Open Access Open Access  Restricted Access Subscription or Fee Access

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

Bahareh Ebrahimi, Esfandiar Eslami, Lida Torkzadeh


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.


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

Full Text:


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.