Abstract
This paper focuses on refined non-clausal resolution methods in a Łukasiewicz first order logic \(\fancyscript{L}_n\)F(X), i.e., \(\alpha \)-generalized lock resolution with deleting strategies, which can further improve the efficiency of \(\alpha \)-generalized lock resolution. First, the concepts of strong implication, weak implication, and \(\alpha \)-generalized lock resolution with these two deleting strategies are given, respectively. Then the compatibilities of \(\alpha \)-generalized lock resolution with strong implication deleting and weak implication deleting are shown in \(\fancyscript{L}_n\)F(X), respectively. Finally, an algorithm for \(\alpha \)-generalized resolution with these deleting strategies is given.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Boyer R (1971) Locking: a restriction of resolution. PhD thesis, University of Texas, Austin
Chen XC (1998) On compatibility of deletion strategy. Chin J Comput 21(2):176–182
Deng AS (1998) Deletion strategy in boolean operator fuzzy logic. J Northwest Normal Univ 1(1):1–2
He XX, Liu J, Xu Y, Martínez L, Ruan D (2012) On \(\alpha \)-satisfiability and its \(\alpha \)-lock resolution in a finite lattice-valued propositional logic. Logic J IGPL 20(3):579–588
He XX, Xu Y, Liu J, Ruan D (2011) \(\alpha \)-lock resolution method for a lattice-valued first-order logic. Eng Appl Artif Intell 24(7):1274–1280
He XX, Xu Y, Liu J, Chen SW (2011) On compatibilities of \(\alpha \)-lock resolution method in linguistic truth-valued lattice-valued logic. Soft Comput 16(4):699–709
Liu XH (1994) Automated reasoning based on resolution methods. Science Press, Beijing (In Chinese)
Murray NV (1982) Completely non-clausal theorem proving. Artif Intell 18:67–85
Robinson JA (1965) A machine-oriented logic based on the resolution principle. J ACM 12(1):23–41
Sun JG, Liu XH (1994) Deletion strategy using weak subsumption relation for modal resolution. Chin J Comput 17(5):321–329
Tang RK, Liu XH (1993) Deletion strategy in generalized \(\lambda \)-resolution. J JinLin Univ 2(2):37–41 (in Chinese)
Xu Y (1993) Lattice implication algebras. J Southwest Jiaotong Univ 89(1):20–27 (in Chinese)
Xu Y, Ruan D, Kerre EE, Liu J (2000) \(\alpha \)-resolution principle based on lattice-valued propositional logic LP(X). Inf Sci 130:195–223
Xu Y, Ruan D, Kerre EE, Liu J (2001) \(\alpha \)-resolution principle based on first-order lattice-valued logic LF(X). Inf Sci 132:221–239
Xu Y, Ruan D, Qin KY, Liu J (2003) Lattice-valued logic: an alternative approach to treat fuzziness and incomparability. Springer-Verlag, Berlin
Xu Y, Xu WT, Zhong XM, He XX (2010) \(\alpha \)-generalized resolution principle based on lattice-valued propositional logic system LP(X). In: The 9th international FLINS conference on foundations and applications of computational intelligence (FLINS2010), Chengdu, 2–4 Aug, pp 66–71
Xu Y, He XX, Liu J, Chen SW (2011) A general form of \(\alpha \)-generalized resolution based on lattice-valued logic (Submitted to Int J Computat Intell Syst)
Acknowledgments
This work is partially supported by the National Natural Science Foundation of China (Grant No. 61175055, 61105059, 61100046) and Sichuan Key Technology Research and Development Program under Grant No. 2011FZ0051.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
He, X., Xu, Y., Liu, J., Xu, P. (2014). \(\alpha \)-Generalized Lock Resolution with Deleting Strategies in \(\fancyscript{L}_n\)F(X). In: Sun, F., Li, T., Li, H. (eds) Knowledge Engineering and Management. Advances in Intelligent Systems and Computing, vol 214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37832-4_34
Download citation
DOI: https://doi.org/10.1007/978-3-642-37832-4_34
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-37831-7
Online ISBN: 978-3-642-37832-4
eBook Packages: EngineeringEngineering (R0)