On the structure of Bochvar algebras

Bochvar algebras consist of the quasivariety BCA playing the role of equivalent algebraic semantics for Bochvar (external) logic, a logical formalism introduced by Bochvar [4] in the realm of (weak) Kleene logics. In this paper, we provide an algebraic investigation of the structure of Bochvar algebras. In particular, we prove a representation theorem based on Płonka sums and investigate the lattice of subquasivarieties, showing that Bochvar (external) logic has only one proper extension (apart from classical logic), algebraized by the subquasivariety NBCA of BCA. Furthermore, we address the problem of (passive) structural completeness ((P)SC) for each of them, showing that NBCA is SC, while BCA is not even PSC. Finally, we prove that both BCA and NBCA enjoy the Amalgamation Property (AP).