Abstract
We provide a semantics for relevant logics with addition of Aristotle's Thesis, ∼(A→∼A) and also Boethius,(A→B)→∼(A→∼B). We adopt the Routley-Meyer affixing style of semantics but include in the model structures a regulatory structure for all interpretations of formulae, with a view to obtaining a lessad hoc semantics than those previously given for such logics. Soundness and completeness are proved, and in the completeness proof, a new corollary to the Priming Lemma is introduced (c.f.Relevant Logics and their Rivals I, Ridgeview, 1982).
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References
A. R. Anderson andN. D. Belnap, Jr.,Entailment, The Logic of Relevance and Necessity, Vol. 1, Princeton U.P., 1975.
C. Mortensen,Aristotle's thesis in consistent and inconsistent logics,Studia Logica, Vol. 43 (1984), pp. 107–116.
R. Routley, R. K. Meyer, et al.,Relevant Logics and their Rivals, Vol. 1, Ridgeview, 1982.
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Brady, R.T. A Routley-Meyer affixing style semantics for logics containing Aristotle's Thesis. Stud Logica 48, 235–241 (1989). https://doi.org/10.1007/BF02770514
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DOI: https://doi.org/10.1007/BF02770514