# A Cyclic Proof System for HFL_ℕ

@inproceedings{Kori2021ACP, title={A Cyclic Proof System for HFL\_ℕ}, author={Mayuko Kori and Takeshi Tsukada and Naoki Kobayashi}, booktitle={CSL}, year={2021} }

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…

## 2 Citations

An Overview of the HFL Model Checking Project

- Computer ScienceHCVS@ETAPS
- 2021

This article presents its methods for automatically solving the HFL(Z) model/validity checking problems, using higher-order model checkers and CHC solvers as backends.

A Cyclic Proof System for HFLN

- Computer ScienceArXiv
- 2020

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.

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