Minspaces上概念相似性的比较：公理化和表演算
Comparative concept similarity over Minspaces: Axiomatisation and Tableaux Calculus
摘要：
我们研究的逻辑比较概念相似性$\CSL$介绍谢列梅特，Tishkovsky，沃尔特和Zakharyaschev捕捉一种形式的定性相似性比较。在这个逻辑中，我们可以用公式表示断言的形式“对象A与B比与C更相似”。这种逻辑的语义定义的距离函数评估对象的相似度配备的结构。我们认为在这里的特殊情况下的语义引起的\emph{minspaces}，后者是距离空间的最小值的一组距离总是存在的。事实证明，任意极小空间上的语义可以等价地用条件逻辑的典型优先结构来指定。我们首先给出一个直接的公理化这个逻辑在Minspaces。接下来，我们定义一个决策过程的形式tableaux演算。演算和公理化都利用了优先结构的语义重构。
英文摘要：
We study the logic of comparative concept similarity $\CSL$ introduced by Sheremet, Tishkovsky, Wolter and Zakharyaschev to capture a form of qualitative similarity comparison. In this logic we can formulate assertions of the form " objects A are more similar to B than to C". The semantics of this logic is defined by structures equipped by distance functions evaluating the similarity degree of objects. We consider here the particular case of the semantics induced by \emph{minspaces}, the latter being distance spaces where the minimum of a set of distances always exists. It turns out that the semantics over arbitrary minspaces can be equivalently specified in terms of preferential structures, typical of conditional logics. We first give a direct axiomatisation of this logic over Minspaces. We next define a decision procedure in the form of a tableaux calculus. Both the calculus and the axiomatisation take advantage of the reformulation of the semantics in terms of preferential structures.
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