References

  1. David Baelde (2009): Least and greatest fixed points in linear logic. CoRR abs/0910.3383v4. Available at http://arxiv.org/abs/0910.3383v4.
  2. Kai Brünnler & Thomas Studer (2009): Syntactic cut-elimination for common knowledge. Annals of Pure and Applied Logic 160(1), pp. 82–95, doi:10.1016/j.apal.2009.01.014.
  3. Kai Brünnler & Thomas Studer (preprint): Syntactic cut-elimination for a fragment of the modal mu-calculus.
  4. Wilfried Buchholz (1981): The Ω_μ+1-rule. In: Wilfried Buchholz, Solomon Feferman, Wolfram Pohlers & Wilfried Sieg: Iterated Inductive Definitions and Subsystems of Analysis: Recent Proof Theoretic Studies, Lecture Notes in Mathematics 897. Springer, pp. 189–233, doi:10.1007/BFb0091898.
  5. Wilfried Buchholz (2001): Explaining the Gentzen-Takeuti reduction steps: a second-order system. Archive for Mathematical Logic 40(4), pp. 255–272, doi:10.1007/s001530000064.
  6. Wilfried Buchholz & Kurt Schütte (1988): Proof Theory of Impredicative Subsystems of Analysis. Bibliopolis.
  7. Brian Hill & Francesca Poggiolesi (2010): A Contraction-free and Cut-free Sequent Calculus for Propositional Dynamic Logic. Studia Logica 94(1), pp. 47–72, doi:10.1007/s11225-010-9224-z.
  8. Gerhard Jäger, Mathis Kretz & Thomas Studer (2008): Canonical completeness for infinitary μ. Journal of Logic and Algebraic Programming 76(2), pp. 270–292, doi:10.1016/j.jlap.2008.02.005.
  9. Gerhard Jäger & Thomas Studer (2011): A Buchholz rule for modal fixed point logics. Logica Universalis 5, pp. 1–19, doi:10.1007/s11787-010-0022-1.
  10. Dexter Kozen (1988): A finite model theorem for the propositional μ–calculus. Studia Logica 47(3), pp. 233–241, doi:10.1007/BF00370554.
  11. Grigori Mints (to appear): Effective Cut-elimination for a fragment of Modal mu-calculus. Studia Logica.
  12. Regimantas Pliuskevicius (1991): Investigation of Finitary Calculus for a Discrete Linear Time Logic by means of Infinitary Calculus. In: Baltic Computer Science, Selected Papers. Springer, pp. 504–528, doi:10.1007/BFb0019366.
  13. Gaisi Takeuti (1987): Proof Theory. North-Holland.
  14. Alwen Tiu & Alberto Momigliano (2010): Cut Elimination for a Logic with Induction and Co-induction. CoRR abs/1009.6171v1. Available at http://arxiv.org/abs/1009.6171v1.

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