every state resolving both polars lies in some corner. A wh-question whose cells contain these corners therefore satisfies polar p ⊓ polar q ≤ which D P.

L128–132