Abstract
In the paper, it defines a λ-level rough equality relation in rough logic and establishes a rough sets on real-valued information systems with it. We obtain some related properties and relative rough paramodulation inference rules. They will be used in the approximate reasoning and deductive resolutions of rough logic. Finally, it proves that λ-level rough paramodulant reasoning is sound.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Z. Pawlak, Rough Sets, Theoretical Aspects of Reasoning about Data, Dordrecht: Kluwer (1991).
M. Banerjee and M. K. Chakraborty, Rough Algebra, Ics Research Report, Institute of Computer Science, Warsaw University of Technology,47/93.
Q. Liu, The Resolution for Rough Prepositional Logic with Lower (L) and Upper (H) Approximate Operators,LNAI 1711, Springer,ll,(1999), 352–356.
Q. Liu, Operator Rough Logic and Its Resolution Principles, Journal of Computer 5, (1998), 476–480,(in Chinese).
A. Nakamura, Graded Modalities in Rough Logic, Rough Sets in Knowledge Discovery I, by L. Polkaowski and A. Skowron, Phsica-verlag,Heidelberg, (1998).
J. Stepaniuk, Rough Relation and Logics, Rough Sets in Knowledge Discovery I, by L. Polkaowski and A. Skowron, Physica-Verlag, Heidelberg,(1998).
Q. Liu, The OI-Resolution of Operator Rough Logic, LNAI 1424, Springer, 6, (1998), 432–435.
C. L. Chang and R. C. T. Lee, Symbolic Logic and Mechanical Theorem Proving, Academic Press., INC,1973, 163–180.
T. Y. Lin and Q. Liu, First-order Rough Logic I: Approximate Reasoning via Rough Sets,Fundamenta Informaticae, Vol.27, No.2,3,8 (1996),137–154.
E. Orlowska, A logic of Indiscernibility Relation, Lecture Notes on Computer Science, 208, (1985), 172–186.
Y. Y. Yao and Q. Liu, A Generalized Decision Logic in Interval-Set-Valued Information Tables, LNAI1711, Springer,ll,(1999),285–293.
Z. Pawlak, Rough Logic, Bulletin of the Polish Academy of Sciences Tech-niques,(1987), 253–258.
X. H. Liu, Fuzzy Logic and Fuzzy Reasoning,Publisher of JiLin University, 6, (1989),(in Chinese).
Q. Liu and Q. Wang, Rough Number Based on Rough Sets and Logic Values of λ Operator, Journal of Software, Sup., (1996),455–461), (in Chinese).
Q. Liu, The Course of Artificial Intelligence, High College Join Publisher in JiangXi, 9,(1992), (in Chinese).
Q. Liu, Accuracy Operator Rough Logic and Its Resolution Reasoning, In: Proc. RSFD'96, Inc. Conf. The University of Tokyo, Japan, (1996), 55–59.
T. Y. Lin, Q. Liu and Y. Y. Yao, Logic Systems for Approximate Reasoning: Via Rough Sets and Topology,LNAI 869, 1994, 65–74.
R. C. T. Lee, Fuzzy Logic and the Resolution Principles, Journal of the Association for Computing Machinery, Vol.19, No. 1,1, (1972), 109–119.
R. C. T. Lee and C. L. Chang, Some Properties of Fuzzy Logic,Information Control, 5, (1971).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Vcrlag Berlin Heidelberg
About this paper
Cite this paper
Liu, Q. (2001). λ-Level Rough Equality Relation and the Inference of Rough Paramodulation. In: Ziarko, W., Yao, Y. (eds) Rough Sets and Current Trends in Computing. RSCTC 2000. Lecture Notes in Computer Science(), vol 2005. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45554-X_57
Download citation
DOI: https://doi.org/10.1007/3-540-45554-X_57
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43074-2
Online ISBN: 978-3-540-45554-7
eBook Packages: Springer Book Archive