Ruitenburg's Theorem via Duality and Bounded Bisimulations

Abstract : For a given intuitionistic propositional formula A and a propositional variable x occurring in it, define the infinite sequence of formulae { A _i | i≥1} by letting A_1 be A and A_{i+1} be A(A_i/x). Ruitenburg's Theorem [8] says that the sequence { A _i } (modulo logical equivalence) is ultimately periodic with period 2, i.e. there is N ≥ 0 such that A N+2 ↔ A N is provable in intuitionistic propositional calculus. We give a semantic proof of this theorem, using duality techniques and bounded bisimulations ranks.
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Contributor : Luigi Santocanale <>
Submitted on : Friday, April 13, 2018 - 6:13:47 PM
Last modification on : Sunday, July 15, 2018 - 2:16:26 PM

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  • HAL Id : hal-01766636, version 1
  • ARXIV : 1804.06130

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Luigi Santocanale, Silvio Ghilardi. Ruitenburg's Theorem via Duality and Bounded Bisimulations. Advances in Modal Logic, Aug 2018, Bern, Switzerland. ⟨hal-01766636⟩

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