An explicit basis for the admissible inference rules of the modal logics extending S4.1 And Grz

Rimatskii VV

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An explicit basis for the admissible inference rules of the modal logics extending S4.1 And Grz

机译：扩展S4.1和Grz的模态逻辑的容许推理规则的明确基础

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We study bases for the admissible inference rules in a broad class of modal logics. We construct an explicit basis for all admissible rules in the logics S4.1, Grz, and their extensions whose number is at least countable. The resulting basis consists of an infinite sequence of rules in a concise and simple form. In the case of a logic of finite width a basis for all admissible rules consists of a finite sequence of rules.

机译：我们在广泛的模态逻辑中研究可允许的推理规则的基础。我们为逻辑S4.1，Grz及其数量至少是可数的扩展构造所有可允许规则的明确基础。由此产生的基础由简洁和简单形式的无数规则组成。对于有限宽度的逻辑，所有可允许规则的基础都由规则的有限序列组成。

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《Siberian Mathematical Journal》 |2009年第4期|共8页
作者
Rimatskii VV;
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正文语种 eng
中图分类数学;
关键词
modal logic; Kripke frame and model; admissible inference rule; basis; for admissible rules;

机译：模态逻辑;克里普克框架和模型;可允许的推理规则;基础;用于可允许的规则;

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1. An explicit basis for the admissible inference rules of the modal logics extending S4.1 And Grz [J] . Rimatskii VV Siberian Mathematical Journal . 2009,第4期

机译：扩展S4.1和Grz的模态逻辑的容许推理规则的明确基础
2. An explicit basis for the admissible inference rules in the Godel-Lob logic GL [J] . B. R. Fedorishin Siberian Mathematical Journal . 2007,第2期

机译：Godel-Lob逻辑GL中允许的推理规则的明确基础
3. An admissibility criterion for inference rules with metavariables in the modal logic S 4. α N [J] . A. N. Rutskii Siberian Mathematical Journal . 2007,第2期

机译：模态逻辑S 4中具有亚变量的推理规则的可采性准则
4. Interpretation of Chance Discovery in Temporal Logic, Admissible Inference Rules [C] . Vladimir Rybakov International conference on knowledge-based and intelligent information and engineering systems;KES 2010 . 2010

机译：解释时间逻辑中的机会发现，可允许的推理规则
5. Epistemic paradox and explicit modal logic. [D] . Dean, Walter. 2010

机译：认知悖论和显性模态逻辑。
6. Logic Learning Machine creates explicit and stable rules stratifying neuroblastoma patients [O] . Davide Cangelosi, Fabiola Blengio, Rogier Versteeg, 2013

机译：Logic学习机创建明确且稳定的规则对成神经细胞瘤患者进行分层
7. Problems of substitution and admissibility in the modal system Grz and in intuitionistic propositional calculus [O] . Rybakov V.V. 1990

机译：模态系统Grz和直觉命题演算中的替代和可容许性问题
8. Explicit Provability: The Intended Semantics for Intuitionistic and Modal Logic [R] . Artemov, S. N. 1998

机译：显式可证性：直觉和模态逻辑的预期语义

An explicit basis for the admissible inference rules of the modal logics extending S4.1 And Grz

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