Modal operators on bounded commutative residuated ℓ -monoids

Jiří Rachůnek; Dana Šalounová

Mathematica Slovaca (2007)

  • Volume: 57, Issue: 4, page [321]-332
  • ISSN: 0139-9918

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Rachůnek, Jiří, and Šalounová, Dana. "Modal operators on bounded commutative residuated $\ell $-monoids." Mathematica Slovaca 57.4 (2007): [321]-332. <http://eudml.org/doc/34650>.

@article{Rachůnek2007,
author = {Rachůnek, Jiří, Šalounová, Dana},
journal = {Mathematica Slovaca},
keywords = {residuated -monoid; residuated lattice; BL-algebra; MV-algebra},
language = {eng},
number = {4},
pages = {[321]-332},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Modal operators on bounded commutative residuated $\ell $-monoids},
url = {http://eudml.org/doc/34650},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Rachůnek, Jiří
AU - Šalounová, Dana
TI - Modal operators on bounded commutative residuated $\ell $-monoids
JO - Mathematica Slovaca
PY - 2007
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 57
IS - 4
SP - [321]
EP - 332
LA - eng
KW - residuated -monoid; residuated lattice; BL-algebra; MV-algebra
UR - http://eudml.org/doc/34650
ER -

References

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  2. BLOUNT K.-TSINAKIS C., The structure of residuated lattices, Intеrnat. J. Algеbra Comput. 13 (2003), 437-461. Zbl1048.06010MR2022118
  3. CIGNOLI R. L. O.-D'OТТAVIANO I. M. L.-MUNDICI D., Algebraic Foundation of Many-valued Reasoning, Kluwеr Acad. Publ., Dordrecht-Boston-London, 2000. MR1786097
  4. DVUREČENSKIJ A.-RACHŮNEK J., Probabilistic averaging in bounded commutative residuated ℓ -monoids, Discrete Math. 306 (2006), 1317-1326 Zbl1105.06011MR2237716
  5. GALAТOS M.- ТSINAKIS C., Generalized MV-algebras, J. Algеbra 283 (2005), 254-291. MR2102083
  6. HÁJEK P., Metamathematics of Fuzzy Logic, Kluwer, Amsterdam, 1998. (1998) Zbl0937.03030MR1900263
  7. HARLENDEROVÁ M.-RACHŮNEK J., Modal operators on MV-algebras, Math. Bohem. 131 (2006), 39-48. Zbl1112.06014MR2211002
  8. JIPSEN P.-ТSINAKIS C., A survey of residuated lattices, In: Ordеrеd Algеbraic Structurеs (J. Martinеz, еd.), Kluwеr Acad. Publ., Dordrеcht, 2002, pp. 19-56. Zbl1070.06005MR2083033
  9. KÜHR J., Dually Residuated Lattice-Ordered Monoids, Ph.D. Тhеsis, Palacký Univ. Olomouc, 2003. Zbl1141.06014
  10. MACNAB D. S., Modal operators on Heyting algebras, Algebra Universalis 12 (1981), 5-29. (1981) Zbl0459.06005MR0608645
  11. RACHŮNEK J., D R ℓ -semigroups and M V -algebras, Czechoslovak Math. J. 48 (1998), 365-372. (1998) MR1624268
  12. RACHŮNEK J., [unknown], Math. Bohem. 123 (1998), 437-441. (1998) MR1667115
  13. RACHŮNEK J., A duality between algebras of basic logic and bounded representable D R ℓ -monoids, Math. Bohem. 126 (2001), 561-569. MR1970259
  14. RACHŮNEK J.-ŠALOUNOVÁ D., Local bounded commutative residuated t-monoids, Czechoslovak Math. J. 57 (2007), 395-406 MR2309973
  15. RACHŮNEK J.- SLEZÁK V., Negation in bounded commutative DRl-monoids, Czechoslovak Math. J. 56 (2006), 755-763 MR2291772
  16. SWAMY K. L. N., Dually residuated lattice ordered semigroups, Math. Ann. 159 (1965), 105-114. (1965) Zbl0138.02104MR0183797

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