Four relevant Gentzen systems

Studia Logica 46 (1):55 - 71 (1987)
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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DOI 10.1007/BF00396905
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References found in this work BETA
Nuel D. Belnap (1982). Display Logic. Journal of Philosophical Logic 11 (4):375-417.
Nuel D. Belnap (1982). Gupta's Rule of Revision Theory of Truth. Journal of Philosophical Logic 11 (1):103-116.
Alasdair Urquhart (1972). Semantics for Relevant Logics. Journal of Symbolic Logic 37 (1):159-169.
Steve Giambrone (1985). TW+ and RW+ Are Decidable. Journal of Philosophical Logic 14 (3):235 - 254.

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Citations of this work BETA
Kosta Došen (1992). Modal Translations in Substructural Logics. Journal of Philosophical Logic 21 (3):283 - 336.
Steve Giambrone & Alasdaire Urquhart (1987). Proof Theories for Semilattice Logics. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (5):433-439.
Anthony Everett (1996). A Dilemma for Priest's Dialethism? Australasian Journal of Philosophy 74 (4):657 – 668.

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