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Generalized Rough Logics with Rough Algebraic Semantics

Generalized Rough Logics with Rough Algebraic Semantics

Jianhua Dai
Copyright: © 2010 |Volume: 4 |Issue: 2 |Pages: 15
ISSN: 1557-3958|EISSN: 1557-3966|EISBN13: 9781609603984|DOI: 10.4018/jcini.2010040103
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MLA

Dai, Jianhua. "Generalized Rough Logics with Rough Algebraic Semantics." IJCINI vol.4, no.2 2010: pp.35-49. http://doi.org/10.4018/jcini.2010040103

APA

Dai, J. (2010). Generalized Rough Logics with Rough Algebraic Semantics. International Journal of Cognitive Informatics and Natural Intelligence (IJCINI), 4(2), 35-49. http://doi.org/10.4018/jcini.2010040103

Chicago

Dai, Jianhua. "Generalized Rough Logics with Rough Algebraic Semantics," International Journal of Cognitive Informatics and Natural Intelligence (IJCINI) 4, no.2: 35-49. http://doi.org/10.4018/jcini.2010040103

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Abstract

The collection of the rough set pairs of an approximation (U, R) can be made into a Stone algebra by defining two binary operators and one unary operator on the pairs. By introducing a more unary operator, one can get a regular double Stone algebra to describe the rough set pairs of an approximation space. Sequent calculi corresponding to the rough algebras, including rough Stone algebras, Stone algebras, rough double Stone algebras, and regular double Stone algebras are proposed in this paper. The sequent calculi are called rough Stone logic (RSL), Stone logic (SL), rough double Stone logic (RDSL), and double Stone Logic (DSL). The languages, axioms and rules are presented. The soundness and completeness of the logics are proved.

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