Heron Suit

[EdS2]

(05-30-2015 06:32 PM)Dave Britten Wrote:  

Quote:No cats have tails unless they have whiskers.

Native English speaker here - from the UK, as is Ian Stewart. Looks like I agree with your analysis:

Quote:No cats have tails unless they have whiskers.

(I agree with the earlier poster that "unless" means "if not" - but it is one of the easiest logical words to misapprehend.)
Let me rewrite a few times:

Quote:All cats are without tails unless they have whiskers.

Quote:if a cat is without whiskers, it will be without a tail.

Quote:no whiskers => no tail.

Quote:tail => whiskers

Quote:tail and no whiskers never happens

which invalidates Stewart's counterexample.

According to http://www.cs.nott.ac.uk/~vxc/g51mcs/ch01_logic.pdf

Quote:No cats have tails unless they have whiskers.

is equivalent to

Quote:(Not tailed) OR whiskered

which we can transform to

Quote:Not (tailed AND not whiskered)

which is the same interpretation, I think.

That pdf concludes that the deduction is correct, and gives a derivation.