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Depth relevance of some paraconsistent logics. (English) Zbl 0581.03014

A propositional logic is said to satisfy the ”depth-relevance condition” iff whenever \(A\to B\) is a thesis then A and B share a variable at the same depth of nested occurrences of \(\to\). The paper under review defines a propositional logic DR which is included in the system T of ”ticket entailment” and includes the system DK of R. Routley [Relevance Logic Newsl. 2, 50-89 and 138-174 (1977; Zbl 0435.03005)], and shows that it satisfies the depth-relevance condition.
Reviewer: D.Makinson

MSC:

03B45 Modal logic (including the logic of norms)

Citations:

Zbl 0435.03005
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References:

[1] A. R. Anderson andN. D. Belnap, Jr.,Entailment, The Logic of Relevance and Necessity, Vol. I, Princeton, 1975.
[2] R. T. Brady,The axiomatization of Meyer’s ?crystal lattice?, in R. Routley, R. K. Meyer et al,Relevant Logics and their Rivals, Vol. 2, Ridgeview, California, forthcoming.
[3] R. T. Brady,The non-triviality of dialectical set theory, in G. Priest, R. Routley and T. Norman (eds.),Paraconsistent Logics, Philosophia Verlag, forthcoming in 1985. · Zbl 0691.03038
[4] R. K. Meyer,Career induction stops here (and here=2),Journal of Philosophical Logic, Vol. 8 (1979), pp. 361-371. · Zbl 0429.03035 · doi:10.1007/BF00258437
[5] R. K. Meyer, R. Routley andJ. M. Dunn,Curry’s paradox,Analysis, Vol. 39 (1978), pp. 124-128. · Zbl 0411.03019 · doi:10.2307/3327248
[6] J. Myhill,Levels of implication, in A. R. Anderson, R. B. Marcus and R. M. Martin (eds.),The Logical Enterprise, Yale, 1975, pp. 179-185.
[7] R. Routley,Ultralogic as universal,Relevance Logic Newsletter, Vol. 2 (1977), pp. 50-89 and pp. 138-175, and inExploring Meinong’s Jungle and Beyond, A. N. U., 1980. · Zbl 0435.03005
[8] R. Routley, R. K. Meyer et al,Relevant Logics and their Rivals, Vol. 1, Ridgeview, California, 1982. · Zbl 0579.03011
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