| 直觉主义量词模态逻辑系统MIPC~*的可靠性定理 |
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| 引用本文： | 高恒珊.直觉主义量词模态逻辑系统MIPC~*的可靠性定理[J].数学学报,2003,46(3):463-468. |
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| 作者姓名： | 高恒珊 |
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| 作者单位： | 中国科学院研究生院数学部,北京,100039 |
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| 摘 要： | 设WMμ为系统MIPC*全部公式的集,再设г∪{A} WMμ,则гMIPC* A意义明显.而 M A指гM-蕴涵A.以前已证明гM A гMIPC*A,即MIPC*为强完全的.本文证明其逆定理成立,即гMIPC*A гM A.是为MIPC*的可靠性定理.
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| 关 键 词： | 直觉主义量词模态逻辑 完全模态化公式 可靠性定理 |
| 文章编号： | 0583-1431(2003)03-0463-06 |
| 修稿时间： | 2001年1月23日 |
Soundness Theorem for Intuitionistic Quantified Modal Logic System MIPC |
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| Heng Shan GAO.Soundness Theorem for Intuitionistic Quantified Modal Logic System MIPC[J].Acta Mathematica Sinica,2003,46(3):463-468. |
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| Authors: | Heng Shan GAO |
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| Institution: | Heng Shan GAO (Graduate School of Academia Sinica, Beijing 100039, P. R. China) |
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| Abstract: | Let WMг be the set of all formulae of MIPC* and г ∪{A} WMμ. The meaning of "г MIPC* A" is obvious, and "г M A" means that г M-implies A. In a previous paper, we proved that F M A гMIPC* A, i.e., MIPC* is strongly complete. In this note we show that its inverse is also true, namely, г MIPC* A гM A. In other words, the system MIPC* is sound. |
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| Keywords: | Intuitionistic quantified modal logic Completely modalized formulae Soundness theorem |
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