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Question entailment

import Linglib.Semantics.Questions.Entailment · namespace Question

Source

Entailment between questions is the lattice order on Question W: P ≤ Q when every state resolving P resolves Q (Ciardelli et al. 2018). Ciardelli 2022 reads a question as a type of information, generated by a family of states when the states resolving it are those included in a member of the family, and checks entailment on generators: every piece of information of the first type implies one of the second (le_iff_forall_exists_subset). A normal question is generated by its alternatives, so it entails exactly the questions all its alternatives resolve (IsNormal.le_iff_forall_alt_mem), and between normal questions entailment is inclusion of each alternative in an alternative (IsNormal.le_iff_forall_alt_exists_alt). A polar question entails exactly the questions both its answers resolve (polar_le_iff), and so no polar question but itself and the tautology (polar_le_polar_iff).

The entailment of Groenendijk & Stokhof 1984, which Roberts 2012 adopts as her (8), asks instead that answering the first question yield a complete answer to the second, completeAnswers P ⊆ completeAnswers Q. On normal partition questions the complete answers are the resolving states (IsPartition.completeAnswers_eq), so the two entailments coincide (IsPartition.completeAnswers_subset_iff_le) and are refinement of the partitions (completeAnswers_fromSetoid_subset_iff). On Hamblin alternative sets they come apart: more alternatives make a question weaker in the lattice order (IsNormal.le_of_alt_subset) and stronger for complete answers (completeAnswers_anti), Roberts's remark that off complete answers the entailments go the other way around.

References

Entailment on generators

L47–50

Normal questions

Polar questions

Complete-answer entailment

L106–112