提出新型条件语法拆分,让推理更灵活高效。
Broadening the Applicability of Conditional Syntax Splitting for Reasoning from Conditional Belief Bases
- 放宽条件语法拆分的原子共享限制,支持非平凡条件
- 新方法可处理共享原子与复杂条件的信念基拆分
- 适合逻辑推理与知识系统构建的研究者
在基于条件信念基的非单调推理中,满足语法拆分公理的推理算子可在信念基按不相交签名分割时仅考虑相关部分。然而实际中不相交性罕见,因此提出安全条件语法拆分以允许子基间共享部分原子。近期研究发现此类重叠仅限于平凡自满足条件。本文提出一种广义安全条件语法拆分,扩展了拆分适用范围:允许子基共享原子与非平凡条件。通过识别真正拆分与无益的简单拆分,我们引入调整后的推理公理,并评估多个主流归纳推理算子。结果表明,满足广义条件语法拆分的算子必满足原条件拆分,但逆命题不成立。
原文摘要 · Abstract (English)
In nonmonotonic reasoning from conditional belief bases, an inference operator satisfying syntax splitting postulates allows for taking only the relevant parts of a belief base into account, provided that the belief base splits into subbases based on disjoint signatures. Because such disjointness is rare in practice, safe conditional syntax splitting has been proposed as a generalization of syntax splitting, allowing the conditionals in the subbases to share some atoms. Recently this overlap of conditionals has been shown to be limited to trivial, self-fulfilling conditionals. In this article, we propose a generalization of safe conditional syntax splittings that broadens the applicability of splitting postulates. In contrast to safe conditional syntax splitting, our generalized notion supports syntax splittings of a belief base Δ where the subbases of Δ may share atoms and nontrivial conditionals. We illustrate how this new notion overcomes limitations of previous splitting concepts, and we identify genuine splittings, separating them from simple splittings that do not provide benefits for inductive inference from Δ. We introduce adjusted inference postulates based on our generalization of conditional syntax splitting, and we evaluate several popular inductive inference operators with respect to these postulates. Furthermore, we show that, while every inductive inference operator satisfying generalized conditional syntax splitting also satisfies conditional syntax splitting, the reverse does not hold.
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