Holena Martin
Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vodárenskou veZí 2, CZ-18207 Praha 8, Czech Republic.
Neural Comput. 2006 Nov;18(11):2813-53. doi: 10.1162/neco.2006.18.11.2813.
This article addresses the topic of extracting logical rules from data by means of artificial neural networks. The approach based on piecewise linear neural networks is revisited, which has already been used for the extraction of Boolean rules in the past, and it is shown that this approach can be important also for the extraction of fuzzy rules. Two important theoretical properties of piecewise-linear neural networks are proved, allowing an elaboration of the basic ideas of the approach into several variants of an algorithm for the extraction of Boolean rules. That algorithm has already been used in two real-world applications. Finally, a connection to the extraction of rules of the Łukasiewicz logic is established, relying on recent results about rational McNaughton functions. Based on one of the constructive proofs of the McNaughton theorem, an algorithm is formulated that in principle allows extracting a particular kind of formulas of the Łukasiewicz predicate logic from piecewise-linear neural networks trained with rational data.
本文探讨了通过人工神经网络从数据中提取逻辑规则这一主题。重新审视了基于分段线性神经网络的方法，该方法过去已用于布尔规则的提取，并且表明此方法对于模糊规则的提取也可能很重要。证明了分段线性神经网络的两个重要理论性质，从而能够将该方法的基本思想细化为布尔规则提取算法的几个变体。该算法已在两个实际应用中使用。最后，基于关于有理麦克诺顿函数的最新结果，建立了与卢卡西维茨逻辑规则提取的联系。基于麦克诺顿定理的一个构造性证明，制定了一种算法，原则上允许从用有理数据训练的分段线性神经网络中提取卢卡西维茨谓词逻辑的特定类型公式。
