Ternary Relational Semantics for the Variants of BN4 and E4 which Contain Routley and Meyer's Logic B
Keywords:Ternary relational semantics, relevant logics, 4-valued logics, Routley and Meyer's logic B, 4-valued quasi-relevant logics
Six interesting variants of the logics BN4 and E4—which can be considered as the 4-valued logics of the relevant conditional and (relevant) entailment, respectively—were previously developed in the literature. All these systems are related to the family of relevant logics and contain Routley and Meyer's basic logic B, which is well-known to be specifically associated with the ternary relational semantics. The aim of this paper is to develop reduced general Routley-Meyer semantics for them. Strong soundness and completeness theorems are proved for each one of the logics.
A. R. Anderson, N. D. Belnap, Entailment: The Logic of Relevance and Necessity, vol. I, Princeton University Press (1975).
A. R. Anderson, N. D. Belnap, J. M. Dunn, Entailment: The Logic of Relevance and Necessity, vol. II, Princeton University Press (1992).
R. T. Brady, Completeness proofs for the systems RM3 and BN4, Logique et Analyse, vol. 25 (1982), pp. 9–32.
R. T. Brady (ed.), Relevant Logics and their Rivals, vol. II, Ashgate (2003).
R. T. Brady, Universal Logic, CSLI (2006).
S. M. López, Belnap-Dunn semantics for the variants of BN4 and E4 which contain Routley and Meyer’s logic B, Logic and Logical Philosophy, (Online First), pp. 1–28, DOI: https://doi.org/10.12775/LLP.2021.004
Google Scholar DOI: https://doi.org/10.12775/LLP.2021.004
H. Omori, H. Wansing, 40 years of FDE: An Introductory Overview, Studia Logica, vol. 105 (2017), pp. 1021–1049, DOI: https://doi.org/10.1007/s11225-017-9748-6
Google Scholar DOI: https://doi.org/10.1007/s11225-017-9748-6
G. Robles, J. M. Blanco, S. M. López, J. R. Paradela, M. M. Recio, Relational Semantics for the 4-valued relevant logics BN4 and E4, Logic and Logical Philosophy, vol. 25(2) (2016), pp. 173–201, DOI: https://doi.org/10.12775/LLP.2016.006
Google Scholar DOI: https://doi.org/10.12775/LLP.2016.006
G. Robles, J. M. Méndez, A companion to Brady’s 4-valued relevant logic BN4: The 4-valued logic of entailment E4, Logic Journal of the IGLP, vol. 24(5) (2016), pp. 838–858, DOI: https://doi.org/10.1093/jigpal/jzw011
Google Scholar DOI: https://doi.org/10.1093/jigpal/jzw011
R. Routley, V. Plumwood, R. K. Meyer, R. T. Brady, Relevant Logics and their Rivals, vol. I, Ridgeview (1982).
J. K. Slaney, Relevant Logic and Paraconsistency, [in:] L. Bertossi, A. Hunter, T. Schaub (eds.), Inconsistency Tolerance, vol. 3300 of Lecture Notes in Computer Science, Springer (2005), pp. 270–293, DOI: https://doi.org/10.1007/978-3-540-30597-2_9
Google Scholar DOI: https://doi.org/10.1007/978-3-540-30597-2_9
R. Sylvan, V. Plumwood, Non-normal relevant logics, [in:] R. T. Brady (ed.), Relevant Logics and their Rivals, vol. II, Western Philosophy Series, Ashgate, Aldershot and Burlington (2003), pp. 10–16.
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