| 模态系统T的Herbrand定理 |
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| 引用本文： | 魏燕侠. 模态系统T的Herbrand定理[J]. 厦门大学学报(哲学社会科学版), 2011, 0(5) |
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| 作者姓名： | 魏燕侠 |
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| 作者单位： | 华侨大学哲学与社会发展学院,福建厦门361021;厦门大学哲学系,福建厦门361005 |
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| 基金项目： | 福建省社会科学规划项目“谓词抽象研究”(2009B2051) |
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| 摘 要： | 模态Herbrand定理研究是模态逻辑领域的重要开放问题.不含Barcan公式的模态系统T的Herbrand定理的获得必须完成两个方向的证明工作:首先是证明相对简单的从右到左方向；而对于相对复杂的从左到右方向,则可以通过在加标公式表列系统K的基础上增加特殊规则获得加标公式表列系统T,证明T的可靠性和完全性,并在此基础上完成从左到右方向的证明.同样的方法还可以用来证明模态系统D、K4、s4的Herbrand定理.
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| 关 键 词： | 模态系统T Herbrand定理 加标公式表列系统 |
On Herbrand Theorem for Modal System T |
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| WEI Yan-xia. On Herbrand Theorem for Modal System T[J]. Journal of Xiamen University(A Quarterly for Studies in Arts & Social Sciences), 2011, 0(5) |
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| Authors: | WEI Yan-xia |
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| Affiliation: | WEI Yan-xia1,2(1.School of Philosophy and Social Development,National Huaqiao University,Xiamen 361021,Fujian 2.Department of Philosophy,Xiamen University,Xiamen 361005,Fujian) |
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| Abstract: | Modal Herbrand Theorem is an important open question in the field of modal logic.A Herbrand theorem for modal system T without Barcan formula must be obtained through proving in two directions,i.e.the right-to-left direction,which is relatively easy;and the left-to-right direction,which is relatively complicated and can be done by adding some special rules to the signed formulas tableau system K to obtain a signed formulas tableau system T and verify T's soundness and completeness.On the basis of this stage... |
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| Keywords: | modal system T Herbrand theorem signed formulas tableau systems |
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