Embedding from multilattice logic into classical logic and vice versa

Kamide Norihiro; Shramko Yaroslav

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Embedding from multilattice logic into classical logic and vice versa

机译：从多晶格逻辑嵌入经典逻辑，反之亦然

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This article presents some theorems for syntactic and semantic embeddings of a Gentzen-type sequent calculus MLn for multilattice logic into a Gentzen-type sequent calculus LK for classical logic and vice versa. These embedding theorems are used to prove cut-elimination, decidability and completeness theorems for MLn, as well as a modified Craig interpolation theorem. Some of these results are then extended to the first-order system FMLn with implications and co-implications.

机译：本文提出了将多格逻辑的Gentzen型顺序演算MLn语法化为经典逻辑的Gentzen型顺序演算LK的句法和语义嵌入定理。这些嵌入定理用于证明MLn的割除定理，可判定性和完整性定理，以及改进的Craig插值定理。然后将其中一些结果扩展到具有含义和共同含义的一阶系统FMLn。

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来源
《Journal of logic and computation》 |2017年第5期|1549-1575|共27页
作者
Kamide Norihiro; Shramko Yaroslav;
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作者单位

Teikyo Univ, Dept Informat & Elect Engn, Toyosatodai 1-1, Utsunomiya, Tochigi 3208551, Japan;

Kryvyi Rih State Pedag Univ, Dept Philosophy, UA-50086 Kryvyi Rih, Ukraine;

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正文语种 eng
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关键词
Multilattice logic; embbeding theorem; completeness theorem; sequent calculus; interpolation theorem; cut-elimination theorem;

机译：多重格逻辑;嵌入定理;完备性定理;后续演算;插值定理;割消定理;

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2. Combining and automating classical and non-classical logics in classical higher-order logics [J] . Christoph Benzmueller Annals of Mathematics and Artificial Intelligence . 2011,第1a2期

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3. From Classical Logic to Fuzzy Logic and Quantum Logic: A General View [J] . Sorin Nadaban IAENG Internaitonal journal of computer science . 2021,第1期

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4. An Extended Paradefinte Belnap-Dunn Logic that is Embeddable into Classical Logic and Vice Versa [C] . Norihiro Kamide International Conference on Agents and Artificial Intelligence . 2019

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5. Bridging the Gap between Classical Logic Based Formalisms and Logic Programs [D] . Palla, Ravi 2012

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6. Implementation of cascade logic gates and majority logic gate on a simple and universal molecular platform [O] . Jinting Gao, Yaqing Liu, Xiaodong Lin, -1

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7. Embedding and automating conditional logics in classical higher-order logic [O] . Christoph Benzmüller, Dov Gabbay, Valerio Genovese, 2012

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Embedding from multilattice logic into classical logic and vice versa

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