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

doi:10.18778/0138-0680.45.2.03

Authors

Gemma Robles Universidad de León, Dpto. de Psicología, Sociología y Filosofía Author
Sandra M. López Universidad de Salamanca, Dpto. de Filosofía, Lógica y Estética Author
José M. Blanco Author
Marcos M. Recio Author
Jesús R. Paradela Author

DOI:

https://doi.org/10.18778/0138-0680.45.2.03

Keywords:

Relevant logics, many-valued logics, 4-valued logics, 2-set-up Routley-Meyer semantics

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.

References

[1] A. R. Anderson, N. D. Belnap, Entailment. The Logic of Relevance and Necessity, vol. I, Princeton University Press (1975).

[2] R. T. Brady, Completeness Proofs for the Systems RM3 and BN4, Logique et Analyse 25 (1982), pp. 9–32.

[3] C. González, MaTest. Available at: http://ceguel.es/matest (2012). Last accessed: 23/03/2016.

[4] R. K. Meyer, S. Giambrone, R. T. Brady, Where gamma fails, Studia Logica 43 (1984), pp. 247–256.

[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] R. Routley, R. K. Meyer, V. Plumwood, R. T. Brady (1982), Relevant Logics and their Rivals, vol. 1, Ridgeview Publishing Co., Atascadero (1982).