Two Generalizations of Bounded Involutive Lattices and of Ortholattices.

We introduce and study two dual independent absorption laws and two generalizations of bounded lattices and, consequently, two corresponding generalizations of bounded involutive lattices and two corresponding generalizations of ortholattices; a proper subclass of MV algebras is obtained. Many examples are provided.

Authors

• Afrodita Iorgulesc
• Michael Kinyon

Keywords

• m-MEL algebra
• m-BE algebra
• m-pre-BCK algebra
• m-BCK algebra
• MV algebra
• lattice
• bounded involutive lattice
• ortholattice
• softlattice
• widelattice
• bounded involutive softlattice
• bounded involutive widelattice
• orthosoftlattice
• orthowidelattice
• Boolean algebra MSC 2020: 06B75
• 06C15
• 06D35