Horn理论内外部的演绎推理
Deductive Inference for the Interiors and Exteriors of Horn Theories
摘要：
本文研究了Horn知识库的内部和外部的演绎推理，其中内部和外部是Makino和Ibaraki为了研究知识库的稳定性而引入的.我们给出了一个线性时间算法的内部推导，并证明了它是co-NP-完全的外部推导。在基于模型的表示下，我们证明了内部的演绎问题是NP-完全的，而外部的演绎问题是co-NP-完全的。对于外部的Horn包络，我们证明了它在基于模型的表示下是线性可解的，而在基于公式的表示下是共NP完全的。我们还讨论了多项式可解的情况下，所有棘手的问题。
英文摘要：
In this paper, we investigate the deductive inference for the interiors and exteriors of Horn knowledge bases, where the interiors and exteriors were introduced by Makino and Ibaraki to study stability properties of knowledge bases. We present a linear time algorithm for the deduction for the interiors and show that it is co-NP-complete for the deduction for the exteriors. Under model-based representation, we show that the deduction problem for interiors is NP-complete while the one for exteriors is co-NP-complete. As for Horn envelopes of the exteriors, we show that it is linearly solvable under model-based representation, while it is co-NP-complete under formula-based representation. We also discuss the polynomially solvable cases for all the intractable problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
