Plausibility Logic

Origin. Friedman and Halpern (1995), Baltag and Smets (2008). Graded belief and plausibility. More/less plausible worlds. Dynamic belief revision. Foundation for epistemic plausibility.

Models. Plausibility ordering on worlds. Most plausible worlds determine belief. Conditional belief: belief given evidence. Dynamic: evidence changes ordering.

Formalism.

Plausibility ordering: ≤: W × W → Bool w ≤ v: w at least as plausible as v — the ≤-minimal worlds are the most plausible. Typically: total preorder per agent.

Belief operator: Bφ: agent believes φ. True iff φ true in all most plausible worlds. Min≤(W) ⊆ ⦃φ⦄

Conditional belief: B^ψ φ: agent believes φ given ψ. Most plausible ψ-worlds satisfy φ. Min≤(⦃ψ⦄) ⊆ ⦃φ⦄

Safe belief: □φ: φ true in all worlds ≤-related to current. Knowledge-like but plausibility-based.

Dynamic operators: [!ψ]φ: after hard evidence ψ, φ holds. [⇑ψ]φ: after radical (lexicographic) upgrade with ψ, φ holds. [↑ψ]φ: after conservative upgrade with ψ.

Upgrade types: Hard (!ψ): eliminate non-ψ worlds. Radical (⇑ψ): all ψ-worlds become more plausible than all non-ψ worlds, order within each block preserved. Conservative (↑ψ): only the best ψ-worlds are promoted to the top; the rest keeps its order.

AGM connection: Revision: [⇑ψ] models belief revision. AGM postulates satisfied. Iterated revision.

Symbols.

Metatheory. Sound and complete. Dynamics axiomatizable. AGM connection. Decidable.

Applies to. Belief revision. Multi-agent belief. Learning. Evidence dynamics. AI reasoning.

Limitations. Ordering assumption. Hard vs soft evidence. Multiple agent complexity. Iteration subtle.

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