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Rough relation properties

100%
do Carmo Nicoletti M., Uchoa J. Q., Baptistini M. T. Z.
International Journal of Applied Mathematics and Computer Science
|
2001
|
tom 11
|
nr 3
621-635
EN
Rough Set Theory (RST) is a mathematical formalism for representing uncertainty that can be considered an extension of the classical set theory. It has been used in many different research areas, including those related to inductive machine learning and reduction of knowledge in knowledge-based systems. One important concept related to RST is that of a rough relation. This paper rewrites some properties of rough relations found in the literature, proving their validity.
2
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Relative sets and rough sets

75%
Mousavi A., Jabedar-Maralani P.
International Journal of Applied Mathematics and Computer Science
|
2001
|
tom 11
|
nr 3
637-653
EN
In this paper, by defining a pair of classical sets as a relative set, an extension of the classical set algebra which is a counterpart of Belnap's four-valued logic is achieved. Every relative set partitions all objects into four distinct regions corresponding to four truth-values of Belnap's logic. Like truth-values of Belnap's logic, relative sets have two orderings; one is an order of inclusion and the other is an order of knowledge or information. By defining a rough set as a pair of definable sets, an integrated approach to relative sets and rough sets is obtained. With this definition, we are able to define an approximation of a rough set in an approximation space, and so we can obtain sequential approximations of a set, which is a good model of communication among agents.
3
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The Dynamic Epistemic Logic for Actual Knowledge

75%
Wójcik A.
Bulletin of the Section of Logic
|
2020
|
tom 49
|
nr 1
EN
The dynamic epistemic logic for actual knowledge models the phenomenon of actual knowledge change when new information is received. In contrast to the systems of dynamic epistemic logic which have been discussed in the past literature, our system is not burdened with the problem of logical omniscience, that is, an idealized assumption that the agent explicitly knows all classical tautologies and all logical consequences of his or her knowledge. We provide a sound and complete axiomatization for this logic.
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