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Logical Characterization of Filters on BL-algebras
M. Moniri, H. Farahani and R.A. Borzooei

In this paper, we review filter theory of BL-algebras from the logical point of view.We introduce the notion of deductive filter on a BL-algebra and give some types of deductive filters related to the classical, Gödel, Lukasiewicz and Product logic.We also investigate the relationship between the notion we introduce and some types of filters on BL-algebras already defined. Furthermore, we show that for any BL-algebra L and any product deductive filter F, the quotient algebra L/F is a product algebra, the corresponding result for Gödel and Lukasiewicz algebras are already known.

Keywords: BL-algebra, deductive filter, product filter

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