Decomposition Method

The Compound Task Head is the high-level, abstract task that the method is designed to decompose. It defines the method's purpose. For example, a method's head could be DeliverPackage(Package, Address). The planner selects methods whose head matches the compound task currently requiring decomposition.

The Precondition Set is a list of logical conditions that must be true in the current world state for the method to be applicable. It acts as a guard, ensuring decomposition is contextually appropriate.

• Example: A method for CookMeal(Recipe) might have preconditions: HasIngredients(Recipe) and KitchenIsClean().
• If preconditions are not met, the planner must either find an alternative method or execute tasks to make them true.

The Subtask Network is the core output of the method: a partially ordered set of tasks that implement the compound task. This network can contain:

• Primitive Tasks: Directly executable actions.
• Compound Tasks: Requiring further decomposition by other methods.
• Ordering Constraints: Specify temporal sequences (e.g., ChopVegetables before CookVegetables).
• Causal Links: Ensure a task's effects satisfy another's preconditions.

The Decomposition Strategy is the logical approach encoded within the method. Common strategies include:

• Sequential: Subtasks must be executed in a strict order.
• Parallel: Subtasks can be executed concurrently if resources allow.
• Conditional: Different subtask networks are selected based on runtime state.
• Iterative: A subtask is repeated until a condition is met (e.g., while(floorIsDirty) { Mop() }).

In algorithms like SHOP (Simple Hierarchical Ordered Planner), methods are applied in a forward-chaining, depth-first manner. The planner:

1. Matches a compound task in the current task network to a method's head.
2. Checks the method's preconditions against the current state.
3. If satisfied, replaces the compound task with the method's subtask network.
4. Progressively updates the world state as primitive tasks are "executed" during planning, making subsequent precondition checks accurate.

It is critical to distinguish a Decomposition Method from a Planning Operator.

• Operator: Represents a single, primitive, executable action (e.g., PickUp(Object)). Defined by its own preconditions and effects.
• Method: A schema for breaking down an abstract task; it contains no direct effects on the world state. Its "effect" is the introduction of a more refined plan structure. A complete HTN domain requires both a library of methods for decomposition and a set of operators for primitive action execution.