| 摘要: |
| 悖论逻辑ＬＰ是一个超协调逻辑，发展超协调逻辑（ＬＰ）的目的是使得不会从矛盾推出任一命题，但它有一个主要缺点：就是一些在经典逻辑中有效的推理在ＬＰ中不再有效；极小悖论逻辑ＬＰｍ能克服这个缺点，使得在没有矛盾的直接影响下超协调逻辑等价于经典逻辑．ＬＰ和ＬＰｍ原来都只给出语义定义，虽然已有ＬＰ的证明论，但如何得到一个ＬＰｍ的证明论仍是一个未解问题．本文提出了一种可靠与完全的表演算作为ＬＰ与ＬＰｍ的证明论． |
| 关键词: 表演算 超协调逻辑 悖论逻辑 极小悖论逻辑 极小非协调模型 |
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| 基金项目:本文研究得到国家自然科学基金,国家863高技术计划与李嘉诚学术基金,国家基础研究攀登计划资助. |
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| TABLEAUX FOR LOGIC OF PARADOX |
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Lin Zuoquan,Li Wei
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| Abstract: |
| The LP (logic of paradox) is a paraconsistent logic. One of the motivationsbehind paraconsistent logic, namely LP, is that it should not allow that everything followsfrom a single contradiction. However it has one important drawback: that some classicalinferences would be invalid in LP. The LP.(logic of minimal paradox) can overcome thisdrawback, such that paraconsistent logic would be equivalent to classical logic when therewas not direct effect of a contradiction. Originally, LP and LP. were only defined in semantic. Although some proof theories for LP were introduced, it has left open how to obtain a satisfactory proof theory for LP.. This paper propose the sound and completestableaux with respect to the semantics of LP and LP., respectively. |
| Key words: Tableaux paraconsistent logic logic of paradox logic of millinlal paradox minimally Inconsistent models. |
