Abstract
Computational reasoning is a practical description of computational logic. In this paper, a new concrete computational reasoning method based on complemented distributive lattices is proposed. Based on some logical operators, an inclusion degree on complemented distributive lattices is defined, which is employed to define the truth degree. Some basic properties of the truth mapping are examined. Then a kind of reasoning by computing in the framework of complemented distributive lattices is developed. The potential value of dealing with knowledge acquisition is expected in future.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Boyer RS, Moore JS (1986) Overview of a theorem-prover for a computational logic. Lect Notes Comput Sci 230:675–678
Bobillo F, Straccia U (2012) Generalized fuzzy rough description logics. Inf Sci 189:43–62
Zou L, Liu X, Pei Z, Huang DG (2013) Implication operators on the set of ∨-irreducible element in the linguistic truth-valued intuitionistic fuzzy lattice. Int J Mach Learn Cybernet 4(4):365–372
Xu ZB, Liang JY, Dang CY (2002) Inclusion degree: a perspective on measures for rough set data analysis. Inf Sci 141(3–4):227–236
Xu WH, Liu SH, Zhang WX (2013) Lattice-valued information systems based on dominance relation. Int J Mach Learn Cybernet 4(3):245–257
Ma JM, Leung Y, Zhang WX (2013) Attribute reductions in object-oriented concept lattice. Int J Mach Learn Cybern. doi:10.1007/s13042-013-0214-0
Li QY, Zhu W (2013) Closed-set lattice of regular sets based on a serial and transitive relation through matroids. Int J Mach Learning Cybern. doi:10.1007/s13042-013-0176-2
Liu Y, Qin XY, Xu Y (2013) Interval-valued intuitionistic (T,S)-fuzzy filters theory on residuated lattices. Int J Mach Learn Cybern. doi:10.1007/s13042-013-0213-1
Bělohlávek R (2002) Fuzzy relational systems: foundations and principles. Kluwer, New York
Acknowledgments
This paper is supported by the National Nature Science Foundation of China (No. 61170107 and No. 61300153) and by Training Program for Leading Talents of Innovation Teams in the Universities of Hebei Province (LJRC 022).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Shu-Rong, J., Ju-Sheng, M. & Li, M. Computational reasoning based on complemented distributive lattices. Int. J. Mach. Learn. & Cyber. 6, 475–478 (2015). https://doi.org/10.1007/s13042-014-0274-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13042-014-0274-9