Basically the title. Are non reflexive logics one such logical system?

  • It is a well-formed formula of propositional logic. The "conditional" operator is a binary connective that takes two formulas as input: that's all. Oct 27, 2023 at 11:34
  • Not a wff or just not a propositional tautology?
    – Conifold
    Oct 27, 2023 at 11:40
  • If you mean a system of logic in which A → A is not a theorem of the logic, then yes there are a few. One such is the logic S, which is part of the family of relevance logics. plato.stanford.edu/entries/logic-relevance/#SysRelLog
    – Bumble
    Oct 27, 2023 at 12:26
  • Not exactly a duplicate question, but it would have an answer that partly duplicated this one. Oct 27, 2023 at 12:45
  • 1
    It is not a wff in syllogistic logic which has no sentential operators. Oct 27, 2023 at 14:09

1 Answer 1


If P → P means that P implies P, then it is true.

If you assume for whatever reason that it is not, then you are just being illogical.

Another way to say this is that any expression "P → P" which is not true does not refer to the implication P implies P.

  • It would be a wtf instead (without truth formula).
    – Scott Rowe
    Oct 28, 2023 at 0:04

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