Abstract
The theory of association rules is an issue in recent years since it has been successfully applied in a wide range of domains, and removing redundant formula in a propositional theory is another issue, but development of the two theory seems independently. In this paper, the mutual relationship between them are investigated by introducing the formal context (ΩΓ, Γ, I), then the theory of ε-reduction of finite theory Γ in two-valued propositional logic is proposed. By introducing the association rules to the formal context (ΩΓ, Γ, I), judgment theorems of ε-consistent theorems are examined, and two approaches to explore ε-reduction are presented.
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References
Liberatore, P.: Redundancy in logic I: CNF propositional formulae. Artificition Intelligence 163(2), 203–232 (2005)
Liberatore, P.: Redundancy in logic II: 2-CNF and Horn propositional formulae. Artificition Intelligence 172(2-3), 265–299 (2008)
Liberatore, P.: Redundancy in logic III: Non-monotonic reasoning. Artificition Intelligence 172(11), 1317–1359 (2008)
Ren, Y., Ma, X.J., Wang, H.T.: Reduction of a propositional set and its roots in \(\mathcal{L}^{*}\) system. Fuzzy Systems and Mathematics 20(2), 23–27 (2006) (in Chinese)
Li, L.F., Zhang, D.X.: The application of concept lattice theory in the reduction of the proposition set in two-valued propositional logic. Acta Electronica Sinica 35(8), 1538–1542 (2007) (in Chinese)
Agrawl, R., Imielinski, A.: Mining association rules between sets of items in large databases. In: Proc. ACM SIGMOD International Conference on Management of Data, Washington, D.C., May 1993, pp. 207–216 (1993)
Pasquier, N., Taouil, R., Bastide, Y., Stumme, G., Lakhal, L.: Generating a condensed representation for association rules. Journal of Intelligent Information Systems 24(1), 29–60 (2005)
Zaki, M.J., Hsiao, C.-J.: Efficient Algorithms for Mining Closed. Itemsets and Their Lattice Structure. IEEE Transactions on Knowledge and Data Engineering 17(4), 462–478 (2005)
Zhou, X.N., Wang, G.J.: Consistency degrees of theories in some systems of propositional fuzzy logic. Fuzzy Sets and System 152(3), 321–331 (2005)
Wang, G.J.: Introduction to mathematical logic and resolution principle. Science in China Press, Beijing (2006) (in Chinese)
Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Berlin (1999)
Wang, G.J., Fu, L., Song, J.S.: Theory of truth degrees of propositions in two-valued logic. Science in China, Ser. A 45(9), 1106–1116 (2002)
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Li, Lf., Yang, N. (2010). Applying Association Rules to ε-Reduction of Finite Theory in Two-Valued Propositional Logic. In: Cao, By., Wang, Gj., Chen, Sl., Guo, Sz. (eds) Quantitative Logic and Soft Computing 2010. Advances in Intelligent and Soft Computing, vol 82. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15660-1_13
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DOI: https://doi.org/10.1007/978-3-642-15660-1_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15659-5
Online ISBN: 978-3-642-15660-1
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