Abstract
We study Haveshki’s and Eslami’s n–fold positive implicative basic logics and prove that they are fragments of Łukasiewicz logic. We introduce n–fold Boolean filters and prove that n–fold positive implicative filters and n–fold Boolean filters coincide in BL–algebras; this generalizes the fact that positive implicative filters and Boolean filters coincide in BL–algebras, moreover this result yields another characterization for the n–fold positive implicative basic logic. Lastly we prove that filters that are both n–fold implicative and n–fold fantastic are exactly n–fold Boolean filters.
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Turunen, E., Tchikapa, N., Lele, C. (2012). A New Characterization for n–Fold Positive Implicative BL–Logics. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances on Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 297. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31709-5_56
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DOI: https://doi.org/10.1007/978-3-642-31709-5_56
Publisher Name: Springer, Berlin, Heidelberg
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