The One-Variable Fragment of Corsi Logic

Caicedo, Xavier; Metcalfe, George; Rodriguez, Ricardo; Tuyt, Olim Frits (2019). The One-Variable Fragment of Corsi Logic. In: Iemhoff, Rosalie; Moortgat, Michael; de Queiroz, Ruy (eds.) Logic, Language, Information, and Computation. Proceedings of WoLLIC 2019. Lecture Notes in Computer Science: Vol. 11541 (pp. 70-83). Berlin: Springer

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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.

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