## A Short and Readable Proof of Cut Elimination for Two First-Order Modal Logics

dc.contributor.author | Gao, Feng | |

dc.contributor.author | Tourlakis, George | |

dc.date.accessioned | 2016-04-28T10:51:48Z | |

dc.date.available | 2016-04-28T10:51:48Z | |

dc.date.issued | 2015 | |

dc.identifier.issn | 0138-0680 | |

dc.identifier.uri | http://hdl.handle.net/11089/17909 | |

dc.description.abstract | A well established technique toward developing the proof theory of a Hilbert-style modal logic is to introduce a Gentzen-style equivalent (a Gentzenisation), then develop the proof theory of the latter, and finally transfer the metatheoretical results to the original logic (e.g., [1, 6, 8, 18, 10, 12]). In the first-order modal case, on one hand we know that the Gentzenisation of the straightforward first-order extension of GL, the logic QGL, admits no cut elimination (if the rule is included as primitive; or, if not included, then the rule is not admissible [1]). On the other hand the (cut-free) Gentzenisations of the first-order modal logics M3 and ML3 of [10, 12] do have cut as an admissible rule. The syntactic cut admissibility proof given in [18] for the Gentzenisation of the propositional provability logic GL is extremely complex, and it was the basis of the proofs of cut admissibility of the Gentzenisations of M3 and ML3, where the presence of quantifiers and quantifier rules added to the complexity and length of the proof. A recent proof of cut admissibility in a cut-free Gentzenisation of GL is given in [5] and is quite short and easy to read. We adapt it here to revisit the proofs for the cases of M3 and ML3, resulting to similarly short and easy to read proofs, only slightly complicated by the presence of quantification and its relevant rules. | pl_PL |

dc.description.sponsorship | This research was partially supported by NSERC grant No. 8250. | pl_PL |

dc.language.iso | en | pl_PL |

dc.publisher | Wydawnictwo Uniwersytetu Łódzkiego | pl_PL |

dc.relation.ispartofseries | Bulletin of the Section of Logic;3/4 | |

dc.subject | Modal logic | pl_PL |

dc.subject | GL | pl_PL |

dc.subject | QGL | pl_PL |

dc.subject | first-order logic | pl_PL |

dc.subject | proof theory | pl_PL |

dc.subject | cut elimination | pl_PL |

dc.subject | cut admissibility | pl_PL |

dc.subject | provability logic | pl_PL |

dc.title | A Short and Readable Proof of Cut Elimination for Two First-Order Modal Logics | pl_PL |

dc.type | Article | pl_PL |

dc.rights.holder | © Copyright by Feng Gao, George Tourlakis, Łódź 2015; © Copyright for this edition by Uniwersytet Łódzki, Łódź 2015 | pl_PL |

dc.page.number | 131–147 | pl_PL |

dc.identifier.eissn | 2449-836X | |

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dc.identifier.doi | 10.18778/0138-0680.44.3.4.03 | |

dc.relation.volume | 44 | pl_PL |