Quantized Linear Logic, Involutive Quantales and Strong Negation
Quantized Linear Logic, Involutive Quantales and Strong Negation
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DOI：
10.1023/b:stud.0000039030.03885.7c
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发表时间：
2004-08
期刊：
影响因子：
0.7
通讯作者：
N. Kamide
中科院分区：
文献类型：
--
作者：
N. Kamide
本文介绍了一种新的逻辑--量化直觉线性逻辑（QILL），它与Mulvey和Pelletier的（交换）对合Quantale逻辑密切相关。得到了QILL的一些无割演算，它们具有新的性质“量子化原理”和一些完整的语义，如对合Quantale模型和Quantale模型。QILL和Wansing的强否定扩展直觉线性逻辑之间的关系也被观察到使用这样的句法和语义框架。
A new logic, quantized intuitionistic linear logic (QILL), is introduced, and is closely related to the logic which corresponds to Mulvey and Pelletier's (commutative) involutive quantales. Some cut-free sequent calculi with a new property “quantization principle” and some complete semantics such as an involutive quantale model and a quantale model are obtained for QILL. The relationship between QILL and Wansing's extended intuitionistic linear logic with strong negation is also observed using such syntactical and semantical frameworks.