Complete calculi for structured specifications in fork algebra

"In previous articles we presented Argentum, a tool for reasoning across heterogeneous specifications based on the language of fork algebras. Argentum’s foundations were formalized in the framework of institutions. The formalization made simple to describe a methodology capable of producing a complete system desription from partial views, eventually written in different logical languages. Structured specifications were introduced by Sannella and Tarlecki and extensively studied by Borzyszkowski. The latter also presented conditions under which the calculus for structured specifications is complete. Using fork algebras as a “universal” institution capable of representing expressive logics (such as dynamic and temporal logics), requires using a fork language that includes a reflexive-transitive closure operator. The calculus thus obtained does not meet the conditions required by Borzyszkowski. In this article we present structure building operators (SBOs) over fork algebras, and provide a complete calculus for these operators."