## 抄録

It is well known that the modal logic S5 can be embedded in the classical predicate logic by interpreting the modal operator in terms of a quantifier. Wajsberg [10] proved this fact in a syntactic way. Mints [7] extended this result to the quantified version of S5; using a purely proof-theoretic method he showed that the quantified S5 corresponds to the classical predicate logic with one-sorted variable. In this paper we extend Mints� result to the basic modal logic S4; we investigate the correspondence between the quantified versions of S4 (with and without the Barcan formula) and the classical predicate logic (with one-sorted variable). We present a purely proof-theoretic proof-transformation method, reducing an LK-proof of an interpreted formula to a modal proof.

本文言語 | English |
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ページ（範囲） | 1403-1414 |

ページ数 | 12 |

ジャーナル | Journal of Symbolic Logic |

巻 | 68 |

号 | 4 |

DOI | |

出版ステータス | Published - 2003 12月 |

## ASJC Scopus subject areas

- 哲学
- 論理