Rough sets and 3-valued logics
Studia Logica 90 (1):69 - 92 (2008)
| Abstract | In the paper we explore the idea of describing Pawlak’s rough sets using three-valued logic, whereby the value t corresponds to the positive region of a set, the value f — to the negative region, and the undefined value u — to the border of the set. Due to the properties of the above regions in rough set theory, the semantics of the logic is described using a non-deterministic matrix (Nmatrix). With the strong semantics, where only the value t is treated as designated, the above logic is a “common denominator” for Kleene and Łukasiewicz 3-valued logics, which represent its two different “determinizations”. In turn, the weak semantics—where both t and u are treated as designated—represents such a “common denominator” for two major 3-valued paraconsistent logics. We give sound and complete, cut-free sequent calculi for both versions of the logic generated by the rough set Nmatrix. Then we derive from these calculi sequent calculi with the same properties for the various “determinizations” of those two versions of the logic (including Łukasiewicz 3-valued logic). Finally, we show how to embed the four above-mentioned determinizations in extensions of the basic rough set logics obtained by adding to those logics a special two-valued “definedness” or “crispness” operator. | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,865 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesArnon Avron, Jonathan Ben-Naim & Beata Konikowska (2007). Cut-Free Ordinary Sequent Calculi for Logics Having Generalized Finite-Valued Semantics. Logica Universalis 1 (1).
Arnon Avron & Beata Konikowska (2009). Proof Systems for Reasoning About Computation Errors. Studia Logica 91 (2):273 - 293.
Alexej P. Pynko (2010). Many-Place Sequent Calculi for Finitely-Valued Logics. Logica Universalis 4 (1).
Richard DeWitt (2005). On Retaining Classical Truths and Classical Deducibility in Many-Valued and Fuzzy Logics. Journal of Philosophical Logic 34 (5-6):545 - 560.
Walter Sinnott-Armstrong & Amit Malhotra (2002). How to Avoid Deviance (in Logic). History and Philosophy of Logic 23 (3):215--36.
Analytics
Monthly downloads |
Added to index2009-01-28Total downloads9 ( #115,463 of 556,788 )Recent downloads (6 months)1 ( #64,847 of 556,788 )How can I increase my downloads? |
My notes
Discussion
