Generalised Kernel Sets for Inverse Entailment
Generalised Kernel Sets for Inverse Entailment
复制标题
逆蕴涵的广义核集
DOI：
10.1007/978-3-540-27775-0_12
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
A. Russo
中科院分区：
文献类型：
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作者：
O. Ray;K. Broda;A. Russo
逆逻辑蕴涵的任务对于溯因和归纳逻辑程序设计（ALP & ILP）学科来说是至关重要的。Bottom Generalisation（BG）是一种广泛应用的逆蕴涵（IE）方法，但仅限于从Plotkin的C-推导概念所限制的假设空间中推导单个子句。此外，BG的已知实际应用仅限于Horn子句逻辑。最近，一个混合的ALP-ILP证明过程，称为HAIL，被证明是概括现有的BG技术，通过推导多个条款，在一个单一的例子，并构建BG的语义之外的假设。冰雹证明过程是基于一个新的语义，称为核心集包容（KSS），这是一个健全的推广BG。但到目前为止，KSS仅定义为Horn子句。本文将KSS的语义从Horn小句逻辑扩展到一般小句逻辑，并证明它仍然是BG的一个合理的扩展。一个概括的C-推导，称为K*-推导，介绍和示出提供一个健全和完整的表征KSS。最后，K*-推导是用来提供一个系统的比较现有的证明程序的基础上IE。
The task of inverting logical entailment is of central importance to the disciplines of Abductive and Inductive Logic Programming (ALP & ILP). Bottom Generalisation (BG) is a widely applied approach for Inverse Entailment (IE), but is limited to deriving single clauses from a hypothesis space restricted by Plotkin’s notion of C-derivation. Moreover, known practical applications of BG are confined to Horn clause logic. Recently, a hybrid ALP-ILP proof procedure, called HAIL, was shown to generalise existing BG techniques by deriving multiple clauses in response to a single example, and constructing hypotheses outside the semantics of BG. The HAIL proof procedure is based on a new semantics, called Kernel Set Subsumption (KSS), which was shown to be a sound generalisation of BG. But so far KSS is defined only for Horn clauses. This paper extends the semantics of KSS from Horn clause logic to general clausal logic, where it is shown to remain a sound extension of BG. A generalisation of the C-derivation, called a K*-derivation, is introduced and shown to provide a sound and complete characterisation of KSS. Finally, the K*-derivation is used to provide a systematic comparison of existing proof procedures based on IE.