On Logics of Perfect Paradefinite Algebras

Joel Gomes
(UFRN)
Vitor Greati
(UFRN)
Sérgio Marcelino
(Instituto de Telecomunicações)
João Marcos
(UFRN)
Umberto Rivieccio
(UFRN)

The present study shows how to enrich De Morgan algebras with a perfection operator that allows one to express the Boolean properties of negation-consistency and negation-determinedness. The variety of perfect paradefinite algebras thus obtained (PP-algebras) is shown to be term-equivalent to the variety of involutive Stone algebras, introduced by R. Cignoli and M. Sagastume, and more recently studied from a logical perspective by M. Figallo-L. Cantú and by S. Marcelino-U. Rivieccio. This equivalence plays an important role in the investigation of the 1-assertional logic and of the order-preserving logic associated to PP-algebras. The latter logic (here called PP<=) is characterized by a single 6-valued matrix and is shown to be a Logic of Formal Inconsistency and Formal Undeterminedness. We axiomatize PP<= by means of an analytic finite Hilbert-style calculus, and we present an axiomatization procedure that covers the logics corresponding to other classes of De Morgan algebras enriched by a perfection operator.

In Mauricio Ayala-Rincon and Eduardo Bonelli: Proceedings 16th Logical and Semantic Frameworks with Applications (LSFA 2021), Buenos Aires, Argentina (Online), 23rd - 24th July, 2021, Electronic Proceedings in Theoretical Computer Science 357, pp. 56–76.
Published: 8th April 2022.

ArXived at: http://dx.doi.org/10.4204/EPTCS.357.5 bibtex PDF
References in reconstructed bibtex, XML and HTML format (approximated).
Comments and questions to: eptcs@eptcs.org
For website issues: webmaster@eptcs.org