Truth-Functionality, Rough Sets and Three-Valued Logics

This paper investigates the significance of truth-functional three valued logics of ill-known sets described by pairs of disjoint (or pairs of nested) subsets. In particular the case of three-valued logics of rough sets is studied in more details, showing that, while the mathematical underpinnings are sound, the relevance of these logics for reasoning about data-tables containing incomplete descriptions of objects is questionable.

[1]  Andrzej Skowron,et al.  Rudiments of rough sets , 2007, Inf. Sci..

[2]  Joan Torrens,et al.  S-implications and R-implications on a finite chain , 2004, Kybernetika.

[3]  Zbigniew Bonikowski,et al.  A Certain Conception of the Calculus of Rough Sets , 1992, Notre Dame J. Formal Log..

[4]  Arnon Avron,et al.  Rough Sets and 3-Valued Logics , 2008, Stud Logica.

[5]  D. Dubois,et al.  Twofold fuzzy sets and rough sets—Some issues in knowledge representation , 1987 .

[6]  Ivo Düntsch,et al.  A Logic for Rough Sets , 1997, Theor. Comput. Sci..

[7]  Yiyu Yao,et al.  Interval-set algebra for qualitative knowledge representation , 1993, Proceedings of ICCI'93: 5th International Conference on Computing and Information.

[8]  Davide Ciucci,et al.  Orthopairs: A Simple and Widely UsedWay to Model Uncertainty , 2011, Fundam. Informaticae.

[9]  Didier Dubois,et al.  On Ignorance and Contradiction Considered as Truth-Values , 2007, Log. J. IGPL.

[10]  Xiaochun Liu,et al.  Rough 3-Valued Lukasiewicz Agebras and MV-Algebras , 2009, RSKT.

[11]  Mohua Banerjee,et al.  Rough Sets and 3-Valued Lukasiewicz Logic , 1997, Fundam. Informaticae.

[12]  Piero Pagliani,et al.  Rough Sets and Nelson Algebras , 1996, Fundam. Informaticae.

[13]  Mohua Banerjee,et al.  Algebras from Rough Sets , 2004, Rough-Neural Computing: Techniques for Computing with Words.

[14]  Yiyu Yao,et al.  Semantics of Fuzzy Sets in Rough Set Theory , 2004, Trans. Rough Sets.

[15]  Gianpiero Cattaneo,et al.  Algebraic Structures for Rough Sets , 2004, Trans. Rough Sets.

[16]  Dai Jian Rough Algebras and 3-Valued Lukasiewicz Algebras , 2007 .

[17]  Mohua Banerjee,et al.  Rough Sets Through Algebraic Logic , 1996, Fundam. Informaticae.

[18]  P. Pagliani Rough Set Theory and Logic-Algebraic Structures , 1998 .

[19]  Joan Torrens,et al.  A Survey on Fuzzy Implication Functions , 2007, IEEE Transactions on Fuzzy Systems.