析取混合MKNF知识库的无基集
Unfounded Sets for Disjunctive Hybrid MKNF Knowledge Bases
摘要：
将回答集编程（ASP）的封闭世界推理与本体论的开放世界推理相结合，拓宽了推理机的应用空间。析取混合MKNF知识库简洁地扩展了ASP，并且在某些情况下不会增加推理任务的复杂性。然而，在许多情况下，求解器的开发是滞后的。因此，解决析取混合MKNF知识库的唯一已知方法是基于猜测和验证，如Motik和Rosati在其原始工作中所制定的。一个主要的障碍是理解如何约束传播可以由求解器执行，其中，在ASP的上下文中，围绕着\textit{unfounded atoms}的计算，原子是假的部分解释。在这项工作中，我们建立了改进求解器的混合MKNF知识库与析取规则：我们正式的概念，这些知识库的无根据集，确定较低的复杂性界限，并演示了我们如何将这些发展集成到一个求解器。我们讨论了本体论所带来的挑战，这些挑战不存在于析取逻辑程序的求解器的开发中，这保证了与传统的无根据集定义的一些偏差。我们比较我们的工作与事先定义的无根据集。
英文摘要：
Combining the closed-world reasoning of answer set programming (ASP) with the open-world reasoning of ontologies broadens the space of applications of reasoners. Disjunctive hybrid MKNF knowledge bases succinctly extend ASP and in some cases without increasing the complexity of reasoning tasks. However, in many cases, solver development is lagging behind. As the result, the only known method of solving disjunctive hybrid MKNF knowledge bases is based on guess-and-verify, as formulated by Motik and Rosati in their original work. A main obstacle is understanding how constraint propagation may be performed by a solver, which, in the context of ASP, centers around the computation of \textit{unfounded atoms}, the atoms that are false given a partial interpretation. In this work, we build towards improving solvers for hybrid MKNF knowledge bases with disjunctive rules: We formalize a notion of unfounded sets for these knowledge bases, identify lower complexity bounds, and demonstrate how we might integrate these developments into a solver. We discuss challenges introduced by ontologies that are not present in the development of solvers for disjunctive logic programs, which warrant some deviations from traditional definitions of unfounded sets. We compare our work with prior definitions of unfounded sets.
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