Handbook of logic in artificial intelligence and logic programming (Vol. 4)
Rough Consequence and Rough Algebra
RSKD '93 Proceedings of the International Workshop on Rough Sets and Knowledge Discovery: Rough Sets, Fuzzy Sets and Knowledge Discovery
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Transactions on rough sets VI
A fuzzy view on rough satisfiability
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Fundamenta Informaticae - New Frontiers in Scientific Discovery - Commemorating the Life and Work of Zdzislaw Pawlak
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The article aims at re-visiting the notion of rough truth proposed by Pawlak in 1987 [15] and investigating some of its ‘logical’ consequences. We focus on the formal deductive apparatus $\cal L_R$, that is sound and complete with respect to a semantics based on rough truth. $\cal L_R$ turns out to be equivalent to the paraconsistent logic J due to Jaśkowski. A significant feature of rough truth is that, a proposition and its negation may well be roughly true together. Thus, in [5], rough consistency was introduced. Completeness of $\cal L_R$ is proved with the help of this notion of consistency. The properties of $\cal L_R$ motivate us to use it for a proposal of rough belief change. During change, the operative constraints on a system of beliefs are that of rough consistency preservation and deductive closure with respect to $\cal L_R$. Following the AGM [1] line, eight basic postulates for defining rough revision and contraction functions are presented. Interrelationships of these functions are also proved. The proposal is, therefore, an example of paraconsistent belief change.