Recovery operators in quasi-Nelson logic: the prelinear case

This paper investigates recovery operators in quasi-Nelson (QN) logic, the algebraizable logical counterpart of QN algebras. These form a variety of three-potent, distributive, but not necessarily involutive residuated lattices that may be regarded as a common generalization of Nelson and Heyting algebras. We consider both consistency and determinedness operators, with a particular focus on logics and algebras that satisfy the prelinearity condition, which is well-known in the area of mathematical fuzzy logics. We show that, essentially, all algebraic and logical results already proved for (prelinear, distributive) involutive residuated lattice-based logics of formal inconsistency/logics of formal undeterminedness can be recovered in the QN setting, where one dispenses with the involutivity assumption. In this setting, consistency and undeterminedness operators are no longer duals of one another, and hence call for a more fine-grained algebraic and logical formalization.