Relational semantics for the 4-valued relevant logics BN4 and E4
DOI:
https://doi.org/10.12775/LLP.2016.006Keywords
relevant logics, many-valued logics, 4-valued logics, Routley-Meyer semanticsAbstract
The logic BN4 was defined by R.T. Brady in 1982. It can be considered as the 4-valued logic of the relevant conditional. E4 is a variant of BN4 that can be considered as the 4-valued logic of (relevant) entailment. The aim of this paper is to define reduced general Routley-Meyer semantics for BN4 and E4. It is proved that BN4 and E4 are strongly sound and complete w.r.t. their respective semantics.References
Anderson, A.R., and N.D. Belnap, Jr., Entailment. The Logic of Relevance and Necessity, vol. I, Princeton University Press, 1975.
Anderson, A.R., N.D. Belnap, Jr., and J.M. Dunn, Entailment. The Logic of Relevance and Necessity, vol. II, Princeton University Press, 1992.
Belnap, N.D., Jr., “Entailment and relevance”, The Journal of Symbolic Logic, 25 (1960): 388–389.
Belnap, N.D., Jr., “How a computer should think”, pages 30–55 in G. Ryle (ed.), Contemporary Aspects of Philosophy, Oriel Press Ltd., Stocksfield, 1977.
Belnap, N.D., Jr., “A useful four-valued logic”, pages 8–37 in J.M. Dunn and G. Epstein (eds.), Modern Uses of Multiple-Valued Logic, D. Reidel Publishing Co., Dordrecht, 1977.
Brady, R.T., “Completeness Proofs for the Systems RM3 and BN4”, Logique et Analyse 25 (1982): 9–32.
Brady, R.T. (ed.), Relevant Logics and Their Rivals, vol. II, Ashgate, Aldershot, 2003.
Brady, R.T., Universal Logic, CSLI, Stanford, CA, 2006.
Dunn, J.M., “Partiality and its Dual”, Studia Logica, 65 (2000): 5–40. DOI: 10.1023/A:1026740726955
González, C., MaTest, 2012. Available at http://ceguel.es/matest (Last access 23/03/2016)
Meyer, R.K., S. Giambrone, and R.T. Brady, “Where gamma fails”, Studia Logica, 43 (1984): 247–256. DOI: 10.1007/BF02429841
Odintsov, S.P., and H. Wansing, “Modal logics with Belnapian truth values”, Journal of Applied Non-Classical Logics, 20 (2010): 279–301. DOI: 10.3166/jancl.20.279-304
Robles, G., “A Routley-Meyer semantics for Gödel 3-valued logic and its paraconsistent counterpart”, Logica Universalis 7 (2013): 507–532. DOI: 10.1007/s11787-013-0088-7
Robles, G., and J.M. Méndez, “A Routley-Meyer semantics for truth-preserving and well-determined Łukasiewicz 3-valued logics”, Logic Journal of the IGPL 22 (2014): 1–23. DOI: 10.1093/jigpal/jzt017
Robles, G., and J. M. Méndez, “The non-relevant De Morgan minimal logic in Routley-Meyer semantics with no designated points”, Journal of Applied Non-Classical Logics, 24 (2014): 321–332. DOI: 10.1080/11663081.2014.972306
Robles, G., and J.M. Méndez, “A companion to Brady’s 4-valued relevant logic BN4: The 4-valued logic of entailment E4”, Logic Journal of the IGPL, First published online: April 11, 2016. DOI: 10.1093/jigpal/jzw011
Routley, R., R.K. Meyer, V. Plumwood, and R.T. Brady, Relevant Logics and their Rivals, vol. 1, Atascadero, CA: Ridgeview Publishing Co., 1982.
Slaney, J.K., “Relevant logic and paraconsistency”, pages 270–293 in L. Bertossi, A. Hunter, and T. Schaub (eds.), Inconsistency Tolerance, vol. 3300 of “Lecture Notes in Computer Science”, 2005. DOI: 10.1007/978-3-540-30597-2_9
Downloads
Published
How to Cite
Issue
Section
Stats
Number of views and downloads: 611
Number of citations: 0
