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首页> 外文会议>Annual ACM/IEEE Symposium on Logic in Computer Science >Quantitative Algebraic Reasoning
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Quantitative Algebraic Reasoning

机译：量化代数推理

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摘要

We develop a quantitative analogue of equational reasoning which we call quantitative algebra. We define an equality relation indexed by rationals: a =e b which we think of as saying that “a is approximately equal to b up to an error of ε”. We have 4 interesting examples where we have a quantitative equational theory whose free algebras correspond to well known structures. In each case we have finitary and continuous versions. The four cases are: Hausdorff metrics from quantitive semilattices; p-Wasserstein metrics (hence also the Kantorovich metric) from barycentric algebras and also from pointed barycentric algebras and the total variation metric from a variant of barycentric algebras.
机译：我们开发了我们呼叫定量代数的等级推理的定量模拟。我们定义了索引的平等关系：a = e b我们认为“a大致等于b最大到ε”的说法。我们有4个有趣的例子，我们具有定量的等式理论，其自由代数对应于众所周知的结构。在每种情况下，我们都有综合和连续版本。四个案例是：来自量化半理解的Hausdorff指标; P-Wassersein度量（因此也是来自重心代数的Kantorovich度量）以及来自尖端的重心代数和来自重心代数的变体的总变化度量。

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