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Redesign Modal Logic

Test project for modal logic redesigning.

Zoo

Strict inclusions between the logics formalized in Neighborhood, extracted from the Lean environment and reduced by transitivity (regenerated on every push to main; see zoo/).

Interactive 3D zoo — the zoo as a rotatable 3D Hasse diagram: equal logics are merged into one node, node color encodes deductive strength, hovering a logic highlights its direct neighbours, and a search box flies to a given logic. Locally, run just zoo and then just zoo-serve.

Axiom status table — for every logic, which of the ten axioms it proves, which it provably does not, and which nobody has settled yet.

The compact static 2D rendering (PNG) — only the extensions of E by M, C, N, D, T, B, 4, 5, with one representative per equivalence class:

Compact Neighborhood logic zoo

The full static 2D rendering (PNG), covering the extensions by P and K as well; as in the 3D zoo, equal logics are merged into one node, and L+n means that n further logics are equal to L:

Neighborhood logic zoo

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Formalization of Modal Logic

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