The logic of hybrid MKNF (minimal knowledge and negation as failure) is a powerful knowledge representation language that elegantly pairs ASP (answer set programming) with ontologies. Disjunctive rules are a desirable extension to normal rule-based reasoning and typically semantic frameworks designed for normal knowledge bases need substantial restructuring to support disjunctive rules. Alternatively, one may lift characterizations of normal rules to support disjunctive rules by inducing a collection of normal knowledge bases, each with the same body and a single atom in its head. In this work, we refer to a set of such normal knowledge bases as a head-cut of a disjunctive knowledge base. The question arises as to whether the semantics of disjunctive hybrid MKNF knowledge bases can be characterized using fixpoint constructions with head-cuts. Earlier, we have shown that head-cuts can be paired with fixpoint operators to capture the two-valued MKNF models of disjunctive hybrid MKNF knowledge bases. Three-valued semantics extends two-valued semantics with the ability to express partial information. In this work, we present a fixpoint construction that leverages head-cuts using an operator that iteratively captures three-valued models of hybrid MKNF knowledge bases with disjunctive rules. This characterization also captures partial stable models of disjunctive logic programs since a program can be expressed as a disjunctive hybrid MKNF knowledge base with an empty ontology. We elaborate on a relationship between this characterization and approximators in AFT (approximation fixpoint theory) for normal hybrid MKNF knowledge bases.
翻译:混合 MKNF (最小知识和否定失败) 的逻辑是一种强大的知识代表语言, 优雅地将 ASP( 问答式编程) 与内涵相配。 分置规则是正常基于规则的推理的可取延伸, 通常为正常知识基础设计的语义框架需要大量重组以支持互兼规则。 或者, 可能会通过引入正常知识基础的集合来提升对正常规则的定性以支持脱节规则。 普通知识基础各有同一体, 头部有一个单一的原子。 在这项工作中, 我们指一组普通知识基础, 将非交错混合MKNF知识基础的语义扩展为正切知识基础。 在这项工作中, 我们用普通的基底部模型来修正固定基底的 mK 。 之前, 我们已经表明, 前端规则可以与固定点操作者操作器操作者匹配, 捕捉取双值的MKNFFF模型的分解混合混合 mK 知识基础。 3- 估值的精度评估将两值的语义包含部分信息。 在此工作中, 我们用一个固定基底的MK 模型来修正模型的基底图图图。