A Refinement Operator for Description Logics
A Refinement Operator for Description Logics
复制标题
描述逻辑的细化算子
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
S. Nienhuys
中科院分区：
文献类型：
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作者：
Liviu Badea;S. Nienhuys
虽然学习逻辑程序的问题已经在ILP中得到了广泛的研究，但描述逻辑（DLs）中的学习问题主要是通过经验方法来解决的。然而，在DL中学习是值得的，因为Horn逻辑和描述逻辑都是广泛使用的知识表示形式主义，它们的表达能力是无与伦比的（两者都不包括另一个片段）。与描述逻辑中的大多数学习方法不同，这些方法提供了自下而上（并且通常过于具体）的示例最小概括，本文使用向下（和向上）细化运算符来解决DL中的学习问题。从技术上讲，我们为ALER描述逻辑构造了一个完整且适当的细化运算符（为了避免过拟合，我们不允许与目标DL进行析取）。虽然没有最小的细化运营商存在的ALER，我们表明，我们可以实现最小的所有细化步骤，除了那些引入的概念。我们还证明了完整的细化运营商ALER不能局部有限，并建议如何克服这个问题可以通过MDL搜索启发式。我们还讨论了开放世界的假设（通常在DL）的例子覆盖率的影响。
While the problem of learning logic programs has been extensively studied in ILP, the problem of learning in description logics (DLs) has been tackled mostly by empirical means. Learning in DLs is however worthwhile, since both Horn logic and description logics are widely used knowledge representation formalisms, their expressive powers being incomparable (neither includes the other as a fragment). Unlike most approaches to learning in description logics, which provide bottom-up (and typically overly specific) least generalizations of the examples, this paper addresses learning in DLs using downward (and upward) refinement operators. Technically, we construct a complete and proper refinement operator for the ALER description logic (to avoid overfitting, we disallow disjunctions from the target DL). Although no minimal refinement operators exist for ALER, we show that we can achieve minimality of all refinement steps, except the ones that introduce the ⊥ concept. We additionally prove that complete refinement operators for ALER cannot be locally finite and suggest how this problem can be overcome by an MDL search heuristic. We also discuss the influence of the Open World Assumption (typically made in DLs) on example coverage.