Involutive equality algebras

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...

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Bibliographic Details
Published in:Soft computing (Berlin, Germany) Germany), 2018-11, Vol.22 (22), p.7505-7517
Main Authors: Borzooei, R. A., Zarean, M., Zahiri, O.
Format: Article
Language:English
Subjects:
Algebra
Artificial Intelligence
Boolean algebra
Computational Intelligence
Control
Engineering
Equality
Foundations
Lattices (mathematics)
Mathematical Logic and Foundations
Mechatronics
Robotics
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Summary: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 equality algebra is a lattice, while it is distributive under a suitable condition. Then, we define ( ∼ 0 ) -involutive deductive systems on bounded equality algebras and represent a condition under which the set of all dense elements of an equality algebra is a ( ∼ 0 ) -involutive deductive system. Finally, we find the relations among 0-compatible equality algebras, residuated lattices and Boolean algebras.
ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-018-3032-1