Lattice-valued simulations for quantitative transition systems
Lattice-valued simulations for quantitative transition systems
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DOI：
10.1016/j.ijar.2014.10.001
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Haiyu Pan;Yongming Li;Yongzhi Cao
中科院分区：
文献类型：
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作者：
Haiyu Pan;Yongming Li;Yongzhi Cao
从非负实数中取值的定量（bi）模拟在标记转换系统的分析中有许多应用，这些系统的转换、状态或标签包含定量信息。为了研究剩余格值逻辑设置中标记转移系统的仿真语义，我们引入了标记转移系统的一种扩展，称为定量转移系统（QTSs），其标记具有剩余格值相等关系。然后，我们建立了QTS状态之间的格值关系，称为近似相似性，以量化一个状态被另一个状态模拟的程度。本文的一个主要贡献是表明，与经典的相似性既有不动点特征又有逻辑特征的设置不同，这些结果并不适用于一般的QTSs近似相似性，但适用于有限Heyting代数中具有真值的QTSs。
Quantitative (bi)simulations taking values from non-negative real numbers enjoy numerous applications in the analysis of labeled transition systems, whose transitions, states, or labels contain quantitative information. To investigate the simulation semantics of labeled transition systems in the residuated lattice-valued logic setting, we introduce an extension of labeled transition systems, called the quantitative transition systems (QTSs), whose labels are equipped with a residuated lattice-valued equality relation. We then establish a lattice-valued relation between states of a QTS, called approximate similarity, to quantify to what extent one state is simulated by another. One main contribution of this paper is to show that unlike the classic setting where similarity has both fixed point and logical characterizations, these results do not hold for approximate similarity on QTSs in general, but they hold for QTSs having truth values from finite Heyting algebras.