Involutive equality algebras

• Published in: Soft computing (Berlin, Germany) Vol. 22; no. 22; pp. 7505 - 7517
• Main Authors: Borzooei, R. A., Zarean, M., Zahiri, O.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2018; Springer Nature B.V
• Subjects: Algebra; Artificial Intelligence; Boolean algebra; Computational Intelligence; Control; Engineering; Equality; Foundations; Lattices (mathematics); Mathematical Logic and Foundations; Mechatronics; Robotics; Equality algebra; Residuated lattice; Involutive equality algebra; Boolean algebra; 03G25; 06F05; 06F35

The present paper aims to study a special class of equality algebras, called involutive equality algebra. We obtain some properties of this structure and prove that every linearly ordered 0-compatible equality algebra includes a ( ∼ 0 ) -involutive subalgebra. We prove that each ( ∼ 0 ) -involutive...