CONSERVATIVELY EXTENDING CLASSICAL LOGIC WITH TRANSPARENT TRUTH
CONSERVATIVELY EXTENDING CLASSICAL LOGIC WITH TRANSPARENT TRUTH
复制标题
用透明的真相保守地扩展经典逻辑
DOI：
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发表时间：
2012
期刊：
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通讯作者：
David Ripley
中科院分区：
文献类型：
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作者：
David Ripley
本文展示了如何保守地扩展一个经典逻辑与一个透明的真谓词，面对由此产生的悖论。所有经典的推论都被保留下来，而且确实扩展到了全部（涉及真理的）词汇。然而，并不是所有的经典元推理都被保留下来;特别是，由此产生的逻辑系统是不可传递的。这种非传递性的一些限制是adumbrated，两个证明系统，并证明是健全和完整的。(One证明系统具有可接受的切割，但另一个没有。
This paper shows how to conservatively extend a classical logic with a transparent truth predicate, in the face of the paradoxes that arise as a consequence. All classical inferences are preserved, and indeed extended to the full (truth-involving) vocabulary. However, not all classical metainferences are preserved; in particular, the resulting logical system is nontransitive. Some limits on this nontransitivity are adumbrated, and two proof systems are presented and shown to be sound and complete. (One proof system features admissible Cut, but the other does not.)