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Depth relevance of some paraconsistent logics

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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- A→B 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, ..., Mω}, 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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References

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Brady, R.T. Depth relevance of some paraconsistent logics. Stud Logica 43, 63–73 (1984). https://doi.org/10.1007/BF00935740

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