Bialgebraic Semantics for Logic Programming
Bialgebraic Semantics for Logic Programming
复制标题
逻辑编程的双代数语义
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
F. Zanasi
中科院分区：
文献类型：
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作者：
F. Bonchi;F. Zanasi
我们研究不同的行为指标，例如
分支和线性时间语义，在山地环境中。给定
calgebra $ alphacolon x o hx $ for foundor $ h colon mathrm {set} o
Mathrm {set} $，我们定义了一个用于在$ x $上衍生伪测量法的框架
测量状态的行为距离。
一个关键步骤是将函数$ h $上升到$ mathrm {set} $上
pseudometric spaces的类别$ MATHRM {PMET} $上的functor $ edielline {h} $。
我们提出了两种不同的方法，可以看作是
Kantorovich和Wasserstein伪测量法进行了概率措施。我们显示
两种方法提供的伪测量学在几个方法上重合
自然的例子，但总体上它们有所不同。
如果$ h $有最终的山地
规范的行为距离通常是分支时间，即
概括性化。为了建模线性时间指标（概括
痕量等价），我们显示出足够的提升分布条件
法律和单调。这些结果使我们能够采用广义的力量
建造。
We study different behavioral metrics, such as those arising from both
branching and linear-time semantics, in a coalgebraic setting. Given a
coalgebra $alphacolon X o HX$ for a functor $H colon mathrm{Set} o
mathrm{Set}$, we define a framework for deriving pseudometrics on $X$ which
measure the behavioral distance of states.
A crucial step is the lifting of the functor $H$ on $mathrm{Set}$ to a
functor $overline{H}$ on the category $mathrm{PMet}$ of pseudometric spaces.
We present two different approaches which can be viewed as generalizations of
the Kantorovich and Wasserstein pseudometrics for probability measures. We show
that the pseudometrics provided by the two approaches coincide on several
natural examples, but in general they differ.
If $H$ has a final coalgebra, every lifting $overline{H}$ yields in a
canonical way a behavioral distance which is usually branching-time, i.e., it
generalizes bisimilarity. In order to model linear-time metrics (generalizing
trace equivalences), we show sufficient conditions for lifting distributive
laws and monads. These results enable us to employ the generalized powerset
construction.
影响因子：
0.7
作者：
Komendantskaya E
通讯作者：
Komendantskaya E