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Conference Papers Year : 2018

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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Dates and versions

hal-01766636 , version 1 (13-04-2018)

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