# How to define a new logical language

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.

• Mathematically, a logical language consists of several given strings (the postulates) and rules to combine those strings (the logic) to form new strings (the theorems). You can adopt and prove meta-rules like, if you decide to create a negation symbol 'N', you could say 'If the string s is a theorem, then Ns is not a theorem, and vice versa' (ie, consistency). Of course, once your system becomes powerful enough, you may not be able to actually show that. Google around for computer science and context-free grammars to get a start on this sort of stuff.
– user935
Jul 13 '19 at 15:23
• You have to start from a "problem" and then try to define a formal language to "describe" the essential feature of that problem. See e.g. Temporal loggic and Deontic logic. Jul 13 '19 at 17:44
• @MauroALLEGRANZA thank you, but what steps to follow to describe the features is what I don't understand. Moreover, how can I formalize such steps? Jul 14 '19 at 3:02
• @barrycarter Thank you. Do you know a good book/reference that may discuss this in a tutorial fashion? Jul 14 '19 at 3:03
• web.mnstate.edu/peil/geometry/C1AxiomSystem/… may or may not be helpful
– user935
Jul 15 '19 at 4:19