A 2-set-up Routley-Meyer Semantics for the 4-valued Relevant Logic E4

Gemma Robles; Sandra M. López; José M. Blanco; Marcos M. Recio; Jesús R. Paradela

Bulletin of the Section of Logic (2016)

  • Volume: 45, Issue: 2
  • ISSN: 0138-0680

Abstract

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The logic BN4 can be considered as the 4-valued logic of the relevant conditional and the logic E4, as the 4-valued logic of (relevant) entailment. The aim of this paper is to endow E4 with a 2-set-up Routley-Meyer semantics. It is proved that E4 is strongly sound and complete w.r.t. this semantics.

How to cite

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Gemma Robles, et al. "A 2-set-up Routley-Meyer Semantics for the 4-valued Relevant Logic E4." Bulletin of the Section of Logic 45.2 (2016): null. <http://eudml.org/doc/295547>.

@article{GemmaRobles2016,
abstract = {The logic BN4 can be considered as the 4-valued logic of the relevant conditional and the logic E4, as the 4-valued logic of (relevant) entailment. The aim of this paper is to endow E4 with a 2-set-up Routley-Meyer semantics. It is proved that E4 is strongly sound and complete w.r.t. this semantics.},
author = {Gemma Robles, Sandra M. López, José M. Blanco, Marcos M. Recio, Jesús R. Paradela},
journal = {Bulletin of the Section of Logic},
keywords = {Relevant logics; many-valued logics; 4-valued logics; 2-set-up Routley-Meyer semantics},
language = {eng},
number = {2},
pages = {null},
title = {A 2-set-up Routley-Meyer Semantics for the 4-valued Relevant Logic E4},
url = {http://eudml.org/doc/295547},
volume = {45},
year = {2016},
}

TY - JOUR
AU - Gemma Robles
AU - Sandra M. López
AU - José M. Blanco
AU - Marcos M. Recio
AU - Jesús R. Paradela
TI - A 2-set-up Routley-Meyer Semantics for the 4-valued Relevant Logic E4
JO - Bulletin of the Section of Logic
PY - 2016
VL - 45
IS - 2
SP - null
AB - The logic BN4 can be considered as the 4-valued logic of the relevant conditional and the logic E4, as the 4-valued logic of (relevant) entailment. The aim of this paper is to endow E4 with a 2-set-up Routley-Meyer semantics. It is proved that E4 is strongly sound and complete w.r.t. this semantics.
LA - eng
KW - Relevant logics; many-valued logics; 4-valued logics; 2-set-up Routley-Meyer semantics
UR - http://eudml.org/doc/295547
ER -

References

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  1. [1] A. R. Anderson, N. D. Belnap, Entailment. The Logic of Relevance and Necessity, vol. I, Princeton University Press (1975). 
  2. [2] R. T. Brady, Completeness Proofs for the Systems RM3 and BN4, Logique et Analyse 25 (1982), pp. 9–32. 
  3. [3] C. González, MaTest. Available at: http://ceguel.es/matest (2012). Last accessed: 23/03/2016. 
  4. [4] R. K. Meyer, S. Giambrone, R. T. Brady, Where gamma fails, Studia Logica 43 (1984), pp. 247–256. 
  5. [5] G. Robles, J. M. Méndez (2016), A companion to Brady’s 4-valued relevant logic BN4: The 4-valued logic of entailment E4, Logic Journal of the IGPL 24(5), pp. 838–858, doi: 10.1093/jigpal/jzw011 
  6. [6] R. Routley, R. K. Meyer, V. Plumwood, R. T. Brady (1982), Relevant Logics and their Rivals, vol. 1, Ridgeview Publishing Co., Atascadero (1982). 

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