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feat(Logic/Modal/BSML): Hintikka formulas; expressive completeness proved - #1982

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bsml-hintikka
Aug 12, 2026
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feat(Logic/Modal/BSML): Hintikka formulas; expressive completeness proved#1982
github-actions[bot] merged 4 commits into
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bsml-hintikka

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@hawkrobe

@hawkrobe hawkrobe commented Aug 11, 2026

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Builds the Hintikka machinery and uses it to discharge the library's expressiveCompleteness_converse sorry, making Logic/Modal/ sorry-free.

  • charFormula M k w (depth-k Hintikka formula: atomic type ∧ of each successor type ∧ of the successor-type disjunction) with the two-directional characterisation classicalEval_charFormula_iff_bisim : … ↔ WorldBisim k M w M v, plus the singleton-support lift and supporting falsum/bigDisj/team-support API.
  • expressiveCompleteness_converse: every convex, union-closed, bounded-bisimulation-closed team property is BSML-definable (within-model finite-atom form of Anttila 2025 Ch 3 — the cross-model theorem indexes bisimulation by finite atom sets, so [Fintype Atom] is the honest hypothesis). The defining formula is δ_U ∧ ⋀_{T ∈ 𝒯} ((δ_T ∧ NE) ∨ δ_U) over flat characteristic disjunctions, with U the union of P's teams and 𝒯 the transversal world-sets; a supporting team's uncovered-worlds set fails transversality, yielding s₀ ∈ P covered by t, and s₀ ∪ (U ∩ cover t) closes via convexity + bisim-closure.
  • expressivelyComplete — the headline theorem — is now fully proved.

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github-actions Bot enabled auto-merge (squash) August 11, 2026 23:25
@hawkrobe hawkrobe changed the title feat(Logic/Modal/BSML): Hintikka formulas characterise k-bisimilarity feat(Logic/Modal/BSML): Hintikka formulas; expressive completeness proved Aug 11, 2026
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github-actions Bot merged commit 034f66f into main Aug 12, 2026
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