We investigate the class of strongly distributive pregroups, a common abstraction of MV-algebras and Abelian l-groups which was introduced by E.Casari. The main result of the paper is a representation theorem which yields both Chang's representation of MV-algebras and Clifford's representation of Abelian l-groups as immediate corollaries.

The paper introduces a concept of logic applied to a formalization of the so-called inferences preserving degrees of truth. Semantical and syntactical characterizations of three kinds of logics preserving degrees of truth are provided. The other approach than in [3] and [9] to the problem of expressing that a sentence is less true than a sentence is presented.