1

Usually when we prove some properties of propositional formulas, we use induction on the complexity of propositional formulas, but instead, we can just use induction on the number of occurrence of connections? (Because, I think we need unique readability to define the complexity of formulas. And I want to avoid it.)

amoogae
  • 606
  • Why would you want to avoid unique readability? – Natalie Clarius Apr 17 '19 at 14:09
  • @MauroALLEGRANZA Thank you. But I think we need unique readability to define the $\text {rank} (\varphi)$. And why do we need Polish notation to use the induction on number of occurrences of connectives? – amoogae Apr 17 '19 at 14:26
  • @lemontree In fact, I have to present about some problem, but I do not have enough time. And I wonder just for logical reasons. – amoogae Apr 17 '19 at 14:32
  • @MauroALLEGRANZA Thank you for your kind answer. I think I am misunderstanding something.. – amoogae Apr 17 '19 at 15:20
  • 1
    You can use induction on the number of connectives, but in many cases you'll still need unique readabiity. – Andreas Blass Apr 17 '19 at 18:53
  • What most logicians do (as I describe here) is treat formulas as trees. You can then just do structural induction on those trees. Treating formulas as special sequences of characters is what leads to parsing concerns like unique readability. Spending any time on parsing concerns seems like a waste of time to me when talking about logic. – Derek Elkins left SE Apr 17 '19 at 19:34
  • You can find examples of inductive proof on number of connectives into Mendelson's textbook. – Mauro ALLEGRANZA Apr 18 '19 at 11:51

0 Answers0