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Logic and Logical Philosophy

Relational Semantics for the Paraconsistent and Paracomplete 4-valued Logic PŁ4
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Relational Semantics for the Paraconsistent and Paracomplete 4-valued Logic PŁ4

Authors

  • Gemma Robles Dpto. de Psicología, Sociología y Filosofía, Universidad de León https://orcid.org/0000-0001-6495-0388
  • Sandra M. López Edificio FES, Campus Unamuno, Universidad de Salamanca https://orcid.org/0000-0003-2584-5950
  • José M. Blanco Department of Systems and Communications, Masaryk University Brno, Czech Republic https://orcid.org/0000-0001-9460-8540

DOI:

https://doi.org/10.12775/LLP.2022.016

Keywords

paraconsistent logics, paracomplete logics, 4-valued logics, modal 4-valued logics, Routley-Meyer semantics, binary Routley semantics, 2 set-up Routley-Meyer semantics, 2 set-up binary Routley semantics

Abstract

The paraconsistent and paracomplete 4-valued logic PŁ4 is originally interpreted with a two-valued Belnap-Dunn semantics. In the present paper, PŁ4 is endowed with both a ternary Routley-Meyer semantics and a binary Routley semantics together with their respective restriction to the 2 set-up cases.

References

Béziau, J.-Y., “A new four-valued approach to modal logic”, Logique et Analyse, 54, 213 (2011): 109–121.

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.

De, M., and H. Omori, “Classical negation and expansions of Belnap-Dunn logic”, Studia Logica, 103, 4 (2015): 825–851. DOI: http://dx.doi.org/10.1007/s11225-014-9595-7

Kamide, N., and H. Omori, “An extended first-order Belnap-Dunn logic with classical negation”, pages 79–93 in A. Baltag, J. Seligman and T. Yamada (eds.), Logic, Rationality, and Interaction, Springer, 2017. DOI: http://dx.doi.org/10.1007/978-3-662-55665-8_6

Łukasiewicz, J., Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic, Clarendon Press, Oxford, 1951.

Łukasiewicz, J., “A system of modal logic”, The Journal of Computing Systems, 1 (1953): 111–149.

Méndez, J. M., and G. Robles, “A strong and rich 4-valued modal logic without Łukasiewicz-type paradoxes”, Logica Universalis, 9, 4 (2015): 501–522. DOI: http://dx.doi.org/10.1007/s11787-015-0130-z

Méndez, J. M., G. Robles and F. Salto, “An interpretation of Łukasiewicz’s 4-valued modal logic”, Journal of Philosophical Logic, 45, 1 (2016), 73–87. DOI: http://dx.doi.org/10.1007/s10992-015-9362-x

Robles, G., and J. M. Méndez, “A binary Routley semantics for intuitionistic De Morgan minimal logic HM and its extensions”, Logic Journal of the IGPL, 23, 2 (2015): 174–193. DOI: http://dx.doi.org/10.1093/jigpal/jzu029

Robles, G., and J. M. Méndez, Routley-Meyer Ternary Relational Semantics for Intuitionistic-Type Negations, Elsevier, 2018.

Robles, G., S. M. López, J. M. Blanco, M. M. Recio and J. R. Paradela, “A 2-set-up Routley-Meyer semantics for the 4-valued relevant logic E4”, Bulletin of the Section of Logic, 45, 2 (2016): 93–109. DOI: http://dx.doi.org/10.18778/0138-0680.45.2.03

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., MaGIC, Matrix Generator for Implication Connectives: Version 2.1, Notes and Guide, Canberra: Australian National University, 1995. users.cecs.anu.edu.au/jks/magic.html (27/01/2021).

Zaitsev, D., “Generalized relevant logic and models of reasoning” (doctoral dissertation), Moscow State Lomonosov University, 2012.

Logic and Logical Philosophy

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Published

2022-04-23

How to Cite

1.
ROBLES, Gemma, LÓPEZ, Sandra M. & BLANCO, José M. Relational Semantics for the Paraconsistent and Paracomplete 4-valued Logic PŁ4. Logic and Logical Philosophy [online]. 23 April 2022, T. 31, nr 4, s. 665–687. [accessed 23.3.2023]. DOI 10.12775/LLP.2022.016.
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Vol. 31 No. 4 (2022): December

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License

Copyright (c) 2022 Gemma Robles, Sandra M. López, José M. Blanco

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This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.

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