# 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

## 1 Answer

There is an art to creating a logical language, just as there is an art to logic.

So what does the statement "logical language" mean? Well you want a language, and you want it to be logical. A language is defined as a form of structured communication, not necessarily visual, but it still needs to be sensory, because there is no communication without senses. The sensory you want to invoke will be a medium. For example, you could make certain smells mean certain things, and certain orders and combinations of smells mean certain things as well. You will need to define these combinations.

So now that you have a language, it needs to be logical. There are all kinds of different forms of logic. But for your language to be logical, you would need to match what you have defined to a sense, to a logical rule. I would suggest looking up the rules of logic; This wikipedia article is pretty good on types of logic. https://en.wikipedia.org/wiki/Logic#Types

So now all you have to do is define a sense to a logic and you can start making your logical language.

• If you have references showing how to do this they would support your answer and give the reader a place to go for more information. Jul 15 '19 at 0:10
• I don't have references. I answered this based on the definitions of logic and language. Unless I should reference the dictionary I got them from. But yeah let me see if I can find something on logical rules. Jul 15 '19 at 0:43