Modal operators on bounded residuated -monoids

Jiří Rachůnek; Dana Šalounová

Mathematica Bohemica (2008)

  • Volume: 133, Issue: 3, page 299-311
  • ISSN: 0862-7959

Abstract

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Bounded residuated lattice ordered monoids (-monoids) form a class of algebras which contains the class of Heyting algebras, i.e. algebras of the propositional intuitionistic logic, as well as the classes of algebras of important propositional fuzzy logics such as pseudo -algebras (or, equivalently, -algebras) and pseudo -algebras (and so, particularly, -algebras and -algebras). Modal operators on Heyting algebras were studied by Macnab (1981), on -algebras were studied by Harlenderová and Rachůnek (2006) and on bounded commutative -monoids in our paper which will apear in Math. Slovaca. Now we generalize modal operators to bounded -monoids which need not be commutative and investigate their properties also for further derived algebras.

How to cite

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Rachůnek, Jiří, and Šalounová, Dana. "Modal operators on bounded residuated $\rm l$-monoids." Mathematica Bohemica 133.3 (2008): 299-311. <http://eudml.org/doc/250536>.

@article{Rachůnek2008,
abstract = {Bounded residuated lattice ordered monoids ($\{\rm R\ell \}$-monoids) form a class of algebras which contains the class of Heyting algebras, i.e. algebras of the propositional intuitionistic logic, as well as the classes of algebras of important propositional fuzzy logics such as pseudo $\mathop \{\rm MV\}$-algebras (or, equivalently, $\mathop \{\rm GMV\}$-algebras) and pseudo $\mathop \{\rm BL\}$-algebras (and so, particularly, $\mathop \{\rm MV\}$-algebras and $\mathop \{\rm BL\}$-algebras). Modal operators on Heyting algebras were studied by Macnab (1981), on $\mathop \{\rm MV\}$-algebras were studied by Harlenderová and Rachůnek (2006) and on bounded commutative $\{\rm R\ell \}$-monoids in our paper which will apear in Math. Slovaca. Now we generalize modal operators to bounded $\{\rm R\ell \}$-monoids which need not be commutative and investigate their properties also for further derived algebras.},
author = {Rachůnek, Jiří, Šalounová, Dana},
journal = {Mathematica Bohemica},
keywords = {residuated l-monoid; residuated lattice; pseudo $\mathop \{\rm BL\}$-algebra; pseudo $\mathop \{\rm MV\}$-algebra; residuated lattice; pseudo BL-algebra; pseudo MV-algebra},
language = {eng},
number = {3},
pages = {299-311},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Modal operators on bounded residuated $\rm l$-monoids},
url = {http://eudml.org/doc/250536},
volume = {133},
year = {2008},
}

TY - JOUR
AU - Rachůnek, Jiří
AU - Šalounová, Dana
TI - Modal operators on bounded residuated $\rm l$-monoids
JO - Mathematica Bohemica
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 133
IS - 3
SP - 299
EP - 311
AB - Bounded residuated lattice ordered monoids (${\rm R\ell }$-monoids) form a class of algebras which contains the class of Heyting algebras, i.e. algebras of the propositional intuitionistic logic, as well as the classes of algebras of important propositional fuzzy logics such as pseudo $\mathop {\rm MV}$-algebras (or, equivalently, $\mathop {\rm GMV}$-algebras) and pseudo $\mathop {\rm BL}$-algebras (and so, particularly, $\mathop {\rm MV}$-algebras and $\mathop {\rm BL}$-algebras). Modal operators on Heyting algebras were studied by Macnab (1981), on $\mathop {\rm MV}$-algebras were studied by Harlenderová and Rachůnek (2006) and on bounded commutative ${\rm R\ell }$-monoids in our paper which will apear in Math. Slovaca. Now we generalize modal operators to bounded ${\rm R\ell }$-monoids which need not be commutative and investigate their properties also for further derived algebras.
LA - eng
KW - residuated l-monoid; residuated lattice; pseudo $\mathop {\rm BL}$-algebra; pseudo $\mathop {\rm MV}$-algebra; residuated lattice; pseudo BL-algebra; pseudo MV-algebra
UR - http://eudml.org/doc/250536
ER -

References

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