Mixed Chaining

• For some cases with 10 blocks, and quite often in other moderately complex cases, you want to use mixed chaining.
• You want to use forward chaining, and backward chaining and see where they meet.
• If in each case you have two possible moves, and you have to make ten moves, how many cases do you have to explore?
• 2+4+8+16+...+512+1024.
• This works for both forward and backward chaining.
• However, if you interleave you only have to try
• 2+4+8+16+32+2+4+8+16+32
• If however, in the forward case there are 10 possibilitities, and in the backward only 2, you want to use backward chaining. The reverse is also true.
• The forward direction is called fan-out, and backward fan-in.
• This chaining stuff can all be applied to logic and rules. We'll talk about rules later, but you know logic. At any state, you can derive new facts by Modus Ponens, forward chaining; or you can use Modus Tolens to derive new subgoals, backward chaining.
• Also note how this fits in with search spaces. If you know the shape and size of the space, you can choose how to explore it.
• You can also use and or trees. When there are multiple ways to achieve a goal, or them. When you need multiple things to achieve a goal, and them.