Equivalences among Various Logical Frameworks of Partial Algebras

We examine a variety of liberal logical frameworks of partial algebras. Therefore we use simple, conjunctive and weak embeddings of institutions which preserve model categories and may map sentences to sentences, nite sets of sentences, or theory extensions using unique-existential quantiiers, respectively. They faithfully represent theories, model categories, theory morphisms, colimit of theories, reducts etc. Moreover, along simple and conjunctive embeddings, theorem provers can be re-used in a way that soundness and completeness is preserved. Our main result states the equivalence of all the logical frameworks with respect to weak embeddability. This gives us compilers between all frameworks. Thus it is a chance to unify the diierent branches of speciication using liberal partial logics. This is important for reaching the goal of formal interoperability of diier-ent speciication languages for software development. With formal inter-operability, a speciication can contain parts written in diierent logical frameworks using a multiparadigm speciication language, and one can re-use tools which are available for one framework also for other frameworks .