Abstract
The article aims at re-visiting the notion of rough truth proposed by Pawlak in 1987 [11] and investigating some of its ‘logical’ consequences. We focus on the formal deductive apparatus \(\mathcal{L}_\mathcal{R}\) [12], that is sound and complete with respect to a semantics based on rough truth (extended to rough validity). The notion of rough consequence [4] is used in a modified form to formulate \(\mathcal{L}_\mathcal{R}\). The system has some desirable features of ‘rough’ reasoning – e.g. roughly true propositions can be derived from roughly true premisses in an information system. Further, rough consistency [4] is used to prove completeness. These properties of \(\mathcal{L}_\mathcal{R}\) 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 \(\mathcal{L}_\mathcal{R}\). Following the AGM [1] line, postulates for defining revision and contraction functions are presented. Interrelationships of these functions are also proved.
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Banerjee, M. (2004). Rough Truth, Consequence, Consistency and Belief Revision. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds) Rough Sets and Current Trends in Computing. RSCTC 2004. Lecture Notes in Computer Science(), vol 3066. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25929-9_10
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DOI: https://doi.org/10.1007/978-3-540-25929-9_10
Publisher Name: Springer, Berlin, Heidelberg
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