Jiří Rachůnek, Zdeněk Svoboda (2013)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Commutative bounded integral residuated lattices form a large class of algebras containing some classes of algebras behind many valued and fuzzy logics. In the paper we introduce and investigate additive closure and multiplicative interior operators on this class of algebras.
Jiří Rachůnek, Zdeněk Svoboda (2012)
Mathematica Bohemica
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Bounded integral residuated lattices form a large class of algebras containing some classes of commutative and noncommutative algebras behind many-valued and fuzzy logics. In the paper, monotone modal operators (special cases of closure operators) are introduced and studied.
David Stanovský (2007)
Czechoslovak Mathematical Journal
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We investigate the variety of residuated lattices with a commutative and idempotent monoid reduct.
Sadegh Khosravi Shoar, Rajab Ali Borzooei, R. Moradian, Atefe Radfar (2018)
Bulletin of the Section of Logic
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In this paper, we define the notion of PC-lattice, as a generalization of finite positive implicative BCK-algebras with condition (S) and bounded commutative BCK-algebras. We investiate some results for Pc-lattices being a new class of BCK-lattices. Specially, we prove that any Boolean lattice is a PC-lattice and we show that if X is a PC-lattice with condition S, then X is an involutory BCK-algebra if and only if X is a commutative BCK-algebra. Finally, we prove that any PC-lattice...
P. Emanovský, Jiří Rachůnek (2008)
Czechoslovak Mathematical Journal
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Pseudo -autonomous lattices are non-commutative generalizations of -autonomous lattices. It is proved that the class of pseudo -autonomous lattices is a variety of algebras which is term equivalent to the class of dualizing residuated lattices. It is shown that the kernels of congruences of pseudo -autonomous lattices can be described as their normal ideals.
Ivan Chajda, Miroslav Kolařík (2008)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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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 -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...