Revisiting four-valued logics from Maple using the Logics Explorer package.

We have recently developed a package in Maple that allows to perform logical computations in any existing or proposed many-valued logic (that can be defined using truth tables). It has applications in logic engineering (e.g. when creating a new logic adapted to some requirements), in theoretical logic (e.g. checking if two axiomatizations of a logic are equivalent), or simply in checking the properties of a well known logic. Now, such a package has been tuned so that it can simultaneously deal with the logic proposed by the end user plus the standard Boolean logic, in order to conveniently check properties. This new approach is used to easily develop some disquisitions on why Belnap's four-valued logic is defined the way it is. Finally, it is shown how a new four valued logic that mixes ideas from Łukasiewicz's and Kleene's logics behaves similarly to Belnap's logic.