There are a number of logical languages defined that are so called flavors of a certain logic (for example, flavors of First Order Logic). Such new logical languages sometimes extend or restrict the main logic.
I am very interested to learn the basics of how a logical language is defined? Given a logic (like propositional or first order), what steps should I follow and what properties I should show to design a new logic?
Could you please suggest some references that explain the process in a tutorial format? Thanks in advance.