Inquisitive Logic

Origin. Groenendijk, Roelofsen (2000s). Questions in logic. Support semantics. Beyond truth conditions. Foundation for question semantics.

Models. Sentences have inquisitive content. Questions are propositions. Support replaces truth. Information states central. Unifies declaratives and interrogatives.

Formalism.

Information states: State σ = set of possible worlds. σ supports φ: σ ⊨ φ. Support replaces truth. Relativized to information.

Inquisitive propositions: Proposition [φ] = {σ : σ ⊨ φ}. Set of sets of worlds. Downward closed under ⊆. Alternatives structure.

Support conditions: σ ⊨ p iff σ ⊆ |p| (atomic) σ ⊨ φ ∧ ψ iff σ ⊨ φ and σ ⊨ ψ σ ⊨ φ ∨ ψ iff σ ⊨ φ or σ ⊨ ψ σ ⊨ ¬φ iff for all τ ⊆ σ: τ ⊨ φ implies τ = ∅

Inquisitive disjunction: φ ∨ ψ raises issue: which? Either φ or ψ settles it. Source of inquisitiveness. Not just truth-functional.

Questions: ?φ := φ ∨ ¬φ "Is φ the case?" Alternatives: φ-worlds or ¬φ-worlds. Settled by either.

Projection operators: !φ (assertion): project to informative content, ignore the issue. ?φ (question): raise the polar issue. Every proposition factors into assertive and inquisitive parts.

Informativeness vs inquisitiveness: Informative: rules out possibilities. Inquisitive: raises issues. Both captured in one framework. Orthogonal dimensions.

Entailment: φ ⊨ ψ iff [φ] ⊆ [ψ]. Every way of supporting φ supports ψ. Questions can entail questions. Cross-type entailment.

Symbols.

Metatheory. Support semantics. Question content. Information-inquisition duality. Unified semantics. Inquisitive propositional logic InqB is decidable, has the disjunction property, and is complete under a known axiomatization; in assertive strength it sits as an intermediate logic between classical and intuitionistic. Not closed under uniform substitution.

Applies to. Question semantics. Dialogue logic. Information dynamics. Linguistics.

Limitations. Classical alternatives exist. Complexity. Foundational debates. Implementation details.

© 2026 Lingenic LLC