Combining and representing logical systems using model-theoretic parchments

Integration of Specification Languages Using Viewpoints

“…The reader should have noticed us having avoided the classification of static versus dynamic frameworks, as proposed, for example, by the D-oids [1] and algebra transformation systems approaches [22]. Any SO language, with a suitable categorical semantics, can be used as a state language to form a new SO language.…”

“…It can be also seen as a generalization of the concepts of institutions and parchments [22], in the sense that sorts in an institution form the particular case of simple types in a specification frame. As the whole theory is very rich [8], we present here its very basic principles.…”

“…The extranaturality condition generates the familiar satisfaction condition for institutions. Institutions provide a universal semantic universe for all algebraic specification languages [22]. An institution for the language used in the data viewpoint of the example is described in [20].…”

On the Algebraization of Many-Sorted Logics

“…An important open question is whether and how our approach can be integrated with the work on the algebraization of logics as institutions reported in [20]. Another interesting line of future work is to study the impact of our proposal with respect to the way a logic is represented within many-sorted equational logic in the context of logic combination, namely in the lines of [17]. In any case, this seems to be an area which is very fit for application of the theory many-sorted algebras, including hidden-sorts and behavioral reasoning, as developed within the formal methods community over the last decade.…”

“…This means that the theory applies essentially only to propositionalbased logics, and that logics over many-sorted languages simply fall out of its scope. It goes without saying that rich logics, with many-sorted languages, are essential to specify and reason about complex systems, as also argued and justified by the theory of combined logics [17,19]. Herein, we propose a way to extend the scope of applicability of AAL by generalizing to the many-sorted case several of the key concepts and results of the current theory, including several alternative characterization results, namely those involving the Leibniz operator and maps of logics.…”