Abstract Logics as Dialgebras

Abstract

AbstractThe aim of this report is to propose a line of research that studies the connections between the theory of consequence operators as developed in [1] and [4] and the theory of dialgebras. The first steps in this direction are taken in this report, namely some of the basic notions of the theory of consequence operators - such as abstract logics - are translated into notions of the theory of dialgebras, and internal characterizations of the corresponding classes of objects are presented. Moreover it is shown that the class of coalgebras that corresponds to abstract logics of empty signature is a covariety