Update Semantics

Origin. Veltman (1996). Meaning as context change. Epistemic modals. Might and must. Foundation of informational semantics.

Models. Information states. Update functions. Epistemic modals. Test semantics. Context change potential.

Formalism.

Information state: σ ⊆ W (set of worlds). Represents what's known/assumed. Eliminative updates. Common ground.

Update function: σ[φ]: result of updating σ with φ. Meaning = update function. Dynamic.

Atomic update: σ[p] = {w ∈ σ : w ⊨ p}. Eliminate p-false worlds. Intersection.

Conjunction: σ[φ ∧ ψ] = σ[φ][ψ]. Sequential update. Order matters sometimes.

Negation: σ[¬φ] = σ - σ[φ]. Worlds not eliminated by φ. Complement in σ.

Might (test): σ[◇φ] = σ if σ[φ] ≠ ∅, else ∅. Test: passes or crashes. Non-eliminative. Epistemic possibility.

Must (test): σ[□φ] = σ if σ[φ] = σ, else ∅. φ holds throughout σ. Epistemic necessity.

Support: σ supports φ (σ ⊨ φ) iff σ[φ] = σ. φ adds no information to σ. Already known.

Absurdity: ∅ = absurd state. σ[⊥] = ∅. Crash/failure.

Symbols.

Metatheory. Context change. Test semantics. Epistemic modals. Information states.

Applies to. Epistemic modals. Discourse. Conditionals. Common ground.

Limitations. Propositional focus. First-order complex. Multiple agent issues. Specific phenomena.