Abstract
One of key issues for α-n(t) ary resolution automated reasoning based on lattice-valued logic with truth-value in a lattice implication algebra is to investigate the α-n(t) ary resolution of some generalized literals. In this article, the determination of α-resolution of any 3-ary generalized literals which include the implication operators not more than 2 in LP(X). It not only lay the foundation for practical implementation of automated reasoning algorithm in LP(X), but also provides the strong support for α-n(t) ary resolution automated reasoning approaches.
Article PDF
Avoid common mistakes on your manuscript.
References
J.P. Robinson, “ A machine-oriented logic based on the resolution principle”, J. ACM., 12, 23–41(1965).
K.Y. Qin, Y. Xu, Z.M. Song, “ Lattice-valued propositional logic LP(X)(I)”, Fuzzy Sys. Math., 11(4), 5–10(1997).
K.Y. Qin, Y. Xu, Z.M. Song, “Compactness and Lowenheim-Skolem property of first-order lattice-valued logic system FM”, Chinese Sci. Bull., 43(4), 371–375(1998).
K.Y. Qin, Y. Xu, “ Lattice-valued propositional logic (II)”, J. Southwest Jiaoong Univ., 2(1), 22–27(1994).
L. Bolc, P. Borowik, “ Many-Valued Logics”, Springer, Berlin, (1992).
R.R. Yager, “ Inference in a multiple-valued logic system”, Int. J. Man Machine Stud., 23, 27–44(1985).
W. Wang, Y. Xu, K.Y. Qin, “ The structure and - resolution field of indecomposable extremely simple forms of lattice-valued propositional logic LP(X)”, The Journal of Fuzzy Mathematics, 11(4), 877–891(2003).
X.H. Liu, “ Resolution-based Automated Reasoning”, Academic Press, China, (1994). (in Chinese)
Y. Xu, “ Lattice implication algebras”, J. Southwest Jiaotong University, 89(1), 20–27(1993). (in Chinese)
Y. Xu, K.Y. Qin, “ Lattice-valued propositional logic (I)”, J. Southwest Jiaotong Univ., 1(2), 123–128(1993).
Y. Xu, K.Y. Qin, Z.M. Song, “ On syntax of first-order lattice-valued logic system FM”, Chinese Sci. Bull., 42(17), 1052–1055(1997).
Y. Xu, D. Ruan, E.E. Kerre, J. Liu, “α-Resolution principle based on lattice-valued propositional logic LP(X)”, Inform. Sci., 130, 195–223(2000).
Y. Xu, D. Ruan, E.E. Kerre, J. Liu, “α-Resolution principle based on lattice-valued first-order lattice-valued logic LF(X)”, Information Science, 132, 221–239(2001).
Y. Xu, D. Ruan, K.Y. Qin, J. Liu, “ Lattice-Valued Logic”, Springer (2003).
Y. Xu, X. B. Li, J. Liu, D. Ruan, “ Determination of α-resolution for lattice-valued first-order logic based on lattice implication algebra”, Proc. the 2007 International Conference on Intelligent Systems and Knowledge Engineering, Chengdu, China, 1567–1573(2007).
Y. Xu, S. W. Chen, J. Liu, D. Ruan, “ Weak completeness of resolution in a linguistic truth-valued propositional logic”, Proc. IFSA2007: Theoretical Advances and Applications of Fuzzy Logic and Soft Computing(IFSA2007), Cancun, Mexico, 358–366(2007).
Y. Xu, J. Liu, D. Ruan, X.B. Li, “ Determination of α-resolution in lattice-valued first-order logic LF(X)”, Information Sciences, 181, 1836–1862(2011)
Y. Xu, X. M. Zhong, “ General form of α-resolution principle based on lattice-valued logic with truth-value in lattice implication algebras”, Information Sciences, (under review)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
About this article
Cite this article
Liu, Y., Jia, H. & Xu, Y. Determination of 3-Ary α-Resolution in Lattice-valued Propositional Logic LP(X). Int J Comput Intell Syst 6, 943–953 (2013). https://doi.org/10.1080/18756891.2013.808802
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1080/18756891.2013.808802