| Title:
|
Monadic basic algebras (English) |
| Author:
|
Chajda, Ivan |
| Author:
|
Kolařík, Miroslav |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
47 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
27-36 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
basic algebra |
| Keyword:
|
monadic basic algebra |
| Keyword:
|
existential quantifier |
| Keyword:
|
universal quantifier |
| Keyword:
|
lattice with section antitone involution |
| MSC:
|
03G25 |
| MSC:
|
06D35 |
| idZBL:
|
Zbl 1172.06006 |
| idMR:
|
MR2482714 |
| . |
| Date available:
|
2009-08-27T11:28:02Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133403 |
| . |
| Reference:
|
[1] Chajda I., Emanovský P.: Bounded lattices with antitone involutions and properties of MV-algebras.Discuss. Math., Gen. Algebra Appl. 24 (2004), 31–42. Zbl 1082.03055, MR 2117673 |
| Reference:
|
[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. Zbl 1145.06003, MR 2377053 |
| Reference:
|
[3] Chajda I., Halaš R., Kühr J.: Distributive lattices with sectionally antitone involutions.Acta Sci. Math. (Szeged) 71 (2005), 19–33. Zbl 1099.06006, MR 2160352 |
| Reference:
|
[4] Chajda I., Halaš R., Kühr J.: Many-valued quantum algebras.Algebra Universalis, to appear. Zbl 1219.06013, MR 2480632 |
| Reference:
|
[5] Chajda I., Halaš R., Kühr J.: Semilattice Structures. : Heldermann Verlag, Lemgo, Germany., 2007. MR 2326262 |
| Reference:
|
[6] Chajda I., Kolařík M.: Independence of axiom system of basic algebras.Soft Computing, to appear, DOI 10.1007/s00500-008-0291-2. Zbl 1178.06007 |
| Reference:
|
[7] Di Nola A., Grigolia R.: On monadic MV-algebras.Ann. Pure Appl. Logic 128 (2006), 212–218. Zbl 1052.06010, MR 2060551 |
| Reference:
|
[8] Rachůnek J., Švrček F.: Monadic bounded commutative residuated $\ell $-monoids.Order, to appear. Zbl 1151.06008, MR 2425951 |
| Reference:
|
[9] Rutledge J. D.: On the definition of an infinitely-many-valued predicate calculus.J. Symbolic Logic 25 (1960), 212–216. Zbl 0105.00501, MR 0138549 |
| . |
