On the completeness of a new intuitionistic connective

A. V. Bessonov suggested an example of an intuitionistic calculus that defines a new connective in the sense of P. S. Novikov. Using the Bessonov logic as an example, this definition is compared with a similar definition suggested by D. M. Gabbay to show that the Bessonov logic does not comply with Gabbay's definition. An example of a calculus that satisfies Novikov's definition but has no disjunctive property is constructed.