关于选言逻辑程序推理复杂性的三分和二分结果
Trichotomy and Dichotomy Results on the Complexity of Reasoning with Disjunctive Logic Programs
摘要：
我们提出了一种描述逻辑推理复杂性的析取逻辑程序的剖分结果。为此，我们引入了一定的定义模式类的程序的基础上，一组允许的规则的arities。我们表明，每个这样的类的程序有一个有限的表示，并为每个类定义的模式，我们的特征的复杂性的存在的答案集问题。接下来，我们推导出类似的特征的复杂性的怀疑和轻信推理与析取逻辑程序。这些结果具有潜在的意义。一方面，它们揭示了造成答案集计算困难的一些原因。另一方面，它们识别问题实例的类别，对于这些问题来说，问题是“容易的”（在P中）或“比一般更容易”（在NP中）。我们得到了类似的结果的推理与析取程序的复杂性下的简化模型语义。逻辑程序设计理论与实践（Theory and Practice of Logic Programming，TPLP）
英文摘要：
We present trichotomy results characterizing the complexity of reasoning with disjunctive logic programs. To this end, we introduce a certain definition schema for classes of programs based on a set of allowed arities of rules. We show that each such class of programs has a finite representation, and for each of the classes definable in the schema we characterize the complexity of the existence of an answer set problem. Next, we derive similar characterizations of the complexity of skeptical and credulous reasoning with disjunctive logic programs. Such results are of potential interest. On the one hand, they reveal some reasons responsible for the hardness of computing answer sets. On the other hand, they identify classes of problem instances, for which the problem is "easy" (in P) or "easier than in general" (in NP). We obtain similar results for the complexity of reasoning with disjunctive programs under the supported-model semantics. To appear in Theory and Practice of Logic Programming (TPLP)
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