Probabilistic averaging in bounded Rℓ-monoids

Semigroup Forum

Volumn 72, Issue 2, 2006, Pages 190-206

  Dvurečenskij, Anatolij ^a   Rachůnek, Jiři ^b  

^a INSTITUTE OF CHEMISTRY   (Slovakia)

^b PALACKÝ UNIVERSITY   (Czech Republic)

Author keywords

Bounded R monoid; Filter; Maximal filter; Normal filter; Pseudo BL algebra; Pseudo MV algebra (= GMV algebra); State (= Bosbach state); State morphism

Indexed keywords

EID: 33645665868     PISSN: 00371912     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00233-005-0545-6     Document Type: Article

References (26)

1. Bahls, P., J. Cole, N. Galatos, P. Jipsen, and C. Tsinakis, Cancellative residuated lattices, Algebra Universalis 50 (2003), 83-106.
2. Blount, K. and C. Tsinakis, The structure of residuated lattices, Internat. J. Algebra Comput. 13 (2003), 437-461.
3. Bosbach, B., Residuation groupoids, Result. Math. 5 (1982), 107-122.
4. Chang, C. C., Algebraic analysis of many valued logics, Trans. Amer. Math. Soc. 88 (1958), 467-490.
5. Cignoli, R., I. M. L. D'Ottaviano and D. Mundici, "Algebraic Foundations of Many-valued Reasoning", Kluwer Acad. Publ., Dordrecht-Boston-London, 2000.
6. Dilworth, R. P., Non-commutative residuated lattices, Trans. Amer. Math. Soc. 46 (1939), 426-444.
7. Di Nola, A., G. Georgescu and A. Iorgulescu, Pseudo-BL algebras I, Multiple Val. Logic 8 (2002), 673-714.
8. Di Nola, A., G. Georgescu, and A. Iorgulescu, Pseudo-BL algebras II, Multiple Val. Logic 8 (2002), 715-750.
9. Dvurečenskij, A., Pseudo MV-algebras are intervals in ℓ-groups, J. Austral. Math. Soc. 70 (2002), 427-445.
10. Dvurečenskij, A., States on pseudo MV-algebras, Studia Logica 68 (2001), 301-327.
11. Dvurečenskij, A. and S. Pulmannová, "New Trends in Quantum Structures", Kluwer Acad. Publ., Dordrecht, Ister Science, Bratislava, 2000.
12. Dvurečenskij, A. and J. Rachůnek, Probabilistic averaging in bounded commutative residuated ℓ-monoids, Discrete Math., to appear.
13. Georgescu, G., Bosbach states on fuzzy structures, Soft Computing 8 (2004), 217-230.
14. Georgescu, G. and A. Iorgulescu, Pseudo-MV algebras, Multiple Val. Logic 6 (2001), 95-135.
15. Goodearl, K. R., "Partially Ordered Abelian Groups with Interpolation", Math. Surveys and Monographs No. 20, Amer. Math. Soc., Providence, Rhode Island, 1986.
16. Hájek, P., "Metamathematics of Fuzzy Logic", Kluwer Acad. Publ., msterdam, 1998.
17. Jipsen, P. and C. Tsinakis, A survey of residuated lattices, in: "Ordered Algebraic Structures" (J. Martinez, ed.) Kluwer Acad. Publ., Dordrecht, 2002, pp. 19-56.
18. Kôpka, F. and F. Chovanec, D-posets, Math. Slovaca 44 (1994), 21-34.
19. Krull, W., Axiomatische Begründung der allgemeinen Idealtheorie, Sitzungsber. phys.-mediz. Soc. Erlangen 56 (1934), 47-63.
20. Kühr, J., "Dually Residuated Lattice Ordered Monoids", Ph.D. thesis, Palacký Univ., Olomouc, 2003.
21. Mundici, D., Averaging the truth-value in Lukasiewicz logic, Studia Logica 55 (1995), 113-127.
22. Rachůnek, J., A non-commutative generalization of MV-algebras, Czechoslovak Math. J. 52 (2002), 255-273.
23. Rachůnek, J., Prime ideals and polars in generalized MV-algebras, Multiple Val. Log. 8 (2002), 127-137.
24. Rachůnek, J. and V. Slezák, Negation in bounded commutative DRℓ-monoids, Czechoslovak Math. J., to appear.
25. Rachůnek, J. and V. Slezák, Bounded dually residuated lattice ordered monoids as a generalization of fuzzy structures, Math. Slovaca, to appear.
26. Swamy, K. L. N., Dually residuated lattice ordered semigroups, Math. Ann. 159 (1965), 105-114.