Some algebraic structures determined by closure operators

Abstract

In this work we obtain axiomatizations of the concepts of lattice, distributive lattice, positive implication algebra, implication algebra, relative pseudocomplemented lattice, pseudoBoolean algebra and Boolean algebra by means of the concept of closure operator. The axiomatics express the algebra as a logical quotient of a logic having properties which reflect some classical rules of inference as adjunction, excluding cases, deduction and reductio at absurdum.