Friday, July 1, 2011

Would you look at that!

OK, now this result does surprise me. I think I just found a ruleset that is not closed under modus ponens! D10+D12+D13+E:

  • validates ~~φ->φ.
  • validates (~~φ->φ)->(φv~&phi).
  • does not validate φv~φ.

And here are my proofs to double check my work, because this is very, very strange:

In fact, the same also holds of D10+D12+D13, without E:

No comments:

Post a Comment