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

Mauro ALLEGRANZA
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Vihan
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  • 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. – Mauro ALLEGRANZA Oct 27 '23 at 11:34
  • Not a wff or just not a propositional tautology? – Conifold Oct 27 '23 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. https://plato.stanford.edu/entries/logic-relevance/#SysRelLog – Bumble Oct 27 '23 at 12:26
  • Not exactly a duplicate question, but it would have an answer that partly duplicated this one. – Kristian Berry Oct 27 '23 at 12:45
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    It is not a wff in syllogistic logic which has no sentential operators. – David Gudeman Oct 27 '23 at 14:09
  • Just curious, re this question, it got me wondering: would P-->P work in linear logic, or would you need !P-->P to account for its resource awareness? – eigengrau Oct 27 '23 at 15:56

1 Answers1

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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.

Speakpigeon
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