标题： 模糊描述逻辑在Gödel语义下的解释近似最小化 显示英文标题

标题： Approximate minimization of interpretations in fuzzy description logics under the Gödel semantics

摘要： 在模糊描述逻辑（FDLs）中最小化模糊解释的问题在理论上和实践中都很重要。例如，模糊或加权社交网络可以建模为模糊解释，其中个体代表行动者，角色捕捉交互作用。最小化这些解释会产生更紧凑的表示形式，这可以显著提高基于知识的系统中的推理和分析任务的效率。我们提出了第一个算法，在不使用Baaz投影算子和全角色的情况下，保留FDLs中的模糊概念断言，对Gödel语义下的有限模糊解释进行最小化。所考虑的FDLs类从$f\!\mathcal{ALC}$的子逻辑（不包含并运算符和全限制）到扩展了$f\!\mathcal{ALC}_{reg}$的FDL（包含逆角色和标示符）范围。我们的算法以扩展形式给出，支持近似保留：它最小化有限模糊解释$\mathcal{I}$，同时保留模糊概念断言的程度为$\gamma \in (0,1]$。 其时间复杂度为$O((m\log{l} + n)\log{n})$，其中$n$是$\mathcal{I}$域的大小，$m$是$\mathcal{I}$中原子角色的非零实例的数量，$l$是此类实例中使用的不同模糊值的数量加 2。 显示英文摘要

摘要： The problem of minimizing fuzzy interpretations in fuzzy description logics (FDLs) is important both theoretically and practically. For instance, fuzzy or weighted social networks can be modeled as fuzzy interpretations, where individuals represent actors and roles capture interactions. Minimizing such interpretations yields more compact representations, which can significantly improve the efficiency of reasoning and analysis tasks in knowledge-based systems. We present the first algorithm that minimizes a finite fuzzy interpretation while preserving fuzzy concept assertions in FDLs without the Baaz projection operator and the universal role, under the G\"odel semantics. The considered class of FDLs ranges from the sublogic of $f\!\mathcal{ALC}$ without the union operator and universal restriction to the FDL that extends $f\!\mathcal{ALC}_{reg}$ with inverse roles and nominals. Our algorithm is given in an extended form that supports approximate preservation: it minimizes a finite fuzzy interpretation $\mathcal{I}$ while preserving fuzzy concept assertions up to a degree $\gamma \in (0,1]$. Its time complexity is $O((m\log{l} + n)\log{n})$, where $n$ is the size of the domain of $\mathcal{I}$, $m$ is the number of nonzero instances of atomic roles in $\mathcal{I}$, and $l$ is the number of distinct fuzzy values used in such instances plus 2.