Ruitenburg's Theorem via Duality and Bounded Bisimulations

Luigi Santocanale; Silvio Ghilardi

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arXiv · 1804.06130

Ruitenburg's Theorem via Duality and Bounded Bisimulations

Luigi Santocanale·Silvio Ghilardi

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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$\ge$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 $\ge$ 0 such that A N+2 $\leftrightarrow$ 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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BibTeX RIS

Luigi Santocanale, Silvio Ghilardi. 2018-04-17. Ruitenburg's Theorem via Duality and Bounded Bisimulations. https://arxiv.org/abs/1804.06130

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