Abstract In a previous paper, we recast Morgado hyperlattices and Sette implicative hyperlattices (IHLs) in lattice-theoretic terms. By utilizing swap structures induced by implicative lattices, we obtained a direct proof of soundness and completeness for da Costa’s paraconsistent logic C_ with respect to Sette’s hyperalgebraic semantics. Inspired by Kalman functors in the context of twist structures, we introduce the notion of hyper swap structures, a novel class of hyperalgebras that naturally generalize swap structure semantics. We prove that these hyperalgebras, besides providing another class of hyperalgebraic models for C_, induce a Kalman-style functor between the category of Sette IHLs and the category of enriched hyperalgebras for C_. Specifically, we exhibit an equivalence of categories between Sette IHLs and their enriched hyperalgebraic counterparts using Kalman and forgetful functors. Similar results are extended to two axiomatic extensions of C_.
Coniglio et al. (Tue,) studied this question.