Monadic basic algebras. (English) Zbl 1172.06006

Basic algebras, as algebras of type \(\langle2,1,0\rangle\), generalize, e.g., MV-algebras and orthomodular lattices. The authors introduce and study certain unary operators on basic algebras, called existential (resp. universal) quantifiers, which are special cases of the closure (resp. interior) operators with respect to the naturally defined orders.


06D35 MV-algebras
03G25 Other algebras related to logic
Full Text: EuDML


[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
[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
[3] Chajda I., Halaš R., Kühr J.: Distributive lattices with sectionally antitone involutions. Acta Sci. Math. (Szeged) 71 (2005), 19-33. · Zbl 1099.06006
[4] Chajda I., Halaš R., Kühr J.: Many-valued quantum algebras. Algebra Universalis, to appear. · Zbl 1219.06013
[5] Chajda I., Halaš R., Kühr J.: Semilattice Structures. : Heldermann Verlag, Lemgo, Germany. 2007.
[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
[7] Di Nola A., Grigolia R.: On monadic MV-algebras. Ann. Pure Appl. Logic 128 (2006), 212-218. · Zbl 1052.06010
[8] Rachůnek J., Švrček F.: Monadic bounded commutative residuated \(\ell \)-monoids. Order, to appear. · Zbl 1151.06008
[9] Rutledge J. D.: On the definition of an infinitely-many-valued predicate calculus. J. Symbolic Logic 25 (1960), 212-216. · Zbl 0105.00501
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.