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Eduardo Alejandro Barrio, Federico Matias Pailos, Damian Enrique Szmuc, A paraconsistent route to semantic closure, Logic Journal of the IGPL, Volume 25, Issue 4, August 2017, Pages 387–407, https://doi.org/10.1093/jigpal/jzx009
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Abstract
In this article, we present a non-trivial and expressively complete paraconsistent naïve theory of truth, as a step in the route towards semantic closure. We achieve this goal by expressing self-reference with a weak procedure, that uses equivalences between expressions of the language, as opposed to a strong procedure, that uses identities. Finally, we make some remarks regarding the sense in which the theory of truth discussed has a property closely related to functional completeness, and we present a sound and complete three-sided sequent calculus for this expressively rich theory.