Modal operators on MV-algebras

Magdalena Harlenderová; Jiří Rachůnek

Mathematica Bohemica (2006)

  • Volume: 131, Issue: 1, page 39-48
  • ISSN: 0862-7959

Abstract

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Modal operators on Heyting algebras were introduced by Macnab. In this paper we introduce analogously modal operators on MV-algebras and study their properties. Moreover, modal operators on certain derived structures are investigated.

How to cite

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Harlenderová, Magdalena, and Rachůnek, Jiří. "Modal operators on MV-algebras." Mathematica Bohemica 131.1 (2006): 39-48. <http://eudml.org/doc/249900>.

@article{Harlenderová2006,
abstract = {Modal operators on Heyting algebras were introduced by Macnab. In this paper we introduce analogously modal operators on MV-algebras and study their properties. Moreover, modal operators on certain derived structures are investigated.},
author = {Harlenderová, Magdalena, Rachůnek, Jiří},
journal = {Mathematica Bohemica},
keywords = {MV-algebra; modal operator; closure operator; residuated $\ell $-monoid; Heyting algebra; closure operator; residuated -monoid},
language = {eng},
number = {1},
pages = {39-48},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Modal operators on MV-algebras},
url = {http://eudml.org/doc/249900},
volume = {131},
year = {2006},
}

TY - JOUR
AU - Harlenderová, Magdalena
AU - Rachůnek, Jiří
TI - Modal operators on MV-algebras
JO - Mathematica Bohemica
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 131
IS - 1
SP - 39
EP - 48
AB - Modal operators on Heyting algebras were introduced by Macnab. In this paper we introduce analogously modal operators on MV-algebras and study their properties. Moreover, modal operators on certain derived structures are investigated.
LA - eng
KW - MV-algebra; modal operator; closure operator; residuated $\ell $-monoid; Heyting algebra; closure operator; residuated -monoid
UR - http://eudml.org/doc/249900
ER -

References

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  1. Algebraic Foundations of Many- valued Reasoning, Kluwer, Dordrecht, 2000. (2000) MR1786097
  2. New Trends in Quantum Structures, Kluwer Acad. Publ., Dordrecht, Ister Science, Bratislava, 2000. (2000) MR1861369
  3. 10.1007/BF02483860, Algebra Univers. 12 (1981), 5–29. (1981) Zbl0459.06005MR0608645DOI10.1007/BF02483860
  4. Modal operators on ordered sets, Acta Univ. Palacki. Olomuc., Fac. Rer. Nat., Math. 24 (1985), 9–14. (1985) MR0879015
  5. 10.1023/A:1022801907138, Czechoslovak Math. J. 48 (1998), 365–372. (1998) MR1624268DOI10.1023/A:1022801907138
  6. MV-algebras are categorically equivalent to a class of D R ℓ 1 ( i ) -semigroups, Math. Bohem. 123 (1998), 437–441. (1998) MR1667115
  7. Local bounded commutative residuated ℓ -monoids (submitted), . 
  8. MV-algebras with additive closure operators, Acta Univ. Palacki. Olomuc., Fac. Rer. Mat., Math. 39 (2000), 183–189. (2000) MR1826361

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