The One-Variable Fragment of Corsi Logic

The one-variable fragment of the first-order logic of linear intuitionistic Kripke models, referred to here as Corsi logic, is shown to have as its modal counterpart the many-valued modal logic S5(G). It is also shown that S5(G) can be interpreted in the crisp many-valued modal logic S5(Gc), the modal counterpart of the one-variable fragment of first-order Gödel logic. Finally, an algebraic finite model property is proved for S5(Gc) and used to establish co-NP-completeness for validity in the aforementioned modal logics and one-variable fragments.