Approximation fixpoint theory (AFT) provides an algebraic framework for the study of fixpoints of operators on bilattices and has found its applications in characterizing semantics for various classes of logic programs and nonmonotonic languages. In this paper, we show one more application of this kind: the alternating fixpoint operator by Knorr et al. for the study of the well-founded semantics for hybrid MKNF knowledge bases is in fact an approximator of AFT in disguise, which, thanks to the power of abstraction of AFT, characterizes not only the well-founded semantics but also two-valued as well as three-valued semantics for hybrid MKNF knowledge bases. Furthermore, we show an improved approximator for these knowledge bases, of which the least stable fixpoint is information richer than the one formulated from Knorr et al.'s construction. This leads to an improved computation for the well-founded semantics. This work is built on an extension of AFT that supports consistent as well as inconsistent pairs in the induced product bilattice, to deal with inconsistencies that arise in the context of hybrid MKNF knowledge bases. This part of the work can be considered generalizing the original AFT from symmetric approximators to arbitrary approximators.
翻译:近似点定点理论( AFT) 为两极理论操作者固定点的研究提供了一个代数框架, 并发现其应用为各类逻辑程序和非调子语言的语义特征。 在本文中, 我们展示了另一种应用: Knorr 等人的交替固定点操作者, 用于研究混合MKKNF知识基础的有根有根的语义, 事实上, 是一个伪装的AFT 的代数工具, 由于AFT的抽象力量, 它不仅描述有根有根有根的语义, 而且还为混合的MKNFF知识基础具有两种价值和三种价值的语义。 此外, 我们展示了这些知识基础的更接近性工具, 其中最不稳定的定点比从Knor 等人的构造所制成的语义更丰富。 这导致对有根有根的语义的语义学计算方法得到改进。 这项工作建立在AFTFT的延伸上, 支持该导导出产品双基基础的一致和不一面的对立。