Abstract
Tuples in an information system are taken as terms in a logical system, attributes as function symbols, a tuple taking a value at an attribute as an atomic formula. In such a way, an information system is represented by a logical theory in a logical language. The roughness of an information system is represented by the roughness of the logical theory, and the roughness of logical theories is a generalization of that of information systems. A logical theory induces an indiscernibility relation on the Herbrand universe of the logical language, the set of all the ground terms. It is imaginable that there is some connection between the logical implication of logical theories and the refinement of indiscernibility relations induced by the logical theories. It shall be proved that there is no such a connection of simple form.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Düntsch, I.: A logic for rough sets. Theoretical Computer Science 179, 427–436 (1997)
Komorowski, J., Pawlak, Z., Polkowski, L., Skowron, A.: Rough sets: a tutorial. In: Pal, S.K., Skowron, A. (eds.) Rough Fuzzy Hybridization: A New Trends in Decision-making, pp. 3–98. Springer, Heidelberg (1999)
Hájek, P.: Basic fuzzy logic and BL-algebras. Soft Computing 2, 124–128 (1998)
Hughes, G., Cresswell, M.: A new introduction to modal logic. Routledge, London (1996)
Haack, S.: Deviant logic, fuzzy logic, beyond the formalism. The University of Chicago Press (1996)
Liau, C.: An overview of rough set semantics for modal and quantifier logics. International J. of Uncertainty, Fuzziness and Knowledge-Based Systems 8, 93–118 (2000)
Pawlak, Z.: Rough sets - theoretical aspects of reasoning about data. Kluwer Academic Publishers, Dordrecht (1991)
Pawlak, Z.: Rough sets, rough function and rough calculus. In: Pal, S.K., Skowron, A. (eds.) Rough Fuzzy Hybridization: A New Trends in Decision-making, pp. 99–109. Springer, Heidelberg (1999)
Pomykala, J., Pomykala, J.A.: The Stone algebra of rough sets. Bull. Polish Acad. Sci. Math. 36, 495–508 (1988)
Yao, Y.Y., Wong, S.K.M., Lin, T.Y.: A review of rough set models. In: Lin, T.Y., Cercone, N. (eds.) Rough sets and data mining: analysis for imprecise data, pp. 47–75. Kluwer Academic Pub., Dordrecht (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cao, C., Sui, Y., Zhang, Z. (2006). The Rough Logic and Roughness of Logical Theories. In: Wang, GY., Peters, J.F., Skowron, A., Yao, Y. (eds) Rough Sets and Knowledge Technology. RSKT 2006. Lecture Notes in Computer Science(), vol 4062. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11795131_89
Download citation
DOI: https://doi.org/10.1007/11795131_89
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-36297-5
Online ISBN: 978-3-540-36299-9
eBook Packages: Computer ScienceComputer Science (R0)