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2016 | 25 | 2 | 173–201
Article title

Relational semantics for the 4-valued relevant logics BN4 and E4

Authors
Title variants
Languages of publication
EN
Abstracts
EN
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.
Year
Volume
25
Issue
2
Pages
173–201
Physical description
Dates
online
2016-04-25
Contributors
author
  • Dpto. de Psicología, Sociología y Filosofía, Universidad de León, Campus de Vegazana, s/n 24071, León, Spain , gemma.robles@unileon.es
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
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.desklight-279de21d-29dd-4d0b-ab28-76782e33d20d
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