On the structure of rotation-invariant semigroups

Archive for Mathematical Logic

Volumn 42, Issue 5, 2003, Pages 489-514

  Jenei, Sándor ^a  

^a UNIVERSITY OF PÉCS   (Hungary)

Author keywords

Conjunction for non classical logics; Residuated lattice

Indexed keywords

EID: 0038336663     PISSN: 09335846     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00153-002-0165-8     Document Type: Article

References (35)

1. Agliano, P., Montagna, F.: Varieties of BL-algebras I: general properties. To appear in the Journal of Pure and Applied Algebra.
2. Birkhoff, G.: Lattice Theory, Amer. Math Soc. Colloquium Publications, third edition (Amer. Math. Soc., RI), 1973
3. Blok, W. J., Pigozzi, D.: Algebraizable Logics, Memoirs of the American Mathematical Society, Number 396, Amer. Math. Soc., Providence, 1989
4. Chang, C. C.: Algebraic analysis of many valued logics, TAMS 88, 467-490 (1958)
5. Ciabattoni, A., Luchi, D.: Two connections between linear logic and Lukasiewicz logics, in.: G. Gottlob, et al. (Ed.), Computational logic and proof theory, Proc. KGC '97, Lecture Notes in Computer Science vol. 1289, Springer, Berlin, pp. 128-139 (1997)
6. Cignoli, R., Esteva, P., Godo, L., Montagna, F.: On a class of left-continuous t-norms, Fuzzy Sets and Systems 131, 283-296 (2002)
7. Cignoli, R., Mundici, D.: An elementary proof of Chang's completeness theorem for the infinite-valued calculus of Łukasiewicz logic, and AF C*-algebras, Studia Logica 58, 79-97 (1997)
8. Cignoli, R., D'Ottaviano, I. M. L., Mundici, D.: Algebraic Foundations of Many-Valued Reasoning, Kluwer, Dordrecht, 2000
9. Cignoli, R., Esteva, F., Godo, L., Torrens, A.: Basic Fuzzy Logic is the logic of continuous t-norms and of their residua, Soft Comput. 4, 106-112 (2000)
10. Clifford, A. H.: Naturally totally ordered commutative semigroups, Amer. J. Math. 76, 631-646 (1954)
11. Climescu, A. C.: Sur l'équation fonctionelle de l'associativité, Bull. École Polytechn. lassy 1, 1-16 (1946)
12. Esteva, P., Godo, L.: Monoidal t-norm based Logic: towards a logic for left-continuous t-norms, Fuzzy Sets and Systems 124, 271-288 (2001)
13. Fuchs, L.: Partially ordered algebraic systems, Pergamon Press, Oxford-London-New York-Paris, 1963
14. Girard, J.Y.: Linear Logic, Theor. Comp. Sci. 50 1-102 (1987)
15. Grišhin, V.N.: On algebraic semantics for logic without the contraction rule (in Russian). Isslédovanija po formalizovannym jazykam i néklassičéskim logikam, Moskva, pp. 247-264 (1976)
16. Grišhin, V.N.: Predicate and set-theoretical calculi based on logic without the contraction rule (in Russian), Izvéstia Akademii Nauk SSSR 45 pp. 47-68 (1981) (English translation in Math. USSR Izvestiya 18 pp. 41-59 (1982))
17. Hájek, P.: Metamathematics of fuzzy logic, Kluwer, Dordrecht, (1998)
18. Höhle, U.: Monoidal logic, in: R. Kruse, J. Gebhardt, F. Klawonn, (Ed.), Fuzzy-Systeme, Teubner, Stuttgart, pp. 233-243 (1993)
19. Höhle, U.: Commutative, residuated 1-monoids, in: U. Höhle, E. P. Klement (Ed.), Non-Classical Logics and Their Applications to Fuzzy subsets, Kluwer Academic Publishers, Dordrecht, pp. 53-106 (1995)
20. Höhle, U., Weber, S.: Uncertainty measures, realizations and entropies, in: J. Goutaias, R.P.S. Mahler, H.T. Nguyen (Ed.), Random Sets: Theory and Applications, Springer, Heidelberg, pp. 259-295 (1997)
21. Jenei, S.: New family of triangular norms via contrapositive symmetrization of residuated implications, Fuzzy Sets and Systems 110, 157-174 (2000)
22. Johnstone, P.T.: Stone spaces, Cambridge University Press, Cambridge, 1982
23. Kowalski, T., Ono, H.: Variety of residuated lattices is generated by its finite simple members, Reports on Mathematical Logic 34, 57-75 (2000)
24. Kowalski, T., Ono, H.: Residuated lattices: an algebraic glimpse at logics without contraction, monograph, 2001
25. Mangani, P.: Su certe algebre connesse con logiche a piú valori, Boll. Unione Math. Italiana, ser. 8, 4, 68-78 (1973)
26. Mostert, P.S., Shields, A.L.: On the structure of semigroups on a compact manifold with boundary. Ann. Math. 65, 117-143 (1957)
27. Mundici, D.: Free products in the category of Abelian l-groups with strong unit, J. Algebra 113, 89-109 (1988)
28. 0 of AF C*-algebras, Adv. Math. 68, 23-39 (1988)
29. Mundici, D.: Interpretation of AF C*-algebras in Lukasiewicz sentential calculus, J. Funct. Anal. 65, 15-63 (1986)
30. Mundici, D.: Averaging the truth value in Łukasiewicz logic, Studia Logica 5, 113-127 (1991)
31. Mundici, D.: Ulam games, Łukasiewicz logic, and AF C*-algebras, Fund. Inf. 18, 151-161 (1993)
32. Nakada, O.: Partially ordered Abelian semigroups. I-II, Journ. Fac. Sci. Hokkaido Univ. 11, 181-189 (1951)
33. Ono, H.: Structural rules and a logical hierarchy, in: Mathematical Logic, Proceedings of the Summer School and Conference on Mathematical Logic, Heyting'88, P.P. Petrov (ed.), Plenum Press, 95-104 (1990)
34. Rasiowa, H., Sirkoski, R.: The Mathematics of Metamathematics, third edition, Polish Scientific Publishers, Warsawa, 1970
35. Schweizer, B., Sklar, A.: Probabilistic metric spaces, North Holland, New York, 1983