The Fmla-Fmla Axiomatizations of the Exactly True and Non-falsity Logics and Some of Their Cousins

Journal of Philosophical Logic:1-22 (forthcoming)
Alexander Belikov
Moscow State University
Dmitry Zaitsev
Lomonosov Moscow State University
In this paper we present a solution of the axiomatization problem for the Fmla-Fmla versions of the Pietz and Rivieccio exactly true logic and the non-falsity logic dual to it. To prove the completeness of the corresponding binary consequence systems we introduce a specific proof-theoretic formalism, which allows us to deal simultaneously with two consequence relations within one logical system. These relations are hierarchically organized, so that one of them is treated as the basic for the resulting logic, and the other is introduced as an extension of this basic relation. The proposed bi-consequences systems allow for a standard Henkin-style canonical model used in the completeness proof. The deductive equivalence of these bi-consequence systems to the corresponding binary consequence systems is proved. We also outline a family of the bi-consequence systems generated on the basis of the first-degree entailment logic up to the classic consequence.
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DOI 10.1007/s10992-018-9494-x
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References found in this work BETA

Nothing but the Truth.Andreas Pietz & Umberto Rivieccio - 2013 - Journal of Philosophical Logic 42 (1):125-135.
Partiality and its Dual.J. Michael Dunn - 2000 - Studia Logica 66 (1):5-40.

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