Fork Algebras as a Sufficiently Rich Universal Institution

Algebraization of computational logics in the theory of fork algebras has been a research topic for a while. This research allowed us to interpret classical first-order logic, several propositional monomodal logics, propositional and first-order dynamic logic, and propositional and first-order linear temporal logic in the theory of fork algebras.In this paper we formalize these interpretability results as institution representations from the institution of the corresponding logics to that of fork algebra. We also advocate for the institution of fork algebras as a sufficiently rich universal institution into which institutions meaningful in software development can be represented.