Using a bitwise xor operator as a logical xor operator can be dangerous.

sub true {
  return 1;
}

sub True {
  return 2;
}

if (true() xor True()) {
  print "xor is true.\n";
}

if (true() ^ True()) {
  print "^ is true.\n";
}

__END__
^ is true.
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The obvious choice for a high-precedence logical xor is ^^. It's consistent with && and ||, and it doesn't conflict with anything already in the language.