Monadic basic algebras

Ivan Chajda; Miroslav Kolařík

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2008)

  • Volume: 47, Issue: 1, page 27-36
  • ISSN: 0231-9721

Abstract

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The concept of monadic MV-algebra was recently introduced by A. Di Nola and R. Grigolia as an algebraic formalization of the many-valued predicate calculus described formerly by J. D. Rutledge [9]. This was also genaralized by J. Rachůnek and F. Švrček for commutative residuated ℓ -monoids since MV-algebras form a particular case of this structure. Basic algebras serve as a tool for the investigations of much more wide class of non-classical logics (including MV-algebras, orthomodular lattices and their generalizations). This motivates us to introduce the monadic basic algebra as a common generalization of the mentioned structures.

How to cite

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Chajda, Ivan, and Kolařík, Miroslav. "Monadic basic algebras." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 47.1 (2008): 27-36. <http://eudml.org/doc/32471>.

@article{Chajda2008,
abstract = {The concept of monadic MV-algebra was recently introduced by A. Di Nola and R. Grigolia as an algebraic formalization of the many-valued predicate calculus described formerly by J. D. Rutledge [9]. This was also genaralized by J. Rachůnek and F. Švrček for commutative residuated $\ell $-monoids since MV-algebras form a particular case of this structure. Basic algebras serve as a tool for the investigations of much more wide class of non-classical logics (including MV-algebras, orthomodular lattices and their generalizations). This motivates us to introduce the monadic basic algebra as a common generalization of the mentioned structures.},
author = {Chajda, Ivan, Kolařík, Miroslav},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {basic algebra; monadic basic algebra; existential quantifier; universal quantifier; lattice with section antitone involution; basic algebra; monadic basic algebra; quantifier},
language = {eng},
number = {1},
pages = {27-36},
publisher = {Palacký University Olomouc},
title = {Monadic basic algebras},
url = {http://eudml.org/doc/32471},
volume = {47},
year = {2008},
}

TY - JOUR
AU - Chajda, Ivan
AU - Kolařík, Miroslav
TI - Monadic basic algebras
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2008
PB - Palacký University Olomouc
VL - 47
IS - 1
SP - 27
EP - 36
AB - The concept of monadic MV-algebra was recently introduced by A. Di Nola and R. Grigolia as an algebraic formalization of the many-valued predicate calculus described formerly by J. D. Rutledge [9]. This was also genaralized by J. Rachůnek and F. Švrček for commutative residuated $\ell $-monoids since MV-algebras form a particular case of this structure. Basic algebras serve as a tool for the investigations of much more wide class of non-classical logics (including MV-algebras, orthomodular lattices and their generalizations). This motivates us to introduce the monadic basic algebra as a common generalization of the mentioned structures.
LA - eng
KW - basic algebra; monadic basic algebra; existential quantifier; universal quantifier; lattice with section antitone involution; basic algebra; monadic basic algebra; quantifier
UR - http://eudml.org/doc/32471
ER -

References

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  1. Chajda I., Emanovský P., Bounded lattices with antitone involutions and properties of MV-algebras, Discuss. Math., Gen. Algebra Appl. 24 (2004), 31–42. Zbl1082.03055MR2117673
  2. Chajda I., Halaš R., A basic algebra is an MV-algebra if and only if it is a BCC-algebra, Intern. J. Theor. Phys., to appear. Zbl1145.06003MR2377053
  3. Chajda I., Halaš R., Kühr J., Distributive lattices with sectionally antitone involutions, Acta Sci. Math. (Szeged) 71 (2005), 19–33. Zbl1099.06006MR2160352
  4. Chajda I., Halaš R., Kühr J., Many-valued quantum algebras, Algebra Universalis, to appear. Zbl1219.06013MR2480632
  5. Chajda I., Halaš R., Kühr J.: Semilattice Structures., Heldermann Verlag, Lemgo, Germany, , 2007. MR2326262
  6. Chajda I., Kolařík M., Independence of axiom system of basic algebras, Soft Computing, to appear, DOI 10.1007/s00500-008-0291-2. Zbl1178.06007
  7. Di Nola A., Grigolia R., On monadic MV-algebras, Ann. Pure Appl. Logic 128 (2006), 212–218. Zbl1052.06010MR2060551
  8. Rachůnek J., Švrček F., Monadic bounded commutative residuated ℓ -monoids, Order, to appear. Zbl1151.06008MR2425951
  9. Rutledge J. D., On the definition of an infinitely-many-valued predicate calculus, J. Symbolic Logic 25 (1960), 212–216. (1960) Zbl0105.00501MR0138549

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