The satisfiability problem in multiple-valued Horn formulae

Proceedings of 24th International Symposium on Multiple-Valued Logic (ISMVL'94) Pub Date : 1994-05-25 DOI:10.1109/ISMVL.1994.302194

G. Escalada-Imaz, F. Manyà

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引用次数: 26

Abstract

Testing the satisfiability of propositional Horn formulae is an important problem within artificial intelligence due to its repercussions in rule-based systems. This problem has been widely studied and its linearity has been proved for the classical case. However, nothing has been published to solve the satisfiability of multiple-valued Horn formulae, although it is closely related to deduction in expert systems frameworks (where a certainty degree is attached to each fact and rule). In this paper, we propose several new results. First, we present a calculus for multiple-valued Horn clauses and claim its soundness and completeness. Second, we offer a detailed description of an almost linear algorithm for testing the satisfiability of multiple-valued Horn formulae. Finally, the minimal model, the minimal inconsistent interpretation and the maximal set of consistent clauses are defined and furnished by another algorithm which is almost linear too. This information is particularly helpful when validating a rule-based system with a knowledge base formed by a set of multiple-valued clauses.<>

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多值Horn公式的可满足性问题

由于命题霍恩公式在基于规则的系统中的影响，测试命题霍恩公式的可满足性是人工智能中的一个重要问题。这一问题得到了广泛的研究，并在经典情况下证明了其线性性。然而，没有任何出版物来解决多值Horn公式的可满足性，尽管它与专家系统框架中的演绎密切相关(其中每个事实和规则都附加了确定性程度)。在本文中，我们提出了几个新的结果。首先，我们给出了多值Horn子句的一个演算，并证明了它的完备性。其次，我们详细描述了一种几乎线性的算法来检验多值Horn公式的可满足性。最后，用另一种近似线性的算法定义和提供了最小模型、最小不一致解释和最大一致子句集。当使用由一组多值子句组成的知识库验证基于规则的系统时，此信息特别有用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Proceedings of 24th International Symposium on Multiple-Valued Logic (ISMVL'94)

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