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2026-02-00 yamamoto-2026-proof-calculus Added Yamamoto (2026) proof calculus formalization

Arrow's Impossibility Theorem

Arrow's impossibility theorem demonstrates that no rank-order voting system can satisfy a set of seemingly reasonable fairness criteria simultaneously when there are three or more alternatives.

Yamamoto (2026) Proof Calculus Formalization

Yamamoto (2026) provides a complete derivation in proof calculus that makes the theorem's structure mechanically verifiable. This formal representation confirms that Arrow's theorem is not only mathematically proven but fully formalizable in rigorous proof calculus, demonstrating machine-checkable derivability. This work differs from Tang & Lin's computer-aided proof (AAAI 2008), which focused on automated verification rather than human-readable formal derivation.

The proof calculus approach upgrades the evidentiary basis by enabling direct inspection of logical dependencies and providing a foundation for mechanized theorem proving applications.