Abstract
This paper is a study of four subscripted Gentzen systems G u R +, G u T +, G u RW + and G u TW +. [16] shows that the first three are equivalent to the semilattice relevant logics u R +, u T + and u RW + and conjectures that G u TW + is, equivalent to u TW +. Here we prove Cut Theorems for these systems, and then show that modus ponens is admissible — which is not so trivial as one normally expects. Finally, we give decision procedures for the contractionless systems, G u TW + and G u RW +.
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Giambrone, S., Kron, A. Four relevant Gentzen systems. Stud Logica 46, 55–71 (1987). https://doi.org/10.1007/BF00396905
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DOI: https://doi.org/10.1007/BF00396905