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.