Notes on the Logic of Perfect Paradefinite Algebras
Resumo
This work introduces the variety of perfect paradefinite algebras (PPalgebras), consisting of De Morgan algebras enriched with a perfect operator o, which turns out to be equivalent to the variety of involutive Stone algebras (IS-algebras). The corresponding order-preserving logic PP≤ is a Logic of Formal Inconsistency, a Logic of Formal Undeterminedness, a C-system and a D-system, some of these features being evident in the proposed axiomatization of PP-algebras. After proving the mentioned algebraic equivalence, we show how to axiomatize, by means of Hilbert-style calculi, certain extensions of De Morgan algebras with a perfect operator and, in particular, the logic PP≤.
Palavras-chave:
perfect paradefinite algebras, involutive Stone algebras, perfection operator, paradefinite logics, LFIUs
Referências
Barrio, E. A. and Carnielli, W. (2019). Volume I: Recovery operators in logics of formalinconsistency.Logic Journal of the IGPL, 28(5):615–623.
Belnap, N. D. (1977).A Useful Four-Valued Logic, pages 5–37. Springer Netherlands,Dordrecht.
Caleiro, C. and Marcelino, S. (2019). Analytic calculi for monadic PNmatrices. InIemhoff, R., Moortgat, M., and Queiroz, R., editors,Logic, Language, Informationand Computation (WoLLIC 2019), volume 11541 ofLNCS, pages 84–98. Springer.
Cantú, L. M. (2019). Sobre la lógica que preserva grados de verdad asociada a las álgebras de Stone involutivas. Master’s thesis, Universidad Nacional del Sur, Bahía Blanca, Argentina.
Cantú, L. M. and Figallo, M. (2018). On the logic that preserves degrees of truth associ-ated to involutive Stone algebras. Logic Journal of the IGPL, 28(5):1000–1020.
Font, J. (1997). Belnap’s four-valued logic and De Morgan lattices.Logic Journal of theIGPL, 5:1–29.
Marcelino, S. and Rivieccio, U. (2021). Logics of involutive stone algebras.arXivpreprint arXiv:2102.05455.
Marcos, J. (2005a). Logics of Formal Inconsistency. PhD thesis, Unicamp.
Marcos, J. (2005b). Nearly every normal modal logic is paranormal. Logique et Analyse,48:279–300.
Shoesmith, D. J. and Smiley, T. J. (1978). Multiple-Conclusion Logic. Cambridge Uni-versity Press.
Belnap, N. D. (1977).A Useful Four-Valued Logic, pages 5–37. Springer Netherlands,Dordrecht.
Caleiro, C. and Marcelino, S. (2019). Analytic calculi for monadic PNmatrices. InIemhoff, R., Moortgat, M., and Queiroz, R., editors,Logic, Language, Informationand Computation (WoLLIC 2019), volume 11541 ofLNCS, pages 84–98. Springer.
Cantú, L. M. (2019). Sobre la lógica que preserva grados de verdad asociada a las álgebras de Stone involutivas. Master’s thesis, Universidad Nacional del Sur, Bahía Blanca, Argentina.
Cantú, L. M. and Figallo, M. (2018). On the logic that preserves degrees of truth associ-ated to involutive Stone algebras. Logic Journal of the IGPL, 28(5):1000–1020.
Font, J. (1997). Belnap’s four-valued logic and De Morgan lattices.Logic Journal of theIGPL, 5:1–29.
Marcelino, S. and Rivieccio, U. (2021). Logics of involutive stone algebras.arXivpreprint arXiv:2102.05455.
Marcos, J. (2005a). Logics of Formal Inconsistency. PhD thesis, Unicamp.
Marcos, J. (2005b). Nearly every normal modal logic is paranormal. Logique et Analyse,48:279–300.
Shoesmith, D. J. and Smiley, T. J. (1978). Multiple-Conclusion Logic. Cambridge Uni-versity Press.
Publicado
18/07/2021
Como Citar
GOMES, Joel Felipe Ferreira; GREATI, Vitor Rodrigues.
Notes on the Logic of Perfect Paradefinite Algebras. In: WORKSHOP BRASILEIRO DE LÓGICA (WBL), 2. , 2021, Evento Online.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2021
.
p. 41-48.
ISSN 2763-8731.
DOI: https://doi.org/10.5753/wbl.2021.15777.
