Generalising Interpretations Between Theories in the Context of (π-)institutions

The structural property of π-institutions which requires consequence to be preserved under changes of language is weakened. The proposed weakly structural π-institutions encompass logics in which consequence does depend on the choice of non-logical symbols by associating locality conditions with signatures or signature morphisms. They also enable new logics to be defined by reusing existing ones, extending and adapting them in order to build formalisms that better fit the applications whose specification they are intended to support.