Graph-based abduction

1. Given "Goals"= {a,b} and "In"= {x,y,z}, what are the paths from goals back to the Ins?

   if x then not_j
   if not_j then d
   if y then not_d
   if not_d then j
   if j  then e
   if d then c
   if e then c
   if c then a
   if e then k
   if k then b
   

2. Your paths use terms such as "not d", a, etc. Let "Facts" = "In" + "Goals", and assumptions "A" be "Used - Facts". Some assumptions contract other assumptions. Assuming "inconsistent(X, not_X)", write down
   • Used
   • Facts
   • Assumptions
   • Controversial assumptions
3. Some controversial assumptions are "base", i.e. they depend on no upstream controversial assumption. Write down the base "B" for this example.
4. One world "W" exists for each maximal consistent subset of the base controversial assumptions. Write those subsets.
5. Worlds contain paths and, internally, each world is consistent. For each of the subsets from the last question, write down the paths in each world.
6. Using the above, propose a "probe"; i.e. the single most informative question that rules out the most worlds.
7. If this is some medical diagnosis domain, where further data collection is expensive, propose a monitoring strategy which, when data data becomes available, we can refer to our worlds to determine the remaining set of beliefs.