A Cyclic Proof System for HFL_ℕ

  title={A Cyclic Proof System for HFL\_ℕ},
  author={Mayuko Kori and Takeshi Tsukada and Naoki Kobayashi},
A cyclic proof system allows us to perform inductive reasoning without explicit inductions. We propose a cyclic proof system for HFLN, which is a higher-order predicate logic with natural numbers and alternating fixed-points. Ours is the first cyclic proof system for a higher-order logic, to our knowledge. Due to the presence of higher-order predicates and alternating fixed-points, our cyclic proof system requires a more delicate global condition on cyclic proofs than the original system of… Expand
2 Citations
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A Cyclic Proof System for HFLN
This work proposes a cyclic proof system for HFLN, which is a higher-order predicate logic with natural numbers and alternating fixed-points, and proves the decidability of checking the global condition and soundness of this system, and also proves a restricted form of standard completeness for an infinitary variant of the system. Expand


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