Abstract
In classical logic and many-valued logic, Modus Ponens rule (MP rule) is very useful for a formal deduction. In this chapter, we establish the concept of filters, which is an abstraction of MP rule. We also extend the concept of filters, establish the concepts of implicative filters, prime filters, ultra-filters, I-filters, involution filters and so on, and discuss their properties as well.
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© 2003 Springer-Verlag Berlin Heidelberg
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Xu, Y., Qin, K., Ruan, D., Liu, J. (2003). Filters. In: Lattice-Valued Logic. Studies in Fuzziness and Soft Computing, vol 132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44847-1_3
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DOI: https://doi.org/10.1007/978-3-540-44847-1_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07279-6
Online ISBN: 978-3-540-44847-1
eBook Packages: Springer Book Archive