Functorial representation theorems for MVΔ algebras with additional operators

Journal of Algebra

Volumn 238, Issue 1, 2001, Pages 99-125

  Montagna, Franco ^a  

^a UNIVERSITY OF SIENA   (Italy)

Author keywords

Functorial equivalence; Fuzzy algebras; Fuzzy logic

Indexed keywords

EID: 0035315237     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1006/jabr.2000.8633     Document Type: Article

References (26)

1. Alsina C., Trillas E., Valverde L. On some logical connectives for fuzzy set theory. J Math. Anal. Appl. 93:1983;15-26.
2. Baaz M. Infinite-valued Gödel logics with 0-1 projections and relativizations. Hájek P., GÖDEL'96 - Logical Foundations of Mathematics, Computer Science and Physics. Lecture Notes in Logic. 6:1996;23-33 Springer-Verlag, Berlin/New York.
3. Balbes R., Dwinger Ph. Distributive Lattices. 1974;Univ. Missouri Press, Columbia.
4. Bigard A., Keimel K., Wolfenstein S. Groupes et anneaux reticulès. Lecture Notes in Mathematics. 608:1977;Springer-Verlag, Berlin.
5. Birkhoff G., Pierce R. S. Lattice ordered rings. Anais Acad. Brasil. Ci. 28:1956;41-69.
6. Burris S., Sankappanavar H. P. A Course in Universal Algebra. 1981;Springer-Verlag, Berlin/Heidelberg/New York.
7. Chang C. C. Algebraic analysis of many-valued logics. Trans. Amer. Math. Soc. 88:1958;467-490.
8. Chang C. C. A new proof of the completeness of Lukasiewicz axioms. Trans Amer. Math. Soc. 93:1959;74-80.
9. Cignoli R., Mundici D. An invitation to Chang's MV algebras. Droste M., Goebel R., Advanced Algebra and Model Theory. 1997;171-197 Gordon and Breach Publishing Group, Reading.
10. Cignoli R., Mundici D. An elementary proof of Chang's completeness theorem for the infinite-valued calculus of Lukasiewicz. Studia Logica. 58:1997;79-97.
11. Cignoli R., D'Ottaviano I. M. L., Mundici D. Algebras das Logicas de Lukasiewicz. 1995.
12. Esteva F., Godo L. Putting Lukasiewicz and product logics together. Proceedings of ESTYLF'98. September 1998;. p. 339-346.
13. F. Esteva, L. Godo, and, F. Montagna, The L/π and L/π 1 2 logics: two complete fuzzy systems joining Lukasiewicz and product logics, Arch. Math. Logic, to appear.
14. Gödel K. Zum intuitionistischen Aussagenkalkül. Anzeiger Akademie der Wissenschaften Wien, Math-Naturwissensch. 69:1932;. p. 65-66.
15. Goodearl K. R. Partially Ordered Abelian Groups with Interpolation. Mathematical Surveys and Monographs. 20:1986;Am. Math. Soc. Providence.
16. Gumm H. P., Ursini A. Ideals in universal algebra. Algebra Universalis. 19:1984;45-54.
17. Hajek P. Metamathematics of Fuzzy Logic. 1998;Kluwer, Dordrecht.
18. Keimel K. Some trends in lattice ordered groups and rings. Baker K. A., Wille R., Lattice Theory and Its Applications. 1995;131-161 Helderman Verlag, Darmstadt.
19. McKenzie R. On spectra, and the negative solution of the decision problem for identities having a finite nontrivial model. J. Symbolic Logic. 40:1975;186-196.
20. Mackenzie R., McNulty G., Taylor W. Algebras, Lattices, Varieties. 1987;Wadsworth and Brooks/Cole, Monterey.
21. Montagna F. An algebraic approach to propositional fuzzy logic. J. Logic Lang. Inform. 9:2000;91-124.
22. Mundici D. Interpretation of AFC* algebras in Lukasiewicz sentential calculus. J. Funct. Anal. 65:1986;15-63.
23. Panti G. A geometric proof of the completeness of the calculus of Lukasiewicz. J. Symbolic Logic. 60:1995;563-578.
24. Pavelka J. On fuzzy logic, I, II, III. Z. Math. Log. Grundlagen Math. 25:1979;45-52.
25. Takeuti G., Titani S. Fuzzy logic and fuzzy set theory. Arch. Math. Logic. 32:1992;1-32.
26. Torrens A. Boolean products of CW algebras and pseudocomplementation. Rep. Math. Logic. 23:1989;31-38.