Classes of pseudo-BCK algebras - Part I

Journal of Multiple-Valued Logic and Soft Computing

Volumn 12, Issue 1-2, 2006, Pages 71-130

  Iorgulescu, Afrodita ^a  

^a BUCHAREST UNIVERSITY OF ECONOMIC STUDIES   (Romania)

Author keywords

Divisible residuated lattice; Generalized pseudo BL algebra; Non commutative residuated lattice; Pseudo BCK algebra; Pseudo BL algebra; Pseudo IMTL algebra; Pseudo MTL algebra; Pseudo MV algebra; Pseudo NM algebra; Pseudo t norm; Pseudo WNM algebra

Indexed keywords

BOUNDARY CONDITIONS; HIERARCHICAL SYSTEMS; LOGIC PROGRAMMING; MATRIX ALGEBRA;

DIVISIBLE RESIDUATED LATTICE; GENERALIZED-PSEUDO-BL ALGEBRA; NON-COMMUTATIVE RESIDUATED LATTICE; PSEUDO-BCK ALGEBRA; PSEUDO-BL ALGEBRA; PSEUDO-IMTL ALGEBRA; PSEUDO-MTL ALGEBRA; PSEUDO-MV ALGEBRA; PSEUDO-NM ALGEBRA; PSEUDO-WNM ALGEBRA;

LINEAR ALGEBRA;

EID: 33645690151     PISSN: 15423980     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (61)

1. Andersen, M. and Feil, T. (1998). Lattice-Ordered Groups - An Introduction -, D. Reidel Publishing Company.
2. Arai, Y., Iséki, K. and Tanaka, S. (1966). Characterizations of BCI, BCK-algebras, Proc. Japan Acad., 42, 105-107.
3. Balbes, R. and Dwinger, P. (1974). Distributive lattices, Univ. Missouri Press.
4. Birkhoff, G. (1967). Lattice Theory, 3rd ed., American Mathematical Society, Providence.
5. Burris, S. and Sankappanavar, H.P. (1981). A Course in Universal Algebra, Springer-Verlag, New York.
6. Ceterchi, R. (1999). On Algebras with Implications, categorically equivalent to Pseudo-MV Algebras, The Proceedings of the Fourth International Symposium on Economic Informatics, Bucharest, Romania, 912-916.
7. Ceterchi, R. (2001). Pseudo-Wajsberg Algebras, Mult. Val. Logic (A special issue dedicated to the memory of Gr. C. Moisil), 6(1-2), 67-88.
8. Chang, C.C. (1958). Algebraic analysis of many valued logics, Trans. Amer. Math. Soc., 88, 467-490.
9. Di Nola, A., Georgescu, G. and Iorgulescu, A. (2002). Pseudo-BL algebras: Part I, Multi. Val. Logic, 8(5-6), 673-714.
10. Di Nola, A. Georgescu, G. and Iorgulescu, A. (2002). Pseudo-BL algebras: Part II, Multi. Val. Logic, 8(5-6), 717-750.
11. Dilworth, R.P. (1939). Non-commutative residuated lattices, Trans. of the American Math. Soc., 46, 426-444.
12. Dvurečenskij, A. (2002). Pseudo MV-algebras are intervals in l-groups, Journal of Australian Mathematical Society, 72, 427-445.
13. Esteva, F. and Godo, L. (2001). Monoidal t-norm based logic: towards a logic for left-continuous t-norms, Fuzzy Sets and Systems, 124(3), 271-288.
14. Flondor, P., Georgescu, G. and Iorgulescu, A. (2001). Pseudo-t-norms and pseudo-BL algebras, Soft Computing, 5(5), 355-371.
15. Fodor, J.C. (1995). Contrapositive symmetry of fuzzy implications, Fuzzy Sets and Systems, 69, 141-156.
16. Font, J.M., Rodriguez, A.J. and Torrens, A. (1984). Wajsberg algebras, Stochastica, 8(1), 5-31.
17. Georgescu, G. and Iorgulescu, A. (1999). Pseudo-MV Algebras: a Noncommutative Extension of MV Algebras, The Proceedings of the Fourth International Symposium on Economic Informatics, Bucharest, Romania, 961-968.
18. Georgescu, G. and Iorgulescu, A. (2001). Pseudo-MV algebras, Mult. Val. Logic, 6(1-2), 95-135.
19. Georgescu, G. and Iorgulescu, A. (2000). Pseudo-BL algebras: A noncommutative extension of BL algebras. Abstracts of The Fifth International Conference FSTA 2000, Slovakia, 90-92.
20. Georgescu, G. and Iorgulescu, A. (2001). Pseudo-BCK algebras: An extension of BCK algebras, Proceedings of DMTCS'01: Combinatorics, Computability and Logic, Springer, London, 97-114.
21. Gottwald, S., (1993). Fuzzy Sets and Fuzzy Logic, Braunschweig, Wiesbaden, Vieweg.
22. Gottwald, S. (2001). A Treatise on Many-Valued Logics. Studies in Logic and Computation, 9, Research Studies Press: Baldock, Hertfordshire, England.
23. Hájek, P. (1996). Metamathematics of fuzzy logic, Inst. of Comp. Science, Academy of Science of Czech Rep., Technical report 682.
24. Hájek, P. (1998). Metamathematics of fuzzy logic, Kluwer Acad. Publ., Dordrecht.
25. Höhle, U. (1995). Commutative, residuated 1-monoids. In: U. Höhle and E.P. Klement eds., Non-Classical Logics and Their Applications to Fuzzy Subsets, Kluwer Acad. Publ., Dordrecht 53-106.
26. Idziak, P.M. (1984). Lattice operations in BCK-algebras, Mathematica Japonica, 29, 839-846.
27. Imai, Y. and Iséki, K. (1966). On axiom systems of propositional calculi XIV, Proc. Japan Academy, 42, 19-22.
28. Iorgulescu, A. (2004). Iséki algebras, Connection with BL algebras, Soft Computing, 8(7), 449-463.
29. Iorgulescu, A. (2003). Some direct ascendents of Wajsberg and MV algebras, Scientiae Mathematicae Japonicae, 57(3), 583-647.
30. Iorgulescu, A. (2004). On pseudo-BCK algebras and porims, Scientiae Mathematicae Japonicae, 10(16), 293-305.
31. Iorgulescu, A. (2004). Classes of BCK algebras - Part I, Preprint Series of the Institute of Mathematics of the Romanian Academy, 1, 1-33.
32. Iorgulescu, A. (2004). Classes of BCK algebras - Part II, Preprint Series of the Institute of Mathematics of the Romanian Academy, 2, 1-27.
33. Iorgulescu, A. (2004). Classes of BCK algebras - Part III, Preprint Series of the Institute of Mathematics of the Romanian Academy, 3, 1-37.
34. Iorgulescu, A. (2004). Classes of BCK algebras - Part IV, Preprint Series of the Institute of Mathematics of the Romanian Academy, 4, 1-25.
35. Iorgulescu, A. (2004). Classes of BCK algebras - Part V, Preprint Series of the Institute of Mathematics of the Romanian Academy, 5, 1-22.
36. Iorgulescu, A. (2005). Pseudo-Iséki algebras. Connection with pseudo-BL algebras, Multiple-Valued Logic and Soft Computing, 11(3-4), 263-308.
37. Iorgulescu, A. On BCK algebras - Part I, submitted.
38. Iséki, K. (1966). An algebra related with a propositional calculus, Proc. Japan Acad., 42, 26-29.
39. Iséki, K. (1977). A special class of BCK-algebras, Math. Seminar Notes, Kobe University, 5, 191-198.
40. Iséki, K. (1977). On a positive implicative algebra with condition (S), Math. Seminar Notes, Kobe University, 5, 227-232.
41. Iséki, K. and Tanaka, S. (1978). An introduction to the theory of BCK-algebras, Math. Japonica, 23(1), 1-26.
42. (42] Jipsen, P. and Tsinakis, C. A Survey of Residuated Lattices, www.math.vanderbilt.edu/pjipsen/
43. Kalman, J. (1958). Lattices with involution, Trans. Amer. Math. Soc., 87, 485-491.
44. Klement, E.P., Mesiar, R. and Pap, E. (2002). Triangular norms, Kluwer Academic Publishers.
45. Kowalski, T. and Ono, H. (2001). Residuated lattices: An algebraic glimpse at logics without contraction, monograph.
46. Krull, W. (1924). Axiomatische Begründung der allgemeinen Idealtheorie, Sitzungsberichte der physikalisch medizinischen Societät der Erlangen, 56, 47-63.
47. Lin, Y.-H. (2002). Some properties on commutative BCK-algebras, Scientiae Mathematicae Japonicae, 55(1), 129-133, 235-239.
48. Mundici, D. (1986). MV-algebras are categorically equivalent to bounded commutative BCK-algebras, Math. Japonica, 31(6), 889-894.
49. Mundici, D. (1986). Interpretation of AF C*-algebras in Lukasiewicz sentential calculus, J. Funct. Anal., 65, 15-63.
50. Okada, M. and Terui, K. (1996). The finite model property for various fragments of intuitionistic logic, Journal of Symbolic Logic, 64, 790-802.
51. Ono, H. and Komori, Y. Logics without the contraction rule, Journal of Symbolic Logic, 50, 169-201.
52. Pavelka, J. (1979). On fuzzy logic II. Enriched residuated lattices and semantics of propositional calculi, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, 25, 119-134.
53. Pei, D. (2003). On equivalent forms of fuzzy logic systems NM and IMTL, Fuzzy Sets and Systems, 138, 187-195.
54. Prior, A.N. (1962). Formal logic, Oxford.
55. Rachunek, J. (2002), A non-commutative generalization of MV-algebras, Czech Mathematical Journal, 52, 255-273.
56. Turunen, E. (1999). Mathematics Behind Fuzzy Logic, Physica-Verlag.
57. Van Alten, C.J. and Raftery, J.G. (1999). On the lattice of varieties of residuation algebras, Algebra univers., 41, 283-315.
58. Wajsberg, M. (1935). Beiträge zum Mataaussagenkalkäl, Monat. Math. Phys., 42, 240.
59. Wang, G.J. (1997). A formal deductive system for fuzzy propositional calculus, Chinese Sci. Bull., 42, 1521-1526.
60. Ward, M. (1940). Residuated distributive lattices, Duke Math. Journal, 6, 641-651.
61. Ward, M. and Dilworth, R.P. (1939). Residuated lattices, Trans. of the American Math. Soc., 45, 335-354.