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A Reduct Part of Relation Algebra and the Lattice of Deductive Systems

Bahareh Ebrahimi, Esfandiar Eslami, Lida Torkzadeh

Abstract



In this paper we concider a reduct part of relation algebras as residuated Lattice and investigate the residual operations through some theorems. We then define different types of deductive systems and give their properties together with some relations among them. We define the prime deductive system on a relation algebra and specify the differences between the definitions of deductive systems and prime deductive systems on lattice and relation algebra. Also the set Ds(A) is defined and investigated if it is a relation algebra.

Keywords


relation algebra, residuated lattice, deductive system, symmetric element, prime deductive system

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