A Post production system

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Main Question or Discussion Point

I want to write a Post production system if we have the set of symbols {A,B} where all strings are wffs, and the set of theorems is [itex]\{A^nB^{3n} : n\geq 1\}[/itex]. Would it the following system be correct:

  • Alphabet is {A,B}

  • The only Axiom is AB3.

  • Rules of inference:
  1. From x infer xAB3

For example, A2B6 is a theorem. To see this, we can provide the following derivation:

1. AB3 (Axiom)
2. AB3AB3 = A2B6 (From 1 by rule 2)

So, is my system correct? Are there better ways to make the rules as simple as possible?
 

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