Studia Logica:1-13 (forthcoming)

Yale Weiss
CUNY Graduate Center
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.
Keywords Arithmetical models  Characteristic frame  Intuitionistic logic  Relevance logic  Semilattice semantics
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DOI 10.1007/s11225-020-09921-2
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References found in this work BETA

Truth-Maker Semantics for Intuitionistic Logic.Kit Fine - 2014 - Journal of Philosophical Logic 43 (2-3):549-577.
A Propositional Calculus with Denumerable Matrix.Michael Dummett - 1959 - Journal of Symbolic Logic 24 (2):97-106.
Semantics for Relevant Logics.Alasdair Urquhart - 1972 - Journal of Symbolic Logic 37 (1):159-169.
A Note on the Relevance of Semilattice Relevance Logic.Yale Weiss - 2019 - Australasian Journal of Logic 16 (6):177-185.
Solution to the P − W Problem.E. P. Martin & R. K. Meyer - 1982 - Journal of Symbolic Logic 47 (4):869-887.

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