Is there any way to prove that an admissible heuristic may not be consistent? Most proof I came across are through examples .Is there a generalized proof?
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$\begingroup$ What have you tried? Where did you get stuck? Do you have a specific instance of the problem that you weren't sure how to handle? One valid way to dis-prove "X is always true" is to exhibit one example where X isn't true, so it's not clear what you are asking -- it seems you already know of some counterexamples, so I can't tell what you are looking for. $\endgroup$– D.W. ♦Jul 21, 2015 at 18:07
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$\begingroup$ A counterexample is a proof. $\endgroup$– David RicherbyJul 21, 2015 at 21:36
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If you want to prove a heuristic is not consistent a counterexample is all you need, you don't need a more "generalized" proof. A counterexample is proof enough.
This is because a heuristic is consistent if some property always holds. It is not consistent if the property doesn't hold once. An example is all you need to show something happens once, if you want to show something always holds then you need a general proof.
answered Jul 21, 2015 at 15:45
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$\begingroup$ "if you want to show something always holds then you need a general proof."Liked this line.Thanks. $\endgroup$– Alex_banJul 21, 2015 at 16:29
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$\begingroup$ @Alex_ban $2$ is a counterexample to the claim "all even numbers are squares". $\endgroup$ Jul 21, 2015 at 22:39