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 inSoft computing (Berlin, Germany) Vol. 22; no. 22; pp. 7505 - 7517
Main Authors Borzooei, R. A., Zarean, M., Zahiri, O.
Format Journal Article
LanguageEnglish
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
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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