Geodesic
Monadic basic algebras
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 47 (2008) no. 1, pp. 27-36.

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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 $\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.
Classification : 03G25, 06D35
Keywords: basic algebra; monadic basic algebra; existential quantifier; universal quantifier; lattice with section antitone involution 
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Chajda, Ivan; Kolařík, Miroslav. Monadic basic algebras. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 47 (2008) no. 1, pp. 27-36. http://geodesic.mathdoc.fr/item/AUPO_2008__47_1_a2/