Abstract
I show that the lattice of the positive integers ordered by division is characteristic for Urquhart’s positive semilattice relevance logic; that is, a formula is valid in positive semilattice relevance logic if and only if it is valid in all models over the positive integers ordered by division. I show that the same frame is characteristic for positive intuitionistic logic, where the class of models over it is restricted to those satisfying a heredity condition. The results of this article highlight deep connections between intuitionistic and semilattice relevance logic.
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The author is grateful to the anonymous referees for comments which led to improvements in this paper.
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Presented by Heinrich Wansing; Received May 12, 2020.
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Weiss, Y. A Characteristic Frame for Positive Intuitionistic and Relevance Logic. Stud Logica 109, 687–699 (2021). https://doi.org/10.1007/s11225-020-09921-2
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DOI: https://doi.org/10.1007/s11225-020-09921-2