Hierarchical Plans in a Description Logic of Time and Action

Robert Weida and Diane Lit-man. Terminological reasoning with constraint networks and an application to plan recognition. In Proc. (a)g where S { called the Step Interpretation { is a function associating a newly generated function to each interval introduced by a decomposition operator. The representation of the Double-Stack plan in the extended language is: Double-Stack : = 3(x y) (x d ])(y d ])(x m y). Since the nodes x and y of the conceptual temporal constraint network introduce distinct individual actions, we can now distinguish the diierent instances of the two Basic-Stack actions occurring in distinct intervals: Double-Stack(i; a) =) where X and Y are newly generated functions, mapping the individual plan a to its individual steps b and c. It is now possible the accomplishment of a plan moving two diierent blocks during two Basic-Stack events in sequence. The case of simultaneous occurrences of the same action type with diierent parameters can be expressed in the extended language. The plan where two possibly different blocks are moved by two Basic-Stack actions at the same time is: Sim-Double-Stack : = 3(x y)(x d ])(y d ])(x = y). (Basic-Stack@@x u Basic-Stack@@y) We want now to address the case where diierent individual actions share common parameters or where a plan is made of the repetition, in diierent intervals, of the same individual action. We exploit the temporal agreement construct { p@@X # q@@Y , which spec-iies equality constraints between features introduced in diierent intervals. In the following example, the Same-Block-Double-Stack plan is constituted of two Basic-Stack actions moving the same ?BLOCK: Same-Block-Double-Stack : = 3(x y) (x d ])(y d ])(x m y). (Basic-Stack@@x u Basic-Stack@@y u ?BLOCK@@x # ?BLOCK@@y) Same-Double-Stack is a plan where a Stack action occurs twice in distinct intervals, with the same llers for the actual parameters: Same-Double-Stack : = 3(x y) (x d ])(y d ])(x m y). (Basic-Stack@@x u Basic-Stack@@y u @@x # @@y) The construct @@X # @@Y { a particular case of temporal agreement { imposes an equality constraint between the functions associated to the nodes X and Y , the same individual object; thus, the actual parameters associated to the Basic-Stack actions are equal. Finally we propose an example where the actions composing the plan have diierent types. Consider, in the cooking domain, the following example: Heat-Noodles : = 3(x y) (x d ])(y d ])(x b; m y). (Make-Noodles@@x u …