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Logic and Planning Lab

Logic and Planning Lab. Propositional Logic. First-order Logic. The 15 Puzzle.

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Logic and Planning Lab

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  1. Logic and Planning Lab

  2. Propositional Logic

  3. First-order Logic

  4. The 15 Puzzle The Fifteen Puzzle consists of 15 tiles on a 4x4 grid, numbered 1-15, but in a random order. There is one empty space. The tiles can slide into an empty space if they are adjacent to it. The goal is to get all tiles in order (1-15), left to right, top to bottom. A solved 15-puzzle Question: Write a STRIPS representation of the slide-tile action for the 15 puzzle.

  5. Situation Calculus The domain for this problem is a combination lock with 4 digits (0-9 each). There are two actions: • dial any combination into the lock. if the right combination is correct (correct combo indicated by the constant C), then the lock opens. • push a lock button (L) which locks the lock Select the correct situation calculus axioms for this domain from the list below. = C L

  6. Vacuum World The Vacuum World consists of two adjacent rooms, each of which is either dirty or clean. The vacuum can move left (L), move right (R), or suck (S). This version of the vacuum world is completely UNOBSERVABLE, with a static environment and deterministic actions. Assume the agent knows nothing about the world state in the initial state. The goal is to clean both rooms and have the vacuum end in the left room. Find the shortest plan that achieves the goal. Also, indicate on the diagram the sequence of belief states that the agent goes through when executing this plan.

  7. Dynamic, Stochastic,Partially-ObservedVacuum World Suppose the vacuum starts in the left location and the room is clean, but we don’t know about how clean the right room is. Suppose that L and R actions are stochastic – they sometimes work, and sometimes fail (S always works). And suppose that dirt sometimes gets added to either room during an L or R action. After the vacuum performs an R action, indicate the possible worlds for the outcome of this action.

  8. Vacuum World with Local Sensing Suppose we have the same possible worlds as at the end of the last problem, but now the vacuum has local sensors that tell it that the vacuum is in the right room, and that room is dirty. The sensors are only local, though, so they can’t tell anything about the other room. Indicate the possible worlds after taking into account the information from the local sensors.

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