The classical (boolean) circuit model of computation is generalized via polynomial ring calculus, an algebraic proof method adequate to non-standard logics (namely, to all truth-functional propositional logics and to some non-truth-functional logics). Such generalization allows us to define models of computation based on non-standard logics in a natural way by using 'hidden variables' in the constitution of the model. Paraconsistent circuits for the paraconsistent logic mbC (and for some extensions) are defined as an example of such models. Some potentialities are explored with respect to computability and computational complexity.