Depth relevance of some paraconsistent logics

Studia Logica 43 (1-2):63 - 73 (1984)
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Abstract

The paper essentially shows that the paraconsistent logicDR satisfies the depth relevance condition. The systemDR is an extension of the systemDK of [7] and the non-triviality of a dialectical set theory based onDR has been shown in [3]. The depth relevance condition is a strengthened relevance condition, taking the form: If DR- AB thenA andB share a variable at the same depth, where the depth of an occurrence of a subformulaB in a formulaA is roughly the number of nested ''s required to reach the occurrence ofB inA. The method of proof is to show that a model structureM consisting of {M 0 , M1, ..., M}, where theM i s are all characterized by Meyer''s 6-valued matrices (c. f, [2]), satisfies the depth relevance condition. Then, it is shown thatM is a model structure for the systemDR.

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Citations of this work

Depth Relevance and Hyperformalism.Shay Allen Logan - 2022 - Journal of Philosophical Logic 51 (4):721-737.
Strong Depth Relevance.Shay Allen Logan - 2021 - Australasian Journal of Logic 18 (6):645-656.
What is a Relevant Connective?Shawn Standefer - 2022 - Journal of Philosophical Logic 51 (4):919-950.
Variable-Sharing as Relevance.Shawn Standefer - forthcoming - In Igor Sedlár, Shawn Standefer & Andrew Tedder (eds.), New Directions in Relevant Logic.

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References found in this work

Relevant Logics and Their Rivals.Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady - 1982 - Ridgeview. Edited by Richard Sylvan & Ross Brady.
The non-triviality of dialectical set theory.Ross T. Brady - 1989 - In Graham Priest, Richard Routley & Jean Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent. Philosophia Verlag. pp. 437--470.
Curry's paradox.Robert K. Meyer & Alonso Church - 1979 - Analysis 39 (3):124-128.
Career induction stops here (and here = 2).Robert K. Meyer - 1979 - Journal of Philosophical Logic 8 (1):361 - 371.

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