Subminimal Logics in Light of Vakarelov’s Logic

Abstract

We investigate a subsystem of minimal logic related to D. Vakarelov’s logic \(\mathbf {SUBMIN}\), using the framework of subminimal logics by A. Colacito, D. de Jongh and A. L. Vargas. In the course of it, the relationship between the two semantics in the respective frameworks is clarified. In addition, we introduce a sequent calculus for the investigated subsystem, and some proof-theoretic properties are established. Lastly, we formulate a new infinite class of subsystems of minimal logics.

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Acknowledgements

This research was supported by the Japan Society for the Promotion of Science (JSPS), Core-to-Core Program (A. Advanced Research Networks). A part of this paper was written during the visit of the author to the Hausdorff Research Institute for Mathematics (HIM), University of Bonn, from May to August 2018. The support for this visit and the hospitality of HIM are gratefully acknowledged. The author thanks anonymous referees for their helpful comments, and Hajime Ishihara and Takako Nemoto for their encouragement and many valuable suggestions during the production of this paper.

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Correspondence to Satoru Niki.

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Niki, S. Subminimal Logics in Light of Vakarelov’s Logic. Stud Logica 108, 967–987 (2020). https://doi.org/10.1007/s11225-019-09884-z

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Keywords

  • Negation
  • Minimal logic
  • Kripke semantics
  • Sequent calculus