Past exam of the computer science course of the University of Oxford / 2021 / Artificial intelligence / 3 / e / Solution

Use balls $a,b$, buckets $1,2$, transition index $k$ and the grounded action schemas from (a). Under a sequential encoding, one example successor-state axiom isBall $a$ is in bucket $1$ afterwards exactly when it is dropped there now, or it was there and is not picked up. Actions involving other balls or arm movement leave this fact unchanged. This is both an effect rule and a persistence rule, rather than an implication that permits spontaneous appearances.

An example action precondition axiom isA selected pick action must have the ball, arm and empty hand in the appropriate current state. The static type conditions have already been satisfied by action grounding.

An example action exclusion axiom isThe single arm cannot pick up both balls in one step. For a serial encoding include such an exclusion for every pair of distinct action occurrences at one layer; with at-most-one rather than exactly-one actions, a layer may idle. Initial-state clauses, goal clauses and corresponding successor-state axioms for all other planning fluents complete the plan-as-SAT construction. The plan-as-SAT approach was introduced by Henry Kautz and Bart Selman in 1992.^[ref]