Abstract
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 \(\mathsf {S5(\mathbf {G})}\). It is also shown that \(\mathsf {S5(\mathbf {G})}\) can be interpreted in the crisp many-valued modal logic \(\mathsf {S5(\mathbf {G})^C}\), the modal counterpart of the one-variable fragment of first-order Gödel logic. Finally, an algebraic finite model property is proved for \(\mathsf {S5(\mathbf {G})^C}\) and used to establish co-NP-completeness for validity in the aforementioned modal logics and one-variable fragments.
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Acknowledgements
The second and fourth authors were supported by the Swiss National Science Foundation grant 200021\(\_\)165850, the first author by the Universidad de los Andes Science Faculty Research Fund, and the third author by the research projects PIP 112-20150100412CO, CONICET, UBA-CyT 20020150100002BA and PICT/O 2016-0215. The authors have also received funding from the EU Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 689176.
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Caicedo, X., Metcalfe, G., Rodríguez, R., Tuyt, O. (2019). The One-Variable Fragment of Corsi Logic. In: Iemhoff, R., Moortgat, M., de Queiroz, R. (eds) Logic, Language, Information, and Computation. WoLLIC 2019. Lecture Notes in Computer Science(), vol 11541. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-59533-6_5
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DOI: https://doi.org/10.1007/978-3-662-59533-6_5
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