Equality Logic

Abstract

In this paper, we introduce and study a corresponding logic toequality-algebras and obtain some basic properties of this logic. We provethe soundness and completeness of this logic based on equality-algebrasand local deduction theorem. Then we introduce the concept of (prelinear)equality-algebras and investigate some related properties. Also, westudy -deductive systems of equality-algebras. In particular, we provethat every prelinear equality-algebra is a subdirect product of linearly orderedequality-algebras. Finally, we construct prelinear equality logicand prove the soundness and strong completeness of this logic respect toprelinear equality-algebras.

Tense operators on frameable equality algebras

“…In [19], F. Zebardast and et al studied and proved that there are relations among equality algebras and some of other logical algebras. Some types of filters of equality algebras are introduced in [2] and the corresponding logic to equality algebras is introduced and studied in [16]. Jenei and Kóródi defined pseudo equality algebras as a generalization of equality algebras in [14].…”

Tense operators on frameable equality algebras

“…In [19], F. Zebardast and et al studied and proved that there are relations among equality algebras and some of other logical algebras. Some types of filters of equality algebras are introduced in [2] and the corresponding logic to equality algebras is introduced and studied in [16].…”