Extended-order algebras

Journal of Applied Logic

Volumn 6, Issue 4, 2008, Pages 609-626

  Guido, Cosimo ^a   Toto, Paola ^a  

^a UNIVERSITY OF SALENTO   (Italy)

Author keywords

Complete lattice; Extended order algebra; Implication algebra; Many valued mathematics; Partially ordered groupoid; Poset; Residuated lattice

Indexed keywords

MATHEMATICAL TECHNIQUES;

COMPLETE LATTICE; EXTENDED-ORDER ALGEBRA; IMPLICATION ALGEBRA; MANY-VALUED MATHEMATICS; PARTIALLY ORDERED GROUPOID; POSET; RESIDUATED LATTICE;

ALGEBRA;

EID: 54449098097     PISSN: 15708683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jal.2008.01.001     Document Type: Article

References (33)

1. Abbott J.C. Algebras of implication and semi-lattices. Séminaire Dubreil. Algèbre Théor. Nombr. 20 2 (1966-1967) 1-8
2. Bělohlávek R. Fuzzy Galois connections. Math. Log. Quart. 45 4 (1999) 497-504
3. Bělohlávek R. Fuzzy Relational Systems. Foundations and Principles (2002), Kluwer Academic Press, New York
4. Bělohlávek R. Fuzzy closure operators induced by similarity. Fund. Inform. 58 2 (2003) 79-91
5. Bělohlávek R. Concept lattices and order in fuzzy logic. Ann. Pure Appl. Logic 128 (2004) 277-298
6. Berman J., and Blok W.J. Algebras defined from ordered sets and the varieties they generate. Order 23 (2006) 65-88
7. G. Birkhoff, Lattice Theory, American Mathematical Society Colloquium Publication, vol. XXV, 1967
8. Bodenhofer U. Representations and constructions of similarity-based fuzzy orderings. Fuzzy Sets and Systems 137 (2003) 113-136
9. Chajda I., and Halaš R. Congruences and ideals in Hilbert algebras. Kyungpook Mathem. J. 39 (1999) 429-432
10. Chajda I., Halaš R., and Jun Y.B. Annihilators and deductive systems in commutative Hilbert algebras. Comment. Math. Univ. Carolinae 43 3 (2002) 407-417
11. Cignoli R., D'Ottaviano I.M.L., and Mundici D. Algebraic Foundation of Many-Valued Reasoning (2000), Kluwer Academic Publishers, Dordrecht
12. De Cooman G., and Kerre E.E. Order norms on bounded partially ordered sets. J. Fuzzy Math. 2 (1994) 281-310
13. Diego A. Sur Les Algèbres De Hilbert. Collection de Logique Mathématique, Sér. A, Fasc. vol. 21 (1966), Gauthier-Villars, Paris (French)
14. Durante F., Klement E.P., Mesiar R., and Sempi C. Conjunctors and their residual implicators: characterizations and construction methods. Mediterr. J. Math. 4 (2007) 343-356
15. Freese R., Jezek J., Jipsen P., Markovic P., Maroti M., and McKenzie R. The variety generated by order algebras. Algebra Universalis 47 (2002) 103-138
16. Frascella A., and Guido C. Transporting many-valued sets along many-valued relations. Fuzzy Sets and Systems 159 1 (2008) 1-22
17. Georgescu G., and Popescu A. Non-dual fuzzy connections. Arch. Math. Logic 43 (2004) 1009-1039
18. Goguen J.A. L-fuzzy sets. J. Math. Anal. Appl. 18 (1967) 145-174
19. S. Gottwald, Many-valued logic and fuzzy set theory, in: [24], Chapter 1, pp. 6-89
20. C. Guido, Lattice-valued categories, Abstract presented in XXIX Linz Seminar on Fuzzy Set Theory, Linz, 2008
21. Halaš R. Remarks on commutative Hilbert algebras. Math. Bohemica 127 4 (2002) 525-529
22. Hájek P. Metamathematics of Fuzzy Logic. Trends in Logic-Studia Logica Library vol. 4 (1998), Kluwer Academic Publisher, Dordrecht
23. Höhle U. Many Valued Topology and Its Applications (2001), Kluwer Academic Publishers, Boston, Dordrecht, London
24. In: Höhle U., and Rodabaugh S.E. (Eds). Mathematics of Fuzzy Sets: Logic Topology, and Measure Theory. The Handbooks of Fuzzy Sets Series vol. 3 (1999), Kluwer Academic Publishers, Boston, Dordrecht, London
25. U. Höhle, A.P. Šostak, Axiomatic foundations of fixed-basis fuzzy topology, in: [24], Chapter 3, pp. 123-272
26. Iorgulescu A. Classes of pseudo-BCK algebras, Part I. J. Multiple-Valued Logic Soft Comput. 12 1-2 (2006) 71-130
27. Iséki K., and Tanaka S. An introduction to the theory of BCK-algebras. Math. Japon. 23 (1978) 1-26
28. Kondo M. Hilbert algebras are dual isomorphic to positive implicative BCK-algebras. Math. Japon. 49 2 (1999) 265-268
29. MacNeille H.M. Partially ordered sets. Trans. Amer. Math. Soc. 42 (1937) 416-460
30. Neggers J., and Kim H.S. On d-algebras. Math. Slovaca 49 (1999) 19-26
31. Neggers J., Dvurečenskij A., and Kim H.S. On d-fuzzy functions in d-algebras. Found. Phys. 30 10 (2000) 1807-1816
32. Rasiowa H. An Algebraic Approach to Non-Classical Logics. Studies in Logics and the Foundations of Mathematics vol. 78 (1974), North-Holland, Amsterdam
33. Zhang Q.-Y., and Fan L. Continuity in quantitative domains. Fuzzy Sets and Systems 154 (2005) 118-131