Compatible deductive systems of pulexes. (English) Zbl 1322.03048
Summary: The notion of (compatible) deductive system of a pulex is defined and some properties of deductive systems are investigated. We also define a congruence relation on a pulex and show that there is a bijective correspondence between the compatible deductive systems and the congruence relations. We define the quotient algebra induced by a compatible deductive system and study its properties.
References:
| [1] | Y. Imai and K. Iséki, “On axiom systems of propositional calculi. XIV,” Proceedings of the Japan Academy, vol. 42, pp. 19-22, 1966. · Zbl 0156.24812 · doi:10.3792/pja/1195522169 |
| [2] | G. Georgescu and A. Iorgulescu, “Pseudo-BCK algebras: an extension of BCK algebras,” in Combinatorics, Computability and Logic, C. S. Calude, M. J. Dinneen, and S. Sburlan, Eds., Discrete Mathematics and Theoretical Computer Science, pp. 97-114, Springer, 2001. · Zbl 0986.06018 |
| [3] | P. Hájek, Metamathematics of Fuzzy Logic, vol. 4 of Trends in Logic, Kluwer Academic Publishers, 1998. · Zbl 0937.03030 |
| [4] | A. Iorgulescu, “Iséki algebras. Connection with BL algebras,” Soft Computing, vol. 8, no. 7, pp. 449-463, 2004. · Zbl 1075.06009 · doi:10.1007/s00500-003-0304-0 |
| [5] | A. Iorgulescu, “Some direct ascendents of Wajsberg and MV algebras,” Scientiae Mathematicae Japonicae, vol. 57, no. 3, pp. 583-647, 2003. · Zbl 1050.06006 |
| [6] | P. Agliano and F. Montagna, “Varieties of BL-algebras. I. General properties,” Journal of Pure and Applied Algebra, vol. 181, no. 2-3, pp. 105-129, 2003. · Zbl 1034.06009 · doi:10.1016/S0022-4049(02)00329-8 |
| [7] | A. di Nola, G. Georgescu, and A. Iorgulescu, “Pseudo-BL algebras. I,” Multiple-Valued Logic, vol. 8, no. 5-6, pp. 673-714, 2002. · Zbl 1028.06007 |
| [8] | F. Esteva and L. Godo, “Monoidal t-norm based logic: towards a logic for left-continuous t-norms,” Fuzzy Sets and Systems, vol. 124, no. 3, pp. 271-288, 2001. · Zbl 0994.03017 · doi:10.1016/S0165-0114(01)00098-7 |
| [9] | P. Hájek, “Fleas and fuzzy logic,” Journal of Multiple-Valued Logic and Soft Computing, vol. 11, no. 1-2, pp. 137-152, 2005. · Zbl 1078.03021 |
| [10] | A. Iorgulescu, “On pseudo-BCK algebras and porims,” Scientiae Mathematicae Japonicae, vol. 10, pp. 293-305, 2004. · Zbl 1066.06018 |
| [11] | J. Kühr, Pseudo-BCK-algebras and related structres [Ph.D. thesis], Univerzita Palackého v Olomouci, 2007. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
